An Efficient Paradigm for Feasibility Guarantees in Legged Locomotion

Developing feasible body trajectories for legged systems on arbitrary terrains is a challenging task. In this article, we present a paradigm that allows to design feasible Center of Mass (CoM) and body trajectories in an efficient manner. In our previous work (Orsolino et al., 2020), we introduced the notion of the two-dimensional feasible region , where static balance and the satisfaction of joint-torque limits were guaranteed, whenever the projection of the CoM lied inside the proposed admissible region. In this work, we propose a general formulation of the improved feasible region that guarantees dynamic balance alongside the satisfaction of both joint-torque and kinematic limits in an efficient manner. To incorporate the feasibility of the kinematic limits, we introduce an algorithm that computes the reachable region of the CoM. Furthermore, we propose an efficient planning strategy that utilizes the improved feasible region to design feasible CoM and body orientation trajectories. Finally, we validate the capabilities of the improved feasible region and the effectiveness of the proposed planning strategy, using simulations and experiments on the 90 kg hydraulically actuated quadruped and the 21 kg Aliengo robots.