Advances in Feedback Control for High-dimensional Bipedal Models

Abstract

The promise of bipedal machines brings with it the promise of advancements in both the work and personal sectors. The robots are coming to work alongside us at our pace. They are coming to work in environments which we deem too dangerous to send our fellow humans. They are coming to help us recover mobility when we suffer neural or muscular impairments. The machines being prototyped and built for these tasks are complex devices, with many links, joints, and actuators. Moreover, these bipedal machines are meant to exhibit diverse gaits, and many are designed with agility in mind. Taking full advantage of their mechanical capabilities requires advanced optimization and feedback design methods, which are the central theme of this dissertation. While bipedal machines typically refer to two legged robots, we also in our research consider full-assist exoskeletons as well. Our specific hardware targets are (1) an exoskeleton designed by Wandercraft that allows people with paraplegia to walk again without the use of crutches, and (2) a Cassie-series bipedal robot that can stand quietly in place, balance on a Segway, and walk at over a meter per second. The high-dimensional and hybrid natures of the dynamical models of these robots pose challenges in optimal gait design and gait stabilization that we identify and address in this dissertation.

The first topic addressed in this dissertation is trajectory optimization. Specifically, we developed a toolset called C-FROST that speeds up the offline trajectory design process by a factor of six to eight times compared to using FROST. This allows the generation of 1000+ gaits for a 20 degrees of freedom (DOF) biped in under two hours. C-FROST allows FROST to generate a stand-alone C++ executable for running optimizations, thereby allowing for parallelization and easy deployment to the cloud. Benchmarking and practical examples demonstrating the capabilities of the C-FROST toolset are provided. The second topic is gait and feedback control design for the full-assist Wandercraft exoskeleton. This work was done early in the dissertation research and provided prototype software to the Wandercraft team. In addition to the exoskeleton’s model being high dimensional (with 36 state variables), its operation poses difficult challenges arising from workspace limitations required for patient safety and torque limits of the hardware. Feedback controllers are designed to meet these challenges using the method of Hybrid Zero Dynamics (HZD), gait libraries, and an extension of HZD by Xingye Da that is called Generalized Hybrid Zero Dynamics, or G-HZD for short.

Work on the Wandercraft exoskeleton revealed a fundamental drawback in the original G-HZD approach, and that motivates the third main topic of the dissertation: a broad extension of the design and stability properties of the hybrid zero dynamics manifold in the G-HZD feedback design approach. In particular, in G-HZD, the manifold is built from trajectories that arise from a boundary-value problem, and thus specifying the proper boundary of the manifold is crucial to the success of the method. This dissertation proposes a novel method for the design of the boundary manifold. The new approach is subsequently demonstrated on an inverted pendulum on a cart and compared to the original approach. We then demonstrate how to implement the new approach on Cassie, an underactuated biped hybrid system, and report experimental results.