Hybrid Zero Dynamics Control of an Underactuated Lower-Limb Exoskeleton for Gait Guidance

Abstract

Hybrid zero dynamics (HZD) control creates dynamically stable gaits by driving a hybrid robot model toward an optimally generated state-dependent reference signal. This paper presents the first application of HZD to an underactuated lower-limb exoskeleton for gait guidance. A phase-based reference gait is generated to follow a nominal walking pattern. Simulation results using a phase-based proportional-derivative (PD) controller validate that stable periodic gait similar to nominal gait is possible for the identified human-exoskeleton model. For hardware application, a bilateral mixing strategy is taken to accommodate the presence of the double support phase, which was assumed to be instantaneous in the hybrid model. A treadmill experiment is conducted with a healthy subject using the Indego Explorer exoskeleton. Comparing the recorded gait to the optimal phase-based reference, the root-mean-square joint tracking errors (RMSE) are 2.87 deg, 2.79 deg, 3.20 deg, and 11.0 deg at the stance hip, stance knee, swing hip, and swing knee, respectively. Similarly, compared to the commanded reference, the RMSE are 2.04 deg, 4.40 deg, 4.58 deg, and 6.83 deg, respectively. A second experiment was conducted wherein the treadmill speed varied from 0.3 to 0.5 m/s. The results show how the HZD controller exhibits remarkable flexibility and robustness for multiple walking speeds and grants the operator greater level of volitional control due to the time-invariant, phase-based nature of the implementation. Taken altogether, the presented results suggest that HZD control can serve as a rehabilitative control method capable of providing gait guidance in underactuated exoskeleton systems.