Multi Pseudo Q-learning Based Deterministic Policy Gradient for Tracking Control of Autonomous Underwater Vehicles

This paper investigates trajectory tracking problem for a class of underactuated autonomous underwater vehicles (AUVs) with unknown dynamics and constrained inputs. Different from existing policy gradient methods which employ single actor-critic but cannot realize satisfactory tracking control accuracy and stable learning, our proposed algorithm can achieve high-level tracking control accuracy of AUVs and stable learning by applying a hybrid actors-critics architecture, where multiple actors and critics are trained to learn a deterministic policy and action-value function, respectively. Specifically, for the critics, the expected absolute Bellman error based updating rule is used to choose the worst critic to be updated in each time step. Subsequently, to calculate the loss function with more accurate target value for the chosen critic, Pseudo Q-learning, which uses sub-greedy policy to replace the greedy policy in Q-learning, is developed for continuous action spaces, and Multi Pseudo Q-learning (MPQ) is proposed to reduce the overestimation of action-value function and to stabilize the learning. As for the actors, deterministic policy gradient is applied to update the weights, and the final learned policy is defined as the average of all actors to avoid large but bad updates. Moreover, the stability analysis of the learning is given qualitatively. The effectiveness and generality of the proposed MPQ-based Deterministic Policy Gradient (MPQ-DPG) algorithm are verified by the application on AUV with two different reference trajectories. And the results demonstrate high-level tracking control accuracy and stable learning of MPQ-DPG. Besides, the results also validate that increasing the number of the actors and critics will further improve the performance.