Reachability-Based Trajectory Design for Robot Walking

A biped robot is a hybrid system and developing trajectory designers and controllers is a challenging task. Current methods like Nonlinear Model Predictive Control (NMPC) and Rapidly-exploring Random Tree (RRT) can't guarantee the safety and efficiency at the same time. Here, safety means avoiding collision on obstacles and keeping states stable. Efficiency means being capable of real-time performance. In our work, we use a semi-passive Spring-loaded Inverted Pendulum (SLIP) as a hybrid system and implement Reach-ability-based Trajectory Design (RTD) on this system to ensure safety and efficiency. RTD consists of an offline computation step, which finds a robot's Forward-Reachable Set (FRS), and an online identify step, which identifies all correct trajectories. Mathematical properties are presented and main elements of the hybrid system are defined. Through numerical simulations, RTD is validated to ensure the control safety in high-density obstacles.