Exponential stabilisation of periodic orbits for running of a three-dimensional monopedal robot
This study presents a motion planning algorithm to generate a feasible periodic solution for a hybrid system describing running by a three-dimensional (3-D), three-link, three-actuator, monopedal robot. In order to obtain a symmetric running gait along a straight line, the hybrid system consists of two stance phases and two flight phases. The motion planning algorithm is developed on the basis of a finite-dimensional optimisation problem with equality and inequality constraints. By extending the concept of hybrid zero dynamics to running, the authors propose a time-invariant control scheme that is employed at two levels to locally exponentially stabilise the generated periodic solution for running of the monopedal robot. The first level includes stance and flight phase feedback laws as within-stride controllers to create attractive parameterised zero dynamics manifolds. In order to render the zero dynamics manifolds hybrid invariant and stabilise the desired periodic orbit for the closed-loop hybrid system, takeoff and impact event-based controllers update the parameters of the within-stride controllers at the second level. This strategy results in a reduced-order hybrid system for which the stability analysis of the periodic orbit can be performed by a 5-D restricted Poincaré return map.
