Gait Adaptation and Iterative Control: A Switched Systems Optimization Framework for Quadrupedal Robots

One of the primary challenges in quadrupedal locomotion pertains to the robot’s ability to adapt its gait to the surrounding environment and the desired task. This capability allows quadrupedal robots to select suitable foothold locations and adjust their gait for optimal performance. We address the problem of gait adaptation using trajectory optimization (TO), which takes into account the simplified switched system’s dynamics and optimizes the different phases of motion in which we split the robot’s movement. The robot dynamic model is a single rigid body (SRB) with a rigid contact model and foot positions. We apply contact and friction cone constraints to ensure a physically feasible motion of the real robot. We tackle the optimization using the direct multiple shooting (DMS) method. Leveraging kinematic inversion to map the base and feet positions into joint positions, velocities, and accelerations, we design a controller that combines iterative learning control (ILC) and proportional derivative (PD) feedback control. The iterative controller compensates for the sim-to-real gap, allowing the real robot to learn the task during the execution of the latter. We evaluate the performance of the proposed approach on two different quadrupedal robots and on different terrains.