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This paper investigates trajectory tracking problem for a class ofunderactuated autonomous underwater vehicles (AUVs) with unknown dynamics andconstrained inputs. Different from existing policy gradient methods whichemploy single actor-critic but cannot realize satisfactory tracking controlaccuracy and stable learning, our proposed algorithm can achieve high-leveltracking control accuracy of AUVs and stable learning by applying a hybridactors-critics architecture, where multiple actors and critics are trained tolearn a deterministic policy and action-value function, respectively.Specifically, for the critics, the expected absolute Bellman error basedupdating rule is used to choose the worst critic to be updated in each timestep. Subsequently, to calculate the loss function with more accurate targetvalue for the chosen critic, Pseudo Q-learning, which uses sub-greedy policy toreplace the greedy policy in Q-learning, is developed for continuous actionspaces, and Multi Pseudo Q-learning (MPQ) is proposed to reduce theoverestimation of action-value function and to stabilize the learning. As forthe actors, deterministic policy gradient is applied to update the weights, andthe final learned policy is defined as the average of all actors to avoid largebut bad updates. Moreover, the stability analysis of the learning is givenqualitatively. The effectiveness and generality of the proposed MPQ-basedDeterministic Policy Gradient (MPQ-DPG) algorithm are verified by theapplication on AUV with two different reference trajectories. And the resultsdemonstrate high-level tracking control accuracy and stable learning ofMPQ-DPG. Besides, the results also validate that increasing the number of theactors and critics will further improve the performance.

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