Trajectory-Free Control of Lower-Limb Exoskeletons Through Underactuated Total Energy Shaping

Kinematic control approaches for exoskeletons replicate normative joint kinematics associated with one specific task and user at a time, which makes it difficult to adjust to continuously-varying activities during gait training. These approaches also overly constrain individuals who have partial or full volitional control of their limbs, preventing these individuals from choosing their own preferred gait patterns. To address these issues, we proposed a matching framework for underactuated total energy shaping (i.e., shaping both the potential and kinetic energies) with human and environmental interaction to provide task-invariant, energetic assistance. In our prior work, we designed assistive strategies to compensate for lower-limb inertia in the actuated part of the mass matrix while leaving mass related terms unshaped. While these strategies have demonstrated potential gait benefits, shaping mass related terms in addition to lower-limb inertia can produce greater benefits as they are more dominant in determining human dynamics during locomotion. Moreover, previous definitions of closed-loop mass matrix with reduced inertial parameters cannot guarantee its positive definiteness. Having a non-positive definite mass matrix in the closed loop can render chaotic behaviors such as unbounded exoskeleton torques that cause danger to human users. In this paper, we generalize our prior work to shape all inertial terms in the actuated part of the mass matrix while ensuring its positive definiteness in the closed loop. In addition, given a positive-definite, closed-loop mass matrix, we prove passivity from human input to joint velocity and highlight two Lyapunov stability results based on common assumptions of human joint control policies. We then show benefits of the proposed approach and its advantages over conventional exoskeleton control methods with simulations on a human-like model. We also show that the corresponding assistive torques closely match the human torques of an able-bodied subject.