Dynamic Trajectory Generation and a Robust Controller to Intercept a Moving Ball in a Game Setting

Abstract

Complex and interactive robot manipulation skills, such as playing a game of table tennis against a human opponent, are a novel problem with multifaceted challenges. Accurate dynamic trajectory generation in order to respond to the tennis ball from the opponent and a novel control scheme for robust and high-performance tracking of the ball in such dynamic situations is a prerequisite to winning the game. In this paper, the dynamic movement primitives (DMPs) are employed for the stable generation of dynamic trajectories in the presence of environmental uncertainties such as ball position and velocity, opponent position and velocity and so on. In DMP, kernels parameters need to be found from expert demonstrations using a learning technique. To mitigate environmental uncertainties by accurate reconstruction of novel dynamic trajectories by combining multiple DMPs, we propose a piecewise linear canonical system (PLCS)-based modified DMP in contrast to the standard exponential canonical system (ECS)-based DMP. To enhance effectiveness and performance, a novel learning technique based on Lyapunov stability is embedded with the above-developed formulation. We show that the proposed learning technique is faster, has the best steady state error performance, and requires almost half the kernels than the state of the art. Next, to intercept the dynamic moving ball in real-time using the DMP, a novel control scheme is needed and designed using fuzzy fractional order sliding mode control. The control scheme results in chatter free tracking of the desired trajectories because the control law is free from sgn( $\cdot $ ) function. The tracking control performance is guaranteed theoretically via the Lyapunov approach and also verified through simulations and experiments. Finally, we have developed a complete system (including a vision system for tracking the ball) using a real 4 degrees-of-freedom (DOFs) Barrett Wam robotic arm and show that the proposed overall framework is able to respond to a hanging ball with high accuracy.