Control Synthesis for Hopping Robots

Project Repository: https://github.com/zexiangliu/hoppingrob

Brief Introduction:

In this work, we study how control synthesis can be applied to the push recovery on a 2D plane, i.e. an uneven ground with holes or areas forbidden to step onto. We consider an abstraction-based synthesis approach. To avoid state space explosion in abstractions, we ask whether the robot can do push recovery on 2D plane using only 1D controllers. We develop an algorithm that extracts a finite set of 1D controllers that can handle a certain 1D map with holes, that when used together, can guarantee recovery on the 2D topology. Moreover, an incremental algorithm is developed, to synthesize 1D controllers from an ideal 1D controller that operates on a map without holes, by taking advantage of the action inclusion relation in the fixed point operations for synthesis. This local patching significantly improves the computation time. Our numerical simulations with a linear inverted pendulum model of the robot demonstrates the efficacy of the proposed approach.