Uniform Global Exponential Stabilizing Passivity-Based Tracking Controller Applied to Planar Biped Robots

This paper presents a novel control approach, based on the interconnection and damping-assignment passivity-based control (IDA-PBC), to achieve stable and periodic walking for underactuated planar biped robots with one degree of underactuation. The system's physical structure is preserved by assigning a target port-Hamiltonian dynamics to the closed-loop system, which also ensures passivity. The control design ensures that the tracking error to the desired periodic gait converges exponentially to zero, and the convergence rate can be adjusted via gain tuning. Besides, through the hybrid zero dynamics, the stability of the full-order system can be retrieved from the stability of the orbit created in a lower-dimensional manifold. The proposed approach is the first example of a tracking controller based on the IDA-PBC applied to underactuated biped robots. Numerical simulations on a five-link planar biped robot with unactuated ankles validate the approach and show the performance of the closed-loop system.