  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.
