Hybrid-state driven autonomous control for planar bipedal locomotion over randomly sloped non-uniform stairs

This paper extends the hybrid-state driven autonomous control (HyDAC) algorithm developed for planar bipedal locomotion to dynamic walking situation over randomly sloped ascending and descending stairs with non-uniform tread depth and riser height. Dynamic walking over non-uniform stairs requires to control the swing foot placement at predetermined feasible foothold on each toe-impact event in addition to forward velocity regulation. HyDAC law is modified in both task level and supervisory level to meet these demands. A novel scheme for forward velocity control by direct regulation of the ground centre of pressure (GCoP) is developed as a part of HyDAC. Nonholonomic constraints corresponding to friction cone and actuator torque limit are also introduced in HyDAC formulation. The agility of the control algorithm is demonstrated for a forward velocity range up to 0.5 m/s over ascending and descending stairs with tread depth of 1.5Lf to 2.5Lf, riser height up to 2Lf and tread slope within ±15°, for a planar biped with foot-sole span of Lf=0.2m, nominal hip height of hhip=0.98m, and nominal centre of mass height of, hcom=1.13m. The robustness of the algorithm is demonstrated through dynamic model simulation of a 12-link planar biped having similar size and mass properties of an adult sized human being restricted to sagittal plane. Cases with wide range of link parameter perturbation, external force disturbance and with random perturbation of stair-parameters have been considered for simulation.