pith. sign in

arxiv: 2606.07855 · v1 · pith:7YQXI37Cnew · submitted 2026-06-05 · 💻 cs.RO · math.OC

Path Planning Using Deep Deterministic Policy Gradient: A Reinforcement Learning Approach

Qiang Le , Yaguang Yang , Isaac E. Weintraub This is my paper

Pith reviewed 2026-06-27 21:26 UTC · model grok-4.3

classification 💻 cs.RO math.OC
keywords path planningreinforcement learningDDPGautonomous vehiclesobstacle avoidancereal-time planningoptimal control
0
0 comments X

The pith

Deep Deterministic Policy Gradient learns a direct mapping from vehicle state to actions that avoids circular no-go zones and reaches the destination faster than optimal control.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that a DDPG reinforcement learning agent can be trained in simulation to produce feasible paths around multiple circular threat zones. The training uses a reward with three components that pull the agent toward the goal, push it away from obstacles, and discourage large heading changes. Once trained, the agent maps its current position and heading straight to control actions without solving an optimization problem at each step. This yields paths that match the quality of a pseudo-spectral solver while running orders of magnitude faster, which the authors argue makes the method viable for real-time use and for pre-checking mission feasibility from many starting locations.

Core claim

The DDPG agent is trained through trial and error in a simulated environment to learn a direct mapping from its current state (position and heading) to a series of feasible actions that guide the agent to safely reach its destination without entering any circular no-go zones. The three-part reward function supplies the necessary incentives, and the resulting policy identifies the largest set of starting points from which a safe path is guaranteed.

What carries the argument

Deep Deterministic Policy Gradient (DDPG) actor-critic network trained with a reward that combines an attractive potential at the destination, repulsive potentials at obstacle centers, and a penalty on the magnitude of heading change.

If this is right

  • The method supplies, before a mission begins, a map of starting locations from which safe arrival is guaranteed.
  • Pre-mission planning can use the trained policy to decide whether a task is achievable from a given start.
  • The learned controller runs fast enough to support real-time replanning during flight.
  • Direct comparison in simulation shows the DDPG paths remain effective while computation time drops substantially relative to the pseudo-spectral solver.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the reward weights are kept fixed across different obstacle layouts, the same trained network might handle new threat configurations without retraining.
  • The policy could be combined with a higher-level mission planner that selects only those starting points already known to be safe.
  • Because the output is a direct state-to-action mapping, the approach may transfer to settings where online nonlinear optimization is too slow.

Load-bearing premise

The simulated environment and the chosen three-part reward function are enough to produce policies that will respect real vehicle dynamics and safety constraints.

What would settle it

Deploy the trained policy on a physical vehicle in a test field containing circular obstacles and measure whether the vehicle enters any restricted zone or fails to reach the destination neighborhood within the allotted time.

read the original abstract

Path-planning for autonomous vehicles in threat-laden environments is a fundamental challenge because the problem is nonlinear and nonconvex even in simplest scenarios. While traditional optimal control methods can be used to find ideal paths, the computational time is often too slow for real-time decision-making. To solve this challenge, we propose a method based on Deep Deterministic Policy Gradient (DDPG) and model the threat as possibly multiple circular 'no-go' zones. A mission is regarded as a failure if the vehicle enters this restricted zone at any time or does not reach a neighborhood of the destination. The DDPG agent is trained through trial and error in a simulated environment, learning a direct mapping from its current state (position and heading) to a series of feasible actions that guide the agent to safely reach its destination. The reword function has three parts: (a) an attractive field centered at the final destination, (b) some repulsive fields centered at the origins of circular obstacles, and (c) a penalty of control energy consumption (the magnitude of heading change) that indirectly in favor for straight path. The DDPG trains the agent using these incentives to find the largest possible set of starting points wherein a safe path to the destination is guaranteed. This provides critical information for mission planning, showing beforehand whether a task is achievable from a given starting point, assisting pre-mission planning activities. The approach is validated in simulation. A comparison between the DDPG method and a traditional optimal control (pseudo-spectral) method is carried out. The results show that the learning-based agent produces effective paths while being significantly faster, making it a better fit for real-time applications.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper proposes a DDPG-based reinforcement learning method for path planning of autonomous vehicles avoiding multiple circular 'no-go' zones. The agent learns a policy from state (position and heading) to actions in a simulated environment using a three-part reward function: attractive field to destination, repulsive fields from obstacles, and control energy penalty. The approach is claimed to generate effective safe paths significantly faster than pseudo-spectral optimal control, making it suitable for real-time use, and to identify feasible starting points for missions. Validation is performed in simulation.

Significance. If the empirical claims are substantiated with quantitative data, the work could demonstrate a practical advantage of RL over traditional optimal control for real-time path planning in constrained environments, with potential applications in pre-mission planning by mapping achievable start regions.

major comments (3)
  1. [Abstract] Abstract: The central claim that 'the learning-based agent produces effective paths while being significantly faster' is not accompanied by any quantitative metrics, success rates, failure cases, computation times, or details on how the comparison with the pseudo-spectral method was conducted.
  2. [Abstract] Abstract: No description is provided of robustness tests, such as model mismatch, actuator delays, sensor noise, or hardware experiments, which are necessary to support the claim of suitability for real-time applications on physical vehicles given the known sensitivity of DDPG policies to simulator artifacts.
  3. [Abstract] The reward function description: The three-part reward (attractive, repulsive, control penalty) is described only qualitatively; the specific functional forms, weighting parameters, and how they ensure safety (hard constraints vs soft penalties) are not specified, making it difficult to assess if the policy guarantees avoidance of restricted zones.
minor comments (2)
  1. [Abstract] Typo: 'reword function' should be 'reward function'.
  2. [Abstract] Grammatical issue: 'indirectly in favor for straight path' should be rephrased for clarity, e.g., 'indirectly favoring straight paths'.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for the constructive comments. We address each major point below and indicate the revisions that will be incorporated into the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that 'the learning-based agent produces effective paths while being significantly faster' is not accompanied by any quantitative metrics, success rates, failure cases, computation times, or details on how the comparison with the pseudo-spectral method was conducted.

    Authors: The Results section of the manuscript contains the quantitative comparison, including computation times for DDPG inference versus pseudo-spectral solves, success rates, and the simulation setup used for the comparison. To address the concern, we will revise the abstract to include specific numerical metrics and a brief statement on the comparison methodology. revision: yes

  2. Referee: [Abstract] Abstract: No description is provided of robustness tests, such as model mismatch, actuator delays, sensor noise, or hardware experiments, which are necessary to support the claim of suitability for real-time applications on physical vehicles given the known sensitivity of DDPG policies to simulator artifacts.

    Authors: The study is limited to simulation-based validation, and no hardware experiments or robustness tests against model mismatch, delays, or noise were performed. We will revise the abstract and add a limitations paragraph to clarify that claims of real-time suitability refer to simulated environments and to acknowledge the sim-to-real transfer gap. revision: yes

  3. Referee: [Abstract] The reward function description: The three-part reward (attractive, repulsive, control penalty) is described only qualitatively; the specific functional forms, weighting parameters, and how they ensure safety (hard constraints vs soft penalties) are not specified, making it difficult to assess if the policy guarantees avoidance of restricted zones.

    Authors: The abstract provides a qualitative overview, while the Methodology section contains the explicit functional forms, weighting parameters, and equations. We will update the abstract to reference these details and explicitly state that safety is promoted through soft reward penalties rather than hard constraints. revision: partial

standing simulated objections not resolved
  • Hardware experiments and physical robustness tests (model mismatch, actuator delays, sensor noise), which were not conducted as the work is simulation-only.

Circularity Check

0 steps flagged

No circularity detected; empirical simulation results stand independently

full rationale

The paper trains a DDPG policy in a simulated environment using an explicitly constructed three-part reward (attractive field, repulsive fields, control penalty) and validates performance via direct comparison of success rates and computation time against a pseudo-spectral optimal control baseline in the same simulator. No load-bearing step reduces by the paper's own equations or self-citations to a fitted parameter, self-defined quantity, or prior author result; the reward terms are stated as domain-motivated incentives rather than derived from the target metrics, and success/failure criteria (zone entry, destination neighborhood) are measured externally. The derivation chain is therefore self-contained as standard RL experimentation without circular reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The approach rests on standard reinforcement-learning assumptions about policy convergence in continuous spaces and the adequacy of the chosen reward components; no explicit free parameters or invented entities are stated in the abstract.

axioms (2)
  • domain assumption DDPG can learn a policy that maps state (position, heading) to actions that avoid circular obstacles and reach the goal in the simulated dynamics.
    Implicit in the training procedure described.
  • domain assumption The three-part reward function (attractive, repulsive, energy penalty) produces safe and near-optimal behavior without additional tuning details.
    Central to the training incentives stated in the abstract.

pith-pipeline@v0.9.1-grok · 5838 in / 1375 out tokens · 24900 ms · 2026-06-27T21:26:03.260985+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

49 extracted references · 2 linked inside Pith

  1. [1]

    X. Hu, L. Chen, B. Tang, D. Cao, and H. He, Dynamic path planning for autonomous driving on various roads with avoidance of static and moving obstacles, Mechanical Systems and Signal Processing, 100(1), pp. 482-500, 2018

    2018

  2. [2]

    Mason, J

    J. Mason, J. Stupl, W. Marshall, and C. Levit, Orbital debris–debris collision avoidance, Advances in Space Research, 48(10), pp. 1643-1655, 2011

    2011

  3. [3]

    P . M. Dillon, M. D. Zollars, I. E. Weintraub, and A. Von Moll, Optimal trajectories for aircraft avoidance of multiple weapon engagement zones, Journal of Aerospace Information Systems, 2023. 10 -600 -400 -200 0 200 400 600 -600 -400 -200 0 200 400 600 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Fig. 10 Feasible area of the specialized agent who is trained u...

    2023

  4. [4]

    I. A. Von Moll, and Weintraub, Basic engagement zones. Journal of Aerospace Information Systems, 21(10), pp.885-891, 2024

    2024

  5. [5]

    Weintraub, and A

    I.E. Weintraub, and A. Von Moll, C.A. Carrizales, N. Hanlon, and Z.E. Fuchs, An optimal engagement zone avoidance scenario in 2-D, In AIAA SciTech 2022 Forum (p. 1587), 2022

    2022

  6. [6]

    Galceran, and M

    E. Galceran, and M. Carreras, A survey on coverage path planning for robotics, Robotics and Autonomous systems, 61(12):1258-76, 2013

    2013

  7. [7]

    Algfoor, M

    Z. Algfoor, M. S. Sunar, and H. Kolivand, A Comprehensive study on pathfinding techniques for robotics and video games, International Journal of Computer Games Technology, Vol. 2015, Article ID 736138, 2015

    2015

  8. [8]

    Bhattacharya and M

    P . Bhattacharya and M. L. Gavrilova, Voronoi diagram in optimal path planning, 4th International Symposium on Voronoi Diagrams in Science and Engineering, 2007

    2007

  9. [9]

    Zheng, Z

    X. Zheng, Z. Wang, D. Liu, and H. Wang, A path planning algorithm for PCB surface quality automatic inspection, Journal of Intelligent Manufacturing 33(6), pp. 1829-1841, 2022

    2022

  10. [10]

    Utyamishev and I

    D. Utyamishev and I. Partin-Vaisband, Multiterminal pathfinding in practical VLSI systems with deep neural networks, ACM Transactions on Design Automation of Electronic Systems, 28(4), Article 51, 2023

    2023

  11. [11]

    D. R. Herber, Basic implementation of multi-interval pseudospectral methods to solve optimal control problem, UIUC technical report, UIUC-ESDL-2015-01, 2015

    2015

  12. [12]

    Hewing, K

    L. Hewing, K. P . Wabersich, M. Menner, and M. N. Zeilinger, Learning-based model predictive control: toward safe learning in control, Annual Review of Control, Robotics, and Autonomous Systems, 3, 269–96, 2020

    2020

  13. [13]

    H. Niu, A. Savvaris, A. Tsourdos, and Ze Ji, Voronoi-visibility roadmap-based path planning algorithm for unmanned surface vehicles, The Journal of Navigation, 72 (4), pp. 850–874, 2019

    2019

  14. [14]

    C. J. C. H. Watkins, Learning from delayed rewards. Ph.D. thesis, Cambridge University, 1989

    1989

  15. [15]

    Chao, and X

    Y . Chao, and X. Xiang, A path planning algorithm for UA V based on improved Q-learning, In 2018 2nd international conference on robotics and automation sciences (ICRAS), pp. 1-5. IEEE, 2018. 11

    2018

  16. [16]

    Maoudj, and A

    A. Maoudj, and A. Hentout, Optimal path planning approach based on Q-learning algorithm for mobile robots, Applied Soft Computing, 97, 106796, 2020

    2020

  17. [17]

    Puente-Castro, D

    A. Puente-Castro, D. Rivero, E. Pedrosa, A. Pereira, A. Lau, & E. Fernandez-Blanco, Q-learning based system for path planning with unmanned aerial vehicles swarms in obstacle environments. Expert Systems with Applications, 235, 121240, 2024

    2024

  18. [18]

    Sonny, S

    A. Sonny, S. R. Y eduri, and L. R. Cenkeramaddi, Q-learning-based unmanned aerial vehicle path planning with dynamic obstacle avoidance. Applied Soft Computing, 147, 110773, 2023

    2023

  19. [19]

    C. Wang, X. Y ang, and H. Li, Improved q-learning applied to dynamic obstacle avoidance and path planning, IEEE Access 10, pp. 92879-92888, 2022

    2022

  20. [20]

    Y . Zhao, Z. Zheng, X. Zhang, and L. Y ang, Q learning algorithm based UA V path learning and obstacle avoidence approach, In 2017 36th Chinese control conference (CCC), pp. 3397-3402, IEEE, 2017

    2017

  21. [21]

    V . Mnih, K. Kavukcuoglu, D. Silver, A. Graves, I. Antonoglou, D. Wierstra, and M. Riedmiller, Playing Atari with Deep Reinforcement Learning, ArXiv:1312.5602 [Cs], December 19, 2013

    Pith/arXiv arXiv 2013

  22. [22]

    Mnih, et al., Human-level control through deep reinforcement learning, Nature 518(7540), pp

    V . Mnih, et al., Human-level control through deep reinforcement learning, Nature 518(7540), pp. 529-533, 2015

    2015

  23. [23]

    V . Mnih, A. P . Badia, M. Mirza, A. Graves, T. Lillicrap, T. Harley, D. Silver, and K. Kavukcuoglu, Asynchronous methods for deep reinforcement learning. In International Conference on Machine Learning, pp. 1928–1937, 2016

    1928

  24. [24]

    P . Chen, J. Pei, W. Lu, and M. Li, A deep reinforcement learning based method for real-time path planning and dynamic obstacle avoidance, Neurocomputing 497 pp. 64-75, 2022

    2022

  25. [25]

    Y . Gu, Z. Zhu, J. Lv, L. Shi, Z. Hou, and S. Xu, DM-DQN: Dueling Munchausen deep Q network for robot path planning, Complex & Intelligent Systems 9(4), pp. 4287-4300, 2023

    2023

  26. [26]

    Zhang, and N

    Le Han, H. Zhang, and N. An, A continuous space path planning method for unmanned aerial vehicle based on particle swarm optimization-enhanced deep q-network, Drones 9(2), 122, 2025

    2025

  27. [27]

    Huang, C

    R. Huang, C. Qin, J. Li, and X. Lan, Path planning of mobile robot in unknown dynamic continuous environment using reward‐modified deep Q‐network, Optimal Control Applications and Methods, 44(3) pp. 1570-1587, 2023

    2023

  28. [28]

    X. Lei, Z. Zhang, and P . Dong, Dynamic path planning of unknown environment based on deep reinforcement learning, Journal of Robotics 2018(1), 5781591, 2018

    2018

  29. [29]

    Nakamura, M

    T. Nakamura, M. Kobayashi, and N. Motoi, Path planning for mobile robot considering turnabouts on narrow road by deep Q-network, IEEE Access 11, pp. 19111-19121, 2023

    2023

  30. [30]

    W. Wang, G. Zhang, Q. Da, D. Lu, Y . Zhao, S. Li, and D. Lang, Multiple unmanned aerial vehicle autonomous path planning algorithm based on whale-inspired deep Q-network, Drones 7(9), 572, 2023

    2023

  31. [31]

    Xie, , X

    T. Xie, , X. Y ao, Z. Jiang, et al. AGV path planning with dynamic obstacles based on deep Q-network and distributed training. Int. J. of Precis. Eng. and Manuf.-Green Tech. 12, 1005–1021 (2025)

    2025

  32. [32]

    Y ang, J, Li

    Y . Y ang, J, Li. and L, Peng, Multi-robot path planning based on a deep reinforcement learning DQN algorithm, CAAI Trans. Intell. Technol., 5, 177-183, 2020

    2020

  33. [34]

    S. Zhou, X. Liu, Y . Xu, and J. Guo, A deep Q-network (DQN) based path planning method for mobile robots, In 2018 IEEE International Conference on Information and Automation (ICIA), pp. 366-371. IEEE, 2018

    2018

  34. [35]

    Lillicrap, J

    T.P . Lillicrap, J. J. Hunt, A. Pritzel, N. Heess, T. Erez, Y . Tassa, D. Silver, and D. Wierstra, Continuous control with deep reinforcement learning, arXiv preprint arXiv:1509.02971, 2015

    Pith/arXiv arXiv 2015

  35. [36]

    Silver, G

    D. Silver, G. Lever, N. Heess, T. Degris, D. Wierstra, M. Riedmiller, Deterministic policy gradient algorithms, Proceedings of the 31 st International Conference on Machine Learning, Beijing, China, 2014

    2014

  36. [37]

    A. A. Ali, J. Shi, and Z. H. Zhu, Path planning of 6-DOF free-floating space robotic manipulators using reinforcement learning, Acta Astronautica, 224 367-378, 2024. 12

    2024

  37. [38]

    Almazrouei, I

    K. Almazrouei, I. Kamel, and T. Rabie, Dynamic obstacle avoidance and path planning through reinforcement learning, Ap- plied Sciences 13(14), 8174, 2023

    2023

  38. [39]

    X. Gao, L. Y an, Z. Li, G. Wang, and I. Chen, Improved deep deterministic policy gradient for dynamic obstacle avoidance of mobile robot, IEEE Transactions on Systems, Man, and Cybernetics: Systems 53(6), 3675-3682, 2023

    2023

  39. [40]

    L. He, N. Aouf, J. F. Whidborne, and B. Song, Deep reinforcement learning based local planner for UA V obstacle avoidance using demonstration data, arXiv preprint arXiv:2008.02521, 2020

    arXiv 2008

  40. [41]

    Ramezani, H

    M. Ramezani, H. Habibi, and H. Voos, UA V path planning employing MPC-reinforcement learning method considering colli- sion avoidance, In 2023 International Conference on Unmanned Aircraft Systems, ICUAS, Warsaw, Poland, 2023

    2023

  41. [42]

    Wang, Y .i Hu, Z

    S. Wang, Y .i Hu, Z. Liu, and L. Ma, Research on adaptive obstacle avoidance algorithm of robot based on DDPG-DW A, Computers and Electrical Engineering, 109, 108753, 2023

    2023

  42. [43]

    S. Wen, J. Chen, S. Wang, H. Zhang, and X. Hu, Path planning of humanoid arm based on deep deterministic policy gradient, In 2018 IEEE International Conference on Robotics and Biomimetics (ROBIO), pp. 1755-1760. IEEE, 2018

    2018

  43. [44]

    X. Xu, P . Cai, Z. Ahmed, V . S. Y ellapu, and W. Zhang, Path planning and dynamic collision avoidance algorithm under COLREGs via deep reinforcement learning, Neurocomputing 468 (2022): 181-197

    2022

  44. [45]

    Q. Y ao, Z. Zheng, L. Qi, H. Yuan, X. Guo, M. Zhao, Z. Liu, and T. Y ang, Path planning method with improved artificial potential field—a reinforcement learning perspective, IEEE access 8, 135513-135523, 2020

    2020

  45. [46]

    T. Zhu, J. Mao, L. Han, C. Zhang, and J. Y ang, Real-time dynamic obstacle avoidance for robot manipulators based on cascaded nonlinear MPC with artificial potential field, IEEE Transactions on Industrial Electronics, 71(7), 7424-7434, 2023

    2023

  46. [47]

    R. Pan, L. Jie, X. Zhao, H. Wang, J. Y ang, and J. Song, Active obstacle avoidance trajectory planning for vehicles based on obstacle potential field and MPC in V2P scenario, Sensors 23(6), 3248, 2023

    2023

  47. [48]

    Hogan, Impedance control: An approach to manipulation, American control conference, 304-313, 1984

    N. Hogan, Impedance control: An approach to manipulation, American control conference, 304-313, 1984

    1984

  48. [49]

    Q. Le, Y . Y ang, and I. Weintraub, A Comparison of Reinforcement Learning and Optimal Control Methods for Path Planning, AAAI 2026 Spring Symposium Series, Burlingame, CA, USA, April 7-9, 2026

    2026

  49. [50]

    Y ang, An arc-search interior-point algorithm for nonlinear constrained optimization, Computational Optimization and Ap- plications, 90(3), (2025), 969-995

    Y . Y ang, An arc-search interior-point algorithm for nonlinear constrained optimization, Computational Optimization and Ap- plications, 90(3), (2025), 969-995. 13

    2025