Haojie Shi

Haojie Shi, Max Q. -H. Meng

Recently Koopman operator has become a promising data-driven tool to facilitate real-time control for unknown nonlinear systems. It maps nonlinear systems into equivalent linear systems in embedding space, ready for real-time linear control methods. However, designing an appropriate Koopman embedding function remains a challenging task. Furthermore, most Koopman-based algorithms only consider nonlinear systems with linear control input, resulting in lousy prediction and control performance when the system is fully nonlinear with the control input. In this work, we propose an end-to-end deep learning framework to learn the Koopman embedding function and Koopman Operator together to alleviate such difficulties. We first parameterize the embedding function and Koopman Operator with the neural network and train them end-to-end with the K-steps loss function. Then, an auxiliary control network is augmented to encode the nonlinear state-dependent control term to model the nonlinearity in the control input. This encoded term is considered the new control variable instead to ensure linearity of the modeled system in the embedding system.We next deploy Linear Quadratic Regulator (LQR) on the linear embedding space to derive the optimal control policy and decode the actual control input from the control net. Experimental results demonstrate that our approach outperforms other existing methods, reducing the prediction error by order of magnitude and achieving superior control performance in several nonlinear dynamic systems like damping pendulum, CartPole, and the seven DOF robotic manipulator.

Haojie Shi, Bo Zhou, Hongsheng Zeng et al.

Recently reinforcement learning (RL) has emerged as a promising approach for quadrupedal locomotion, which can save the manual effort in conventional approaches such as designing skill-specific controllers. However, due to the complex nonlinear dynamics in quadrupedal robots and reward sparsity, it is still difficult for RL to learn effective gaits from scratch, especially in challenging tasks such as walking over the balance beam. To alleviate such difficulty, we propose a novel RL-based approach that contains an evolutionary foot trajectory generator. Unlike prior methods that use a fixed trajectory generator, the generator continually optimizes the shape of the output trajectory for the given task, providing diversified motion priors to guide the policy learning. The policy is trained with reinforcement learning to output residual control signals that fit different gaits. We then optimize the trajectory generator and policy network alternatively to stabilize the training and share the exploratory data to improve sample efficiency. As a result, our approach can solve a range of challenging tasks in simulation by learning from scratch, including walking on a balance beam and crawling through the cave. To further verify the effectiveness of our approach, we deploy the controller learned in the simulation on a 12-DoF quadrupedal robot, and it can successfully traverse challenging scenarios with efficient gaits.