math.OCApr 14, 2026

A Comparison of Reinforcement Learning and Optimal Control Methods for Path Planning

Authors: Qiang Le, Yaguang Yang, Isaac E. Weintraub

Organizations: Department of Electrical and Computer Engineering, Hampton University Hampton, USA · Air Warfare Directorate, Air Force Research Laboratory Wright-Patterson, USA

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Abstract

Path-planning for autonomous vehicles in threat-laden environments is a fundamental challenge. While traditional optimal control methods can 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 a simple, circular no-go' zone. A mission failure is claimed if the vehicle enters this no-go' zone at any time or does not reach a neighborhood of the destination. The DDPG agent is trained to learn a direct mapping from its current state (position and velocity) to a series of feasible actions that guide the agent to safely reach its goal. A reward function and two neural networks, critic and actor, are used to describe the environment and guide the control efforts. The DDPG trains the agent to find the largest possible set of starting points (feasible set'') wherein a safe path to the goal 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 may produce effective paths while being significantly faster, making it a better fit for real-time applications. However, there are areas (infeasible set'') where the DDPG agent cannot find paths to the destination, and the paths in the feasible set may not be optimal. These preliminary results guide our future research: (1) improve the reward function to enlarge the DDPG feasible set, (2) examine the feasible set obtained by the pseudo-spectral method, and (3) investigate the arc-search IPM method for the path planning problem.

Figures & tables

Figure 1: (a) Actor network (b) Critic network
Figure 2: Heat map of the reward function where w3w_{3} =0
w1w_{1}w2w_{2}w3w_{3}σ\sigma
30005001.5(40,00010010040,000)\begin{pmatrix}40,000&100\\ 100&40,000\\ \end{pmatrix}
Table 1: Hyperparameters in reward function
Figure 3: (a) Obtained path by DDPG with the standard deviation 5 degrees in the action noise, the resulting travel time 23×0.25=5.7523\times 0.25=5.75 (b) Instant Reward (c) Action over time steps
Figure 4: (a) Obtained path by further trained DDPG agent with low standard deviation in the action noise, the resulting travel time 22×0.25=5.522\times 0.25=5.5 (b) Instant Reward (c) Action over time steps
Figure 5: Feasible area of the specialized agent who is trained using [400,400]⊤[400,400]^{\top} as the starting point
Figure 6: Feasible area of the general agent who is trained using random initial points
Figure 7: Testing examples of the specialized DDPG agent
Figure 8: Testing examples of the general DDPG agent
Figure 9: Obtained path by PS, Elapsed time ≈8\approx 8 seconds (a) constraining speed ∣V∣=200|V|=200 , (b) no speed constraint
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