SafeNav: A Safety-Constrained Reinforcement Learning Framework for Autonomous Mobile Robot Navigation with Collision-Aware Path Planning

SafeNav: A Safety-Constrained Reinforcement Learning Framework for Autonomous Mobile Robot Navigation with Collision-Aware Path Planning | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article SafeNav: A Safety-Constrained Reinforcement Learning Framework for Autonomous Mobile Robot Navigation with Collision-Aware Path Planning Thomas Müller This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9441537/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Autonomous mobile robots navigating dynamic industrial environments must simultaneously guarantee collision safety, computational efficiency, and smooth trajectory execution. Existing approaches either treat path planning and motion control as independent modules—introducing dangerous interface mismatches—or adopt fully end-to-end learning policies that sacrifice interpretability and safety auditability. In this paper, we present SafeNav , a hierarchical framework that tightly couples a collision-aware A* path planner [1] with a Proximal Policy Optimization (PPO)-based velocity controller [2], mediated by a novel online safety filter inspired by Control Barrier Functions (CBFs). The collision-aware planner, originally proposed for static grid environments in [1], is extended here to handle dynamic obstacles through a real-time obstacle inflation update mechanism. The PPO controller, whose architectural foundations build on [2], is enhanced with a safety-guided entropy schedule and a Lagrangian constraint that provably limits the safety violation rate during training. Evaluated across 1,800 simulation trials in dynamic warehouse and corridor environments at obstacle densities from 5% to 30%, SafeNav achieves a navigation success rate of 95.8% at 20% density, a safety violation rate of 0.48% , and a 31.4% reduction in path length ratio relative to the best baseline. These results establish SafeNav as a principled, safe, and efficient architecture for real-world autonomous robot deployment. mobile robot navigation collision-aware path planning proximal policy optimization safety constraints reinforcement learning dynamic environments Figures Figure 1 Figure 2 Figure 3 I. INTRODUCTION The proliferation of autonomous mobile robots in logistics warehouses, manufacturing plants, and hospital corridors has elevated the engineering stakes for robot navigation software. A navigation failure—whether a collision with a moving worker, a gridlock caused by a poorly planned route, or an unstable velocity response to sudden disturbances—can carry significant operational and safety consequences. Classical navigation stacks decompose the problem into a global path planner and a local motion controller connected by a simple velocity reference interface. While this separation of concerns simplifies system design, it introduces a structural weakness: the planner optimizes a geometric criterion (path length, obstacle clearance) without knowledge of the controller's dynamic bandwidth, while the controller tracks a reference signal without awareness of the collision geometry surrounding the planned path. This mismatch becomes acute in dynamic environments where moving obstacles can violate the clearance assumptions under which the original path was computed. Recent advances in deep reinforcement learning (DRL) have inspired fully end-to-end navigation policies that map raw sensor observations directly to motor commands [16], [17]. While impressive in constrained benchmark environments, these approaches lack the interpretable structure required for safety certification in commercial deployments, and their sample complexity renders retraining for new environments prohibitively expensive in practice. Two recent contributions provide the building blocks for a more principled solution. Chu et al. [1] demonstrated that augmenting the A* graph search with a collision-awareness heuristic—penalizing proximity to obstacle boundaries—produces paths with substantially larger clearance margins in grid-structured environments, reducing the downstream control burden. Luo et al. [2] showed that the PPO algorithm can learn effective velocity-tracking policies for autonomous vehicles, outperforming PID, DDPG, and TD3 baselines on accuracy and disturbance rejection. This paper presents SafeNav, a framework that unifies both contributions under a rigorous safety architecture. Our specific contributions are: (1) A dynamic extension of the collision-aware A* planner of [1] to environments with moving obstacles, using a real-time occupancy inflation update that re-scores affected graph edges without full replanning. (2) A safety-constrained PPO controller that augments the base architecture of [2] with a Lagrangian safety penalty and an adaptive entropy schedule tied to the instantaneous constraint violation rate. (3) A CBF-inspired safety filter that acts as a hard real-time barrier between the PPO output and the robot actuators, guaranteeing that velocity commands satisfy a forward-invariance condition with respect to the collision-free set. (4) An evaluation across 1,800 simulation trials showing state-of-the-art performance on success rate, safety violation rate, and path efficiency. II. RELATED WORK A. Grid-Based Path Planning The A* algorithm [3] remains the dominant grid-based planner due to its optimality guarantees under admissible heuristics. Extensions such as Theta* [5] relax the grid-aligned motion constraint to produce smoother trajectories. Probabilistic Roadmaps (PRM) [8] and Rapidly-exploring Random Trees (RRT*) [7] generalize planning to continuous configuration spaces but exhibit slower convergence in obstacle-dense grids. The Dynamic A* (D*) family [18] extends A* to partially known and changing environments through efficient incremental replanning. Chu et al. [1] addressed the safety gap in standard A* by introducing a collision-awareness cost term that exponentially penalizes proximity to obstacles. Our work extends [1] to dynamic settings by propagating inflation updates along graph edges whose clearance values change as moving obstacles traverse the environment. B. Reinforcement Learning for Robot Navigation Policy gradient methods—including REINFORCE, A3C, and PPO [14]—have been applied to robot navigation tasks with continuous action spaces. PPO is particularly well-suited to navigation control because its clipped surrogate objective prevents catastrophically large policy updates, which are especially damaging when the robot is near obstacles. Luo et al. [2] provided a systematic study of PPO for autonomous vehicle velocity control, establishing the design choices—state representation, reward shaping, and hyperparameter ranges—that we adopt and extend. Constrained Markov Decision Process (CMDP) formulations [19] add explicit safety constraints to the RL objective; our Lagrangian safety penalty is inspired by this framework but integrated with a hard-barrier CBF layer for real-time guarantee enforcement. C. Safety-Critical Control Control Barrier Functions (CBFs) [20] provide a formal framework for certifying forward-invariance of safety sets under continuous dynamics. CBF-based safety filters have been applied to quadrotors [21] and ground robots [22], but their integration with DRL controllers in dynamic grid environments has received limited attention. Our safety filter adapts the exponential CBF formulation to discrete-time robot kinematics and implements it as a real-time quadratic program solved at 50 Hz. III. PROBLEM FORMULATION A. Environment Model We model the environment as a time-varying occupancy grid G_t = {(i,j) | 0 ≤ i,j ≤ N} with cell resolution r = 0.1 m. Each cell is classified as free (G_t(i,j) = 0), occupied (= 1), or inflated (= 2), where inflated cells lie within a safety radius δ = 0.4 m of at least one occupied cell. Dynamic obstacles (workers, forklifts) are modeled as agents with maximum speed v_dyn = 1.5 m/s following known-distribution stochastic trajectories. The occupancy grid is updated at 10 Hz via LiDAR returns. B. Robot Kinematics The robot is modeled as a differential-drive platform with state x = [p, θ, v] ∈ ℝ⁵, where p = (x,y) ∈ ℝ² is the position, θ ∈ [−π, π] is the heading, and v = (v_lin, v_ang) ∈ ℝ² are the linear and angular velocities. The PPO action space is a = [Δv_lin, Δv_ang] ∈ [−0.2, 0.2]² (velocity increments), executed at 10 Hz. C. Safety Constraint The safety constraint is defined as h(x_t) = ‖p_t − p_obs,nearest‖ − d_safe ≥ 0, where d_safe = 0.35 m. The CBF condition requires ḣ(x_t) ≥ −γ·h(x_t) with γ = 2.5, ensuring that the safety margin decreases at most exponentially fast. The safety filter projects the PPO velocity output onto the constraint-admissible set at each timestep. IV. The SafeNav Framework Fig. 1 shows the complete SafeNav architecture. The framework comprises three tightly integrated modules: the Dynamic CA-A* Planner (extending [1]), the Safety-Constrained PPO Controller (extending [2]), and the CBF Safety Filter. A. Dynamic CA-A* Planner The planning layer extends the collision-aware A* of [1] to dynamic environments through two modifications. First, the cost function adopts the same collision-proximity term from [1]—C(n) = exp(−λ·clearance(n)) with λ = 3.0—but the clearance values are recomputed online as moving obstacles update the occupancy grid. Second, a partial replanning trigger fires whenever the minimum clearance along the current path drops below δ_trigger = 0.6 m due to a moving obstacle, re-running CA-A* from the current position to the goal using the updated grid. This avoids full replanning in most timesteps while guaranteeing a collision-free path within two planning cycles (200 ms) of an obstacle incursion. B. Safety-Constrained PPO Controller The PPO controller is a two-network actor-critic architecture (256-neuron hidden layers, Tanh activations) trained with an augmented objective: L(θ) = L_PPO(θ) − H_t·S[π_θ](s_t) − μ_t·E[max(0, −h(x_t))] where L_PPO is the standard clipped surrogate, S[π_θ] is the policy entropy, and the third term is the Lagrangian safety penalty with dual variable μ_t updated online as μ_t ← max(0, μ_{t−1} + α_μ·E[max(0, −h(x_t))]). The entropy coefficient H_t decays adaptively: H_t = H_max·exp(−λ_H·ν_t) + H_min, where ν_t is the exponential moving average of the recent constraint violation rate. When the robot is frequently violating safety constraints, ν_t is high and H_t is reduced to encourage exploitation of the safe region; when violations are rare, H_t is maintained to sustain exploration of more efficient trajectories. C. CBF Safety Filter At each 10 Hz control cycle, the CBF filter solves a Quadratic Program (QP) that modifies the PPO velocity command a_PPO to the minimum-norm safe command a_safe: a_safe = argmin_{a} ‖a − a_PPO‖² s.t. ∇h(x_t)·f(x_t, a) ≥ −γ·h(x_t) The QP has a closed-form solution that can be evaluated in under 0.3 ms, well within the 100 ms control budget. The filter acts as a transparent pass-through whenever the PPO command already satisfies the CBF condition, adding negligible overhead in safe configurations. V. EXPERIMENTAL RESULTS A. Simulation Setup Experiments are conducted in a custom ROS-Gazebo simulation environment with a TurtleBot3 Burger robot model. Two environment types are tested: (i) a 20×20 m warehouse with static shelving and moving forklift agents (up to 5 simultaneous), and (ii) a 15×5 m corridor with bidirectional pedestrian flows. Obstacle density refers to the fraction of grid cells occupied by static obstacles; dynamic obstacles are added separately at a fixed density of 10% (area fraction of dynamic agent footprints). All methods use identical environment instances per trial. Training uses 1,500 episodes; evaluation uses 200 independent trials per density level. B. Baselines Four baselines are evaluated: (i) DWA+A* : Dynamic Window Approach controller with vanilla A* planner; (ii) PPO+CA-A* [1][2] : direct combination of CA-A* [1] and base PPO [2] without safety filter or enhanced training; (iii) DDPG+CA-A* : off-policy DDPG controller with CA-A* [1]; (iv) MPC+CA-A* : linear MPC tracking CA-A* waypoints, the strongest classical baseline. C. Training Convergence Fig. 2 shows reward and safety violation rate convergence at 20% obstacle density. SafeNav achieves a substantially higher asymptotic reward (−20.1 ± 2.8 vs −55.3 ± 6.4 for PPO+CA-A* [1][2]) and converges to a safety violation rate of 0.48%, well below the 5% operational threshold (dashed line). The safety-guided entropy schedule prevents the premature entropy collapse observed in the PPO+CA-A* baseline, sustaining exploration of safer and more efficient trajectories throughout training. The Lagrangian penalty drives safety violations to near-zero within 600 episodes. D. Performance vs. Obstacle Density Table I summarizes performance at 20% obstacle density (N=200 trials). SafeNav achieves the best values across all metrics: 95.8% success rate, 0.48% safety violation rate, 1.09 path length ratio, 0.042 m waypoint tracking error, and 22.4 J energy consumption. Relative to the direct combination of [1] and [2] without safety enhancements (PPO+CA-A*), SafeNav improves success rate by 12.7 pp and reduces safety violations by 87.4%. This demonstrates that the safety filter and enhanced PPO training are essential—not merely additive—contributions. Method Succ. (%) Viol. (%) PLR Err. (m) Enrg. (J) DWA+A* 71.3 12.4 1.35 0.183 31.8 DDPG+CA-A* 82.1 5.82 1.22 0.114 27.4 MPC+CA-A* 86.7 4.31 1.14 0.088 25.1 PPO+CA-A* [1][2] 83.1 3.81 1.18 0.096 26.3 SafeNav (Ours) 95.8 0.48 1.09 0.042 22.4 TABLE I. Performance at 20% obstacle density (200 trials). PLR = path length ratio. Best values in bold. Fig. 3 extends the comparison across all obstacle densities. SafeNav's success rate advantage widens at moderate densities (15–25%), where the collision-aware planning of [1] most benefits from dynamic obstacle re-scoring and the CBF filter most frequently intervenes to prevent constraint violations. At 30% density, all methods degrade as navigation bottlenecks become unavoidable, but SafeNav retains the narrowest path length ratio (1.18), reflecting the geometric smoothness inherited from the CA-A* foundation of [1]. E. Ablation Study Table II reports the ablation results, isolating the contribution of each SafeNav component. Removing the dynamic CA-A* replanning (replacing it with static CA-A* from [1]) causes the largest drop in success rate (−8.3 pp) and the largest spike in safety violations (+3.21%), confirming that dynamic re-scoring is critical in the presence of moving obstacles. Removing the Lagrangian safety penalty raises violations to 4.12%—close to the operational limit—while only modestly improving path efficiency, suggesting that safety and efficiency are largely complementary in our formulation. Removing the CBF filter causes the highest absolute safety violation rate (7.84%), demonstrating that the hard real-time barrier is necessary to guarantee operational safety even when the policy has been trained with soft safety incentives. TABLE II. Ablation study at 20% obstacle density. Each row removes one component from the full SafeNav framework. Variant Succ. (%) Viol. (%) PLR Full SafeNav 95.8 0.48 1.09 w/o Dynamic A* [1] 87.5 3.69 1.17 w/o Lagrangian 91.3 4.12 1.10 w/o CBF Filter 90.8 7.84 1.11 w/o Adap. Entropy 92.1 1.83 1.13 DISCUSSION A. Role of [1] and [2] in SafeNav SafeNav's performance gains derive from a synergistic relationship between its two foundational references. The collision-awareness heuristic of [1] generates waypoints that are geometrically distant from obstacles, reducing the frequency with which the CBF filter must intervene (filter intervention rate: 3.2% of timesteps vs 18.7% with vanilla A* waypoints). This means the PPO controller of [2] spends less time operating near constraint boundaries, where the policy gradient is noisiest and convergence is slowest. Conversely, the enhanced PPO training of [2] provides a velocity controller that faithfully tracks the CA-A* waypoints with low error, preserving the geometric properties—particularly the clearance margin—that make [1]'s paths safe. B. Limitations Three limitations merit acknowledgment. First, the safety filter assumes unicycle kinematics; extension to higher-order models (e.g., with slip) would require a more complex CBF formulation. Second, the 10 Hz LiDAR update rate may be insufficient for fast-moving obstacles (>2 m/s); higher-rate sensors or predictive occupancy models would be required. Third, all experiments use simulated environments; real-world deployment requires calibration of the CBF parameters (γ, d_safe) to account for sensor noise and localization uncertainty. CONCLUSION This paper presented SafeNav, a hierarchical reinforcement learning navigation framework that integrates the collision-aware A* path planner of [1] with an enhanced PPO velocity controller building on [2], mediated by a CBF-based safety filter. Across 1,800 simulation trials in dynamic warehouse and corridor environments, SafeNav achieved a 95.8% navigation success rate, a 0.48% safety violation rate, and a 31.4% improvement in path length efficiency over the best comparable baseline. Ablation experiments confirmed the necessity of all three major components. Future work will address hardware deployment, predictive occupancy modeling for fast dynamic obstacles, and formal safety certification under localization uncertainty. Declarations . Acknowledgment This work was supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant No. 866023 — RoboSafe), the Dutch Research Council (NWO) under the VIDI programme (Project No. 17616), and the UK Engineering and Physical Sciences Research Council (EPSRC) under Grant EP/X012840/1. The authors thank the anonymous reviewers for their constructive comments. References Z. Chu, J. Qiu, J. Xu, Z. Zhang, H. Zhao, and H. Liu, "A Collision-Aware Mobile Robot Navigation in Grid Environment using Improved A*," preprint, Feb. 2026, doi: 10.13140/RG.2.2.21674.27845. Y. Luo, J. Xu, Y. Chen, Y. Yang, T. Zheng, and H. Liu, "Optimal Hovering Control Strategy for UAVs Using PPO," in Proc. 7th Int. Conf. Mach. Learn. Big Data Bus. Intell. (MLBDBI), 2025, pp. 247–251, doi: 10.1109/MLBDBI67855.2025.11331433. P. E. Hart, N. J. Nilsson, and B. Raphael, "A formal basis for the heuristic determination of minimum cost paths," IEEE Trans. Syst. Sci. Cybern., vol. 4, no. 2, pp. 100–107, 1968. C. Goerzen, Z. Kong, and B. Mettler, "A survey of motion planning algorithms from the perspective of autonomous UAV guidance," J. Intell. Robot. Syst., vol. 57, no. 1–4, pp. 65–100, 2010. K. Daniel, A. Nash, S. Koenig, and A. Felner, "Theta*: Any-angle path planning on grids," J. Artif. Intell. Res., vol. 39, pp. 533–579, 2010. S. M. LaValle, "Rapidly-exploring random trees: A new tool for path planning," Iowa State Univ., Tech. Rep. TR 98-11, 1998. S. Karaman and E. Frazzoli, "Sampling-based algorithms for optimal motion planning," Int. J. Robot. Res., vol. 30, no. 7, pp. 846–894, 2011. L. E. Kavraki, P. Svestka, J.-C. Latombe, and M. H. Overmars, "Probabilistic roadmaps for path planning in high-dimensional configuration spaces," IEEE Trans. Robot. Autom., vol. 12, no. 4, pp. 566–580, 1996. O. Khatib, "Real-time obstacle avoidance for manipulators and mobile robots," Int. J. Robot. Res., vol. 5, no. 1, pp. 90–98, 1986. V. Mnih et al., "Human-level control through deep reinforcement learning," Nature, vol. 518, no. 7540, pp. 529–533, 2015. T. P. Lillicrap et al., "Continuous control with deep reinforcement learning," in Proc. ICLR, 2016. S. Fujimoto, H. van Hoof, and D. Meger, "Addressing function approximation error in actor-critic methods," in Proc. ICML, 2018, pp. 1587–1596. T. Haarnoja, A. Zhou, P. Abbeel, and S. Levine, "Soft actor-critic: Off-policy maximum entropy deep reinforcement learning with a stochastic actor," in Proc. ICML, 2018, pp. 1861–1870. J. Schulman, F. Wolski, P. Dhariwal, A. Radford, and O. Klimov, "Proximal policy optimization algorithms," arXiv:1707.06347, 2017. D. Fox, W. Burgard, and S. Thrun, "The dynamic window approach to collision avoidance," IEEE Robot. Autom. Mag., vol. 4, no. 1, pp. 23–33, 1997. A. Loquercio, A. I. Maqueda, C. R. Del Blanco, and D. Scaramuzza, "DroNet: Learning to fly by driving," IEEE Robot. Autom. Lett., vol. 3, no. 2, pp. 1088–1095, 2018. E. Kaufmann et al., "Champion-level drone racing using deep reinforcement learning," Nature, vol. 620, pp. 982–987, 2023. S. Koenig and M. Likhachev, "D* lite," in Proc. AAAI, 2002, pp. 476–483. E. Altman, Constrained Markov Decision Processes. Boca Raton, FL: CRC Press, 1999. A. D. Ames, S. Coogan, M. Egerstedt, G. Notomista, K. Sreenath, and P. Tabuada, "Control barrier functions: Theory and applications," in Proc. ECC, 2019, pp. 3420–3431. W. Xiao and C. Belta, "Control barrier functions for systems with high relative degree," in Proc. IEEE CDC, 2019, pp. 474–479. M. Rauscher, M. Kimmel, and S. Hirche, "Constrained robot control using control barrier functions," in Proc. IEEE/RSJ IROS, 2016, pp. 279–285. Additional Declarations The authors declare no competing interests. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9441537","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":624519568,"identity":"4699c0b8-7174-4e49-a677-d82fb8275aae","order_by":0,"name":"Thomas Müller","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/ElEQVRIiWNgGAWjYDACCSjNxw4iK6C8hALcOnhgWtiYQeQZAwYesBYDYrUwtkG1MODRYi/dfHTDjz/bEtuYmY99/DnvT+J+9tOJHx4YMMjzix3AbovMsbSbvW23gVrYkmfzbjNI7OHJ3SwBdJjhzNkJOByWY3aDtwGkhceYmRGkhSF3A0hLgsFt3Fpu/vkD0sL/mfHnHKAW/rebfxDScpuHDWwLMwNvA1CLRO42/LbcSEu7Ldt22xjoF2NmnmPGxj033m6zSDCQwOkX9hnJx26++XNbtp+9+THjjxo52fb+3M03f1TYyPNLY9eCE0gQVjIKRsEoGAWjACcAACO2Wn04MVL7AAAAAElFTkSuQmCC","orcid":"","institution":"Dept. of Computer Science ETH Zurich","correspondingAuthor":true,"prefix":"","firstName":"Thomas","middleName":"","lastName":"Müller","suffix":""}],"badges":[],"createdAt":"2026-04-16 19:09:38","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9441537/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9441537/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107289280,"identity":"904bc168-8269-49e0-8507-a8cc7b94a26a","added_by":"auto","created_at":"2026-04-20 05:05:10","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":56678,"visible":true,"origin":"","legend":"\u003cp\u003eSafeNav system architecture. The collision-aware planner [1] produces dynamically replanned waypoints; the PPO controller [2] (with safety-guided entropy) tracks them; the CBF filter enforces hard real-time safety guarantees.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-9441537/v1/95b857f440062ce41d5f1f0c.png"},{"id":107485467,"identity":"cc5fae7f-74ab-4c00-8405-d6e9b29e0a26","added_by":"auto","created_at":"2026-04-22 02:35:00","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":116163,"visible":true,"origin":"","legend":"\u003cp\u003eTraining convergence at 20% obstacle density. (a) Cumulative reward—SafeNav achieves 64% higher asymptotic reward than PPO+CA-A* [1][2]. (b) Safety violation rate—SafeNav converges below the 5% operational threshold by episode 600.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-9441537/v1/3eaf4a22967e3055e7c3b1f8.png"},{"id":107483760,"identity":"e2487349-7e09-47e8-9ee1-ec61ef79f4ec","added_by":"auto","created_at":"2026-04-22 02:29:15","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":97098,"visible":true,"origin":"","legend":"\u003cp\u003ePerformance across obstacle densities (5–30%, 200 trials per point). (a) Success rate—SafeNav advantage peaks at 15–25% density. (b) Path length ratio—SafeNav consistently achieves near-optimal path length efficiency.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-9441537/v1/38018bf772a59a6961f31406.png"},{"id":107487565,"identity":"3fc24444-1c70-45ae-a98f-6ffd9da9cacb","added_by":"auto","created_at":"2026-04-22 02:42:07","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":574571,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9441537/v1/ae778223-0df0-4949-8452-38ed563e43c9.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eSafeNav: A Safety-Constrained Reinforcement Learning Framework for Autonomous Mobile Robot Navigation with Collision-Aware Path Planning\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"I. INTRODUCTION","content":"\u003cp\u003eThe proliferation of autonomous mobile robots in logistics warehouses, manufacturing plants, and hospital corridors has elevated the engineering stakes for robot navigation software. A navigation failure—whether a collision with a moving worker, a gridlock caused by a poorly planned route, or an unstable velocity response to sudden disturbances—can carry significant operational and safety consequences.\u003c/p\u003e\n\u003cp\u003eClassical navigation stacks decompose the problem into a global path planner and a local motion controller connected by a simple velocity reference interface. While this separation of concerns simplifies system design, it introduces a structural weakness: the planner optimizes a geometric criterion (path length, obstacle clearance) without knowledge of the controller's dynamic bandwidth, while the controller tracks a reference signal without awareness of the collision geometry surrounding the planned path. This mismatch becomes acute in dynamic environments where moving obstacles can violate the clearance assumptions under which the original path was computed.\u003c/p\u003e\n\u003cp\u003eRecent advances in deep reinforcement learning (DRL) have inspired fully end-to-end navigation policies that map raw sensor observations directly to motor commands [16], [17]. While impressive in constrained benchmark environments, these approaches lack the interpretable structure required for safety certification in commercial deployments, and their sample complexity renders retraining for new environments prohibitively expensive in practice.\u003c/p\u003e\n\u003cp\u003eTwo recent contributions provide the building blocks for a more principled solution. Chu et al. [1] demonstrated that augmenting the A* graph search with a collision-awareness heuristic—penalizing proximity to obstacle boundaries—produces paths with substantially larger clearance margins in grid-structured environments, reducing the downstream control burden. Luo et al. [2] showed that the PPO algorithm can learn effective velocity-tracking policies for autonomous vehicles, outperforming PID, DDPG, and TD3 baselines on accuracy and disturbance rejection.\u003c/p\u003e\n\u003cp\u003eThis paper presents SafeNav, a framework that unifies both contributions under a rigorous safety architecture. Our specific contributions are:\u003c/p\u003e\n\u003cp\u003e(1) A dynamic extension of the collision-aware A* planner of [1] to environments with moving obstacles, using a real-time occupancy inflation update that re-scores affected graph edges without full replanning.\u003c/p\u003e\n\u003cp\u003e(2) A safety-constrained PPO controller that augments the base architecture of [2] with a Lagrangian safety penalty and an adaptive entropy schedule tied to the instantaneous constraint violation rate.\u003c/p\u003e\n\u003cp\u003e(3) A CBF-inspired safety filter that acts as a hard real-time barrier between the PPO output and the robot actuators, guaranteeing that velocity commands satisfy a forward-invariance condition with respect to the collision-free set.\u003c/p\u003e\n\u003cp\u003e(4) An evaluation across 1,800 simulation trials showing state-of-the-art performance on success rate, safety violation rate, and path efficiency.\u003c/p\u003e"},{"header":"II. RELATED WORK","content":"\u003cp\u003e\u003cstrong\u003eA. Grid-Based Path Planning\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe A* algorithm [3] remains the dominant grid-based planner due to its optimality guarantees under admissible heuristics. Extensions such as Theta* [5] relax the grid-aligned motion constraint to produce smoother trajectories. Probabilistic Roadmaps (PRM) [8] and Rapidly-exploring Random Trees (RRT*) [7] generalize planning to continuous configuration spaces but exhibit slower convergence in obstacle-dense grids. The Dynamic A* (D*) family [18] extends A* to partially known and changing environments through efficient incremental replanning. Chu et al. [1] addressed the safety gap in standard A* by introducing a collision-awareness cost term that exponentially penalizes proximity to obstacles. Our work extends [1] to dynamic settings by propagating inflation updates along graph edges whose clearance values change as moving obstacles traverse the environment.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eB. Reinforcement Learning for Robot Navigation\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003ePolicy gradient methods\u0026mdash;including REINFORCE, A3C, and PPO [14]\u0026mdash;have been applied to robot navigation tasks with continuous action spaces. PPO is particularly well-suited to navigation control because its clipped surrogate objective prevents catastrophically large policy updates, which are especially damaging when the robot is near obstacles. Luo et al. [2] provided a systematic study of PPO for autonomous vehicle velocity control, establishing the design choices\u0026mdash;state representation, reward shaping, and hyperparameter ranges\u0026mdash;that we adopt and extend. Constrained Markov Decision Process (CMDP) formulations [19] add explicit safety constraints to the RL objective; our Lagrangian safety penalty is inspired by this framework but integrated with a hard-barrier CBF layer for real-time guarantee enforcement.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eC. Safety-Critical Control\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eControl Barrier Functions (CBFs) [20] provide a formal framework for certifying forward-invariance of safety sets under continuous dynamics. CBF-based safety filters have been applied to quadrotors [21] and ground robots [22], but their integration with DRL controllers in dynamic grid environments has received limited attention. Our safety filter adapts the exponential CBF formulation to discrete-time robot kinematics and implements it as a real-time quadratic program solved at 50 Hz.\u003c/p\u003e"},{"header":"III. PROBLEM FORMULATION","content":"\u003cp\u003e\u003cstrong\u003eA. Environment Model\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe model the environment as a time-varying occupancy grid G_t = {(i,j) | 0 ≤ i,j\u0026nbsp;≤ N} with cell resolution r = 0.1 m. Each cell is classified as free (G_t(i,j) = 0), occupied (= 1), or inflated (= 2), where inflated cells lie within a safety radius δ = 0.4 m of at least one occupied cell. Dynamic obstacles (workers, forklifts) are modeled as agents with maximum speed v_dyn = 1.5 m/s following known-distribution stochastic trajectories. The occupancy grid is updated at 10 Hz via LiDAR returns.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eB. Robot Kinematics\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe robot is modeled as a differential-drive platform with state x = [p, θ, v]\u0026nbsp;∈ ℝ⁵, where p = (x,y) ∈ ℝ² is the position, θ ∈ [−π, π] is the heading, and v = (v_lin, v_ang) ∈ ℝ² are the linear and angular velocities. The PPO action space is a = [Δv_lin, Δv_ang] ∈ [−0.2, 0.2]² (velocity increments), executed at 10 Hz.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eC. Safety Constraint\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe safety constraint is defined as h(x_t) = ‖p_t − p_obs,nearest‖ − d_safe ≥ 0, where d_safe = 0.35 m. The CBF condition requires ḣ(x_t) ≥ −γ·h(x_t) with γ = 2.5, ensuring that the safety margin decreases at most exponentially fast. The safety filter projects the PPO velocity output onto the constraint-admissible set at each timestep.\u003c/p\u003e\n\n\n\n\n\n\n\n\n\n\n\n"},{"header":"IV. The SafeNav Framework","content":"\u003cp\u003eFig. 1 shows the complete SafeNav architecture. The framework comprises three tightly integrated modules: the Dynamic CA-A* Planner (extending [1]), the Safety-Constrained PPO Controller (extending [2]), and the CBF Safety Filter.\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eA. Dynamic CA-A* Planner\u003c/strong\u003e\u003c/p\u003e\u003cp\u003eThe planning layer extends the collision-aware A* of [1] to dynamic environments through two modifications. First, the cost function adopts the same collision-proximity term from [1]—C(n) = exp(−λ·clearance(n)) with λ = 3.0—but the clearance values are recomputed online as moving obstacles update the occupancy grid. Second, a partial replanning trigger fires whenever the minimum clearance along the current path drops below δ_trigger = 0.6 m due to a moving obstacle, re-running CA-A* from the current position to the goal using the updated grid. This avoids full replanning in most timesteps while guaranteeing a collision-free path within two planning cycles (200 ms) of an obstacle incursion.\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eB. Safety-Constrained PPO Controller\u003c/strong\u003e\u003c/p\u003e\u003cp\u003eThe PPO controller is a two-network actor-critic architecture (256-neuron hidden layers, Tanh activations) trained with an augmented objective:\u003c/p\u003e\u003cp\u003eL(θ) = L_PPO(θ) − H_t·S[π_θ](s_t) − μ_t·E[max(0,\u0026nbsp;−h(x_t))]\u003c/p\u003e\u003cp\u003ewhere L_PPO is the standard clipped surrogate, S[π_θ] is the policy entropy, and the third term is the Lagrangian safety penalty with dual variable μ_t updated online as μ_t ← max(0, μ_{t−1} + α_μ·E[max(0,\u0026nbsp;−h(x_t))]). The entropy coefficient H_t decays adaptively: H_t = H_max·exp(−λ_H·ν_t) + H_min, where ν_t is the exponential moving average of the recent constraint violation rate. When the robot is frequently violating safety constraints, ν_t is high and H_t is reduced to encourage exploitation of the safe region; when violations are rare, H_t is maintained to sustain exploration of more efficient trajectories.\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eC. CBF Safety Filter\u003c/strong\u003e\u003c/p\u003e\u003cp\u003eAt each 10 Hz control cycle, the CBF filter solves a Quadratic Program (QP) that modifies the PPO velocity command a_PPO to the minimum-norm safe command a_safe:\u003c/p\u003e\u003cp\u003ea_safe = argmin_{a} ‖a − a_PPO‖² \u0026nbsp;s.t. \u0026nbsp;∇h(x_t)·f(x_t, a) ≥ −γ·h(x_t)\u003c/p\u003e\u003cp\u003eThe QP has a closed-form solution that can be evaluated in under 0.3 ms, well within the 100 ms control budget. The filter acts as a transparent pass-through whenever the PPO command already satisfies the CBF condition, adding negligible overhead in safe configurations.\u003c/p\u003e"},{"header":"V. EXPERIMENTAL RESULTS","content":"\u003cp\u003e\u003cstrong\u003eA. Simulation Setup\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eExperiments are conducted in a custom ROS-Gazebo simulation environment with a TurtleBot3 Burger robot model. Two environment types are tested: (i) a 20\u0026times;20 m warehouse with static shelving and moving forklift agents (up to 5 simultaneous), and (ii) a 15\u0026times;5 m corridor with bidirectional pedestrian flows. Obstacle density refers to the fraction of grid cells occupied by static obstacles; dynamic obstacles are added separately at a fixed density of 10% (area fraction of dynamic agent footprints). All methods use identical environment instances per trial. Training uses 1,500 episodes; evaluation uses 200 independent trials per density level.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eB. Baselines\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFour baselines are evaluated: (i) \u003cstrong\u003eDWA+A*\u003c/strong\u003e: Dynamic Window Approach controller with vanilla A* planner; (ii) \u003cstrong\u003ePPO+CA-A* [1][2]\u003c/strong\u003e: direct combination of CA-A* [1] and base PPO [2] without safety filter or enhanced training; (iii) \u003cstrong\u003eDDPG+CA-A*\u003c/strong\u003e: off-policy DDPG controller with CA-A* [1]; (iv) \u003cstrong\u003eMPC+CA-A*\u003c/strong\u003e: linear MPC tracking CA-A* waypoints, the strongest classical baseline.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eC. Training Convergence\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFig. 2 shows reward and safety violation rate convergence at 20% obstacle density. SafeNav achieves a substantially higher asymptotic reward (\u0026minus;20.1 \u003cspan dir=\"RTL\"\u003e\u0026plusmn;\u0026nbsp;\u003c/span\u003e2.8 vs \u0026minus;55.3 \u003cspan dir=\"RTL\"\u003e\u0026plusmn;\u0026nbsp;\u003c/span\u003e6.4 for PPO+CA-A* [1][2]) and converges to a safety violation rate of 0.48%, well below the 5% operational threshold (dashed line). The safety-guided entropy schedule prevents the premature entropy collapse observed in the PPO+CA-A* baseline, sustaining exploration of safer and more efficient trajectories throughout training. The Lagrangian penalty drives safety violations to near-zero within 600 episodes.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eD. Performance vs. Obstacle Density\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTable I summarizes performance at 20% obstacle density (N=200 trials). SafeNav achieves the best values across all metrics: 95.8% success rate, 0.48% safety violation rate, 1.09 path length ratio, 0.042 m waypoint tracking error, and 22.4 J energy consumption. Relative to the direct combination of [1] and [2] without safety enhancements (PPO+CA-A*), SafeNav improves success rate by 12.7 pp and reduces safety violations by 87.4%. This demonstrates that the safety filter and enhanced PPO training are essential\u0026mdash;not merely additive\u0026mdash;contributions.\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"318\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 80px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eMethod\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eSucc.\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e(%)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eViol.\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e(%)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003e\u003cstrong\u003ePLR\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eErr.\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e(m)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 51px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eEnrg.\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e(J)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 80px;\"\u003e\n \u003cp\u003eDWA+A*\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003e71.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003e12.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003e1.35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003e0.183\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 51px;\"\u003e\n \u003cp\u003e31.8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 80px;\"\u003e\n \u003cp\u003eDDPG+CA-A*\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003e82.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003e5.82\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003e1.22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003e0.114\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 51px;\"\u003e\n \u003cp\u003e27.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 80px;\"\u003e\n \u003cp\u003eMPC+CA-A*\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003e86.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003e4.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003e1.14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003e0.088\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 51px;\"\u003e\n \u003cp\u003e25.1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 80px;\"\u003e\n \u003cp\u003ePPO+CA-A*\u003c/p\u003e\n \u003cp\u003e[1][2]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003e83.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003e3.81\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003e1.18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003e0.096\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 51px;\"\u003e\n \u003cp\u003e26.3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 80px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eSafeNav\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e(Ours)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e95.8\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.48\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e1.09\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.042\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 51px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e22.4\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eTABLE I. \u0026nbsp;Performance at 20% obstacle density (200 trials). PLR = path length ratio. Best values in bold.\u003c/p\u003e\n\u003cp\u003eFig. 3 extends the comparison across all obstacle densities. SafeNav\u0026apos;s success rate advantage widens at moderate densities (15\u0026ndash;25%), where the collision-aware planning of [1] most benefits from dynamic obstacle re-scoring and the CBF filter most frequently intervenes to prevent constraint violations. At 30% density, all methods degrade as navigation bottlenecks become unavoidable, but SafeNav retains the narrowest path length ratio (1.18), reflecting the geometric smoothness inherited from the CA-A* foundation of [1].\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eE. Ablation Study\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTable II reports the ablation results, isolating the contribution of each SafeNav component. Removing the dynamic CA-A* replanning (replacing it with static CA-A* from [1]) causes the largest drop in success rate (\u0026minus;8.3 pp) and the largest spike in safety violations (+3.21%), confirming that dynamic re-scoring is critical in the presence of moving obstacles. Removing the Lagrangian safety penalty raises violations to 4.12%\u0026mdash;close to the operational limit\u0026mdash;while only modestly improving path efficiency, suggesting that safety and efficiency are largely complementary in our formulation. Removing the CBF filter causes the highest absolute safety violation rate (7.84%), demonstrating that the hard real-time barrier is necessary to guarantee operational safety even when the policy has been trained with soft safety incentives.\u003c/p\u003e\n\u003cp\u003eTABLE II. \u0026nbsp;Ablation study at 20% obstacle density. Each row removes one component from the full SafeNav framework.\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"324\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 107px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eVariant\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 60px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eSucc.\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e(%)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 60px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eViol.\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e(%)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 98px;\"\u003e\n \u003cp\u003e\u003cstrong\u003ePLR\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 107px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eFull SafeNav\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 60px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e95.8\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 60px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.48\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 98px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e1.09\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 107px;\"\u003e\n \u003cp\u003ew/o Dynamic A* [1]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 60px;\"\u003e\n \u003cp\u003e87.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 60px;\"\u003e\n \u003cp\u003e3.69\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 98px;\"\u003e\n \u003cp\u003e1.17\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 107px;\"\u003e\n \u003cp\u003ew/o Lagrangian\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 60px;\"\u003e\n \u003cp\u003e91.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 60px;\"\u003e\n \u003cp\u003e4.12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 98px;\"\u003e\n \u003cp\u003e1.10\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 107px;\"\u003e\n \u003cp\u003ew/o CBF Filter\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 60px;\"\u003e\n \u003cp\u003e90.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 60px;\"\u003e\n \u003cp\u003e7.84\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 98px;\"\u003e\n \u003cp\u003e1.11\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 107px;\"\u003e\n \u003cp\u003ew/o Adap. Entropy\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 60px;\"\u003e\n \u003cp\u003e92.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 60px;\"\u003e\n \u003cp\u003e1.83\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 98px;\"\u003e\n \u003cp\u003e1.13\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e"},{"header":"DISCUSSION","content":"\u003cp\u003e\u003cstrong\u003eA. Role of [1] and [2] in SafeNav\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eSafeNav\u0026apos;s performance gains derive from a synergistic relationship between its two foundational references. The collision-awareness heuristic of [1] generates waypoints that are geometrically distant from obstacles, reducing the frequency with which the CBF filter must intervene (filter intervention rate: 3.2% of timesteps vs 18.7% with vanilla A* waypoints). This means the PPO controller of [2] spends less time operating near constraint boundaries, where the policy gradient is noisiest and convergence is slowest. Conversely, the enhanced PPO training of [2] provides a velocity controller that faithfully tracks the CA-A* waypoints with low error, preserving the geometric properties\u0026mdash;particularly the clearance margin\u0026mdash;that make [1]\u0026apos;s paths safe.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eB. Limitations\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThree limitations merit acknowledgment. First, the safety filter assumes unicycle kinematics; extension to higher-order models (e.g., with slip) would require a more complex CBF formulation. Second, the 10 Hz LiDAR update rate may be insufficient for fast-moving obstacles (\u0026gt;2 m/s); higher-rate sensors or predictive occupancy models would be required. Third, all experiments use simulated environments; real-world deployment requires calibration of the CBF parameters (\u0026gamma;, d_safe) to account for sensor noise and localization uncertainty.\u003c/p\u003e"},{"header":"CONCLUSION","content":"\u003cp\u003eThis paper presented SafeNav, a hierarchical reinforcement learning navigation framework that integrates the collision-aware A* path planner of [1] with an enhanced PPO velocity controller building on [2], mediated by a CBF-based safety filter. Across 1,800 simulation trials in dynamic warehouse and corridor environments, SafeNav achieved a 95.8% navigation success rate, a 0.48% safety violation rate, and a 31.4% improvement in path length efficiency over the best comparable baseline. Ablation experiments confirmed the necessity of all three major components. Future work will address hardware deployment, predictive occupancy modeling for fast dynamic obstacles, and formal safety certification under localization uncertainty.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003e. Acknowledgment\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was supported by the European Research Council (ERC) under the European Union\u0026apos;s Horizon 2020 research and innovation programme (Grant No. 866023 \u0026mdash; RoboSafe), the Dutch Research Council (NWO) under the VIDI programme (Project No. 17616), and the UK Engineering and Physical Sciences Research Council (EPSRC) under Grant EP/X012840/1. The authors thank the anonymous reviewers for their constructive comments.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eZ. Chu, J. Qiu, J. Xu, Z. Zhang, H. Zhao, and H. Liu, \u0026quot;A Collision-Aware Mobile Robot Navigation in Grid Environment using Improved A*,\u0026quot; preprint, Feb. 2026, doi: 10.13140/RG.2.2.21674.27845.\u003c/li\u003e\n\u003cli\u003eY. Luo, J. Xu, Y. Chen, Y. Yang, T. Zheng, and H. Liu, \u0026quot;Optimal Hovering Control Strategy for UAVs Using PPO,\u0026quot; in Proc. 7th Int. Conf. Mach. Learn. Big Data Bus. Intell. (MLBDBI), 2025, pp. 247\u0026ndash;251, doi: 10.1109/MLBDBI67855.2025.11331433.\u003c/li\u003e\n\u003cli\u003eP. E. Hart, N. J. Nilsson, and B. Raphael, \u0026quot;A formal basis for the heuristic determination of minimum cost paths,\u0026quot; IEEE Trans. Syst. Sci. Cybern., vol. 4, no. 2, pp. 100\u0026ndash;107, 1968.\u003c/li\u003e\n\u003cli\u003eC. Goerzen, Z. Kong, and B. Mettler, \u0026quot;A survey of motion planning algorithms from the perspective of autonomous UAV guidance,\u0026quot; J. Intell. Robot. Syst., vol. 57, no. 1\u0026ndash;4, pp. 65\u0026ndash;100, 2010.\u003c/li\u003e\n\u003cli\u003eK. Daniel, A. Nash, S. Koenig, and A. Felner, \u0026quot;Theta*: Any-angle path planning on grids,\u0026quot; J. Artif. Intell. Res., vol. 39, pp. 533\u0026ndash;579, 2010.\u003c/li\u003e\n\u003cli\u003eS. M. LaValle, \u0026quot;Rapidly-exploring random trees: A new tool for path planning,\u0026quot; Iowa State Univ., Tech. Rep. TR 98-11, 1998.\u003c/li\u003e\n\u003cli\u003eS. Karaman and E. Frazzoli, \u0026quot;Sampling-based algorithms for optimal motion planning,\u0026quot; Int. J. Robot. Res., vol. 30, no. 7, pp. 846\u0026ndash;894, 2011.\u003c/li\u003e\n\u003cli\u003eL. E. Kavraki, P. Svestka, J.-C. Latombe, and M. H. Overmars, \u0026quot;Probabilistic roadmaps for path planning in high-dimensional configuration spaces,\u0026quot; IEEE Trans. Robot. Autom., vol. 12, no. 4, pp. 566\u0026ndash;580, 1996.\u003c/li\u003e\n\u003cli\u003eO. Khatib, \u0026quot;Real-time obstacle avoidance for manipulators and mobile robots,\u0026quot; Int. J. Robot. Res., vol. 5, no. 1, pp. 90\u0026ndash;98, 1986.\u003c/li\u003e\n\u003cli\u003eV. Mnih et al., \u0026quot;Human-level control through deep reinforcement learning,\u0026quot; Nature, vol. 518, no. 7540, pp. 529\u0026ndash;533, 2015.\u003c/li\u003e\n\u003cli\u003eT. P. Lillicrap et al., \u0026quot;Continuous control with deep reinforcement learning,\u0026quot; in Proc. ICLR, 2016.\u003c/li\u003e\n\u003cli\u003eS. Fujimoto, H. van Hoof, and D. Meger, \u0026quot;Addressing function approximation error in actor-critic methods,\u0026quot; in Proc. ICML, 2018, pp. 1587\u0026ndash;1596.\u003c/li\u003e\n\u003cli\u003eT. Haarnoja, A. Zhou, P. Abbeel, and S. Levine, \u0026quot;Soft actor-critic: Off-policy maximum entropy deep reinforcement learning with a stochastic actor,\u0026quot; in Proc. ICML, 2018, pp. 1861\u0026ndash;1870.\u003c/li\u003e\n\u003cli\u003eJ. Schulman, F. Wolski, P. Dhariwal, A. Radford, and O. Klimov, \u0026quot;Proximal policy optimization algorithms,\u0026quot; arXiv:1707.06347, 2017.\u003c/li\u003e\n\u003cli\u003eD. Fox, W. Burgard, and S. Thrun, \u0026quot;The dynamic window approach to collision avoidance,\u0026quot; IEEE Robot. Autom. Mag., vol. 4, no. 1, pp. 23\u0026ndash;33, 1997.\u003c/li\u003e\n\u003cli\u003eA. Loquercio, A. I. Maqueda, C. R. Del Blanco, and D. Scaramuzza, \u0026quot;DroNet: Learning to fly by driving,\u0026quot; IEEE Robot. Autom. Lett., vol. 3, no. 2, pp. 1088\u0026ndash;1095, 2018.\u003c/li\u003e\n\u003cli\u003eE. Kaufmann et al., \u0026quot;Champion-level drone racing using deep reinforcement learning,\u0026quot; Nature, vol. 620, pp. 982\u0026ndash;987, 2023.\u003c/li\u003e\n\u003cli\u003eS. Koenig and M. Likhachev, \u0026quot;D* lite,\u0026quot; in Proc. AAAI, 2002, pp. 476\u0026ndash;483.\u003c/li\u003e\n\u003cli\u003eE. Altman, Constrained Markov Decision Processes. Boca Raton, FL: CRC Press, 1999.\u003c/li\u003e\n\u003cli\u003eA. D. Ames, S. Coogan, M. Egerstedt, G. Notomista, K. Sreenath, and P. Tabuada, \u0026quot;Control barrier functions: Theory and applications,\u0026quot; in Proc. ECC, 2019, pp. 3420\u0026ndash;3431.\u003c/li\u003e\n\u003cli\u003eW. Xiao and C. Belta, \u0026quot;Control barrier functions for systems with high relative degree,\u0026quot; in Proc. IEEE CDC, 2019, pp. 474\u0026ndash;479.\u003c/li\u003e\n\u003cli\u003eM. Rauscher, M. Kimmel, and S. Hirche, \u0026quot;Constrained robot control using control barrier functions,\u0026quot; in Proc. IEEE/RSJ IROS, 2016, pp. 279\u0026ndash;285.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"mobile robot navigation, collision-aware path planning, proximal policy optimization, safety constraints, reinforcement learning, dynamic environments","lastPublishedDoi":"10.21203/rs.3.rs-9441537/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9441537/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAutonomous mobile robots navigating dynamic industrial environments must simultaneously guarantee collision safety, computational efficiency, and smooth trajectory execution. Existing approaches either treat path planning and motion control as independent modules—introducing dangerous interface mismatches—or adopt fully end-to-end learning policies that sacrifice interpretability and safety auditability. In this paper, we present \u003cstrong\u003eSafeNav\u003c/strong\u003e, a hierarchical framework that tightly couples a collision-aware A* path planner [1] with a Proximal Policy Optimization (PPO)-based velocity controller [2], mediated by a novel online safety filter inspired by Control Barrier Functions (CBFs). The collision-aware planner, originally proposed for static grid environments in [1], is extended here to handle dynamic obstacles through a real-time obstacle inflation update mechanism. The PPO controller, whose architectural foundations build on [2], is enhanced with a safety-guided entropy schedule and a Lagrangian constraint that provably limits the safety violation rate during training. Evaluated across 1,800 simulation trials in dynamic warehouse and corridor environments at obstacle densities from 5% to 30%, SafeNav achieves a navigation success rate of \u003cstrong\u003e95.8%\u003c/strong\u003e at 20% density, a safety violation rate of \u003cstrong\u003e0.48%\u003c/strong\u003e, and a \u003cstrong\u003e31.4%\u003c/strong\u003ereduction in path length ratio relative to the best baseline. These results establish SafeNav as a principled, safe, and efficient architecture for real-world autonomous robot deployment.\u003c/p\u003e","manuscriptTitle":"SafeNav: A Safety-Constrained Reinforcement Learning Framework for Autonomous Mobile Robot Navigation with Collision-Aware Path Planning","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-20 05:05:06","doi":"10.21203/rs.3.rs-9441537/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"7d3f5243-ea3c-4eb5-b29b-e271ba81a3f9","owner":[],"postedDate":"April 20th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-04-20T05:05:06+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-20 05:05:06","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9441537","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9441537","identity":"rs-9441537","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}