Energy Shaping Control of Powered Lower-Limb Exoskeletons for Assistance of Human Locomotion
The majority of powered lower-limb exoskeletons nowadays are designed to rigidly track time-based kinematic patterns, which forces users to follow speciﬁc joint positions. This kinematic control approach is limited to replicating the normative joint kinematics associated with one speciﬁc task and user at a time. These pre-deﬁned trajectories cannot adjust to continuously varying activities or changes in user behavior associated with learning during gait rehabilitation. Time-based kinematic control approach must also recognize the user’s intent to transition from one task-speciﬁc controller to another, which is susceptible to errors in intent recognition and does not allow for a continuous range of activities. Moreover, ﬁxed joint patterns also do not facilitate active learning during gait rehabilitation. People with partial or full volitional control of their lower extremities should be allowed to adjust their joint kinematics during the learning process based on corrections from the therapist. To address this issue, we propose that instead of tracking reference kinematic patterns, kinetic goals (for example, energy or force) can be enforced to provide a ﬂexible learning environment and allow the user to choose their own kinematic patterns for different locomotor tasks. In this dissertation, we focus on an energetic control approach that shapes the Lagrangian of the human body and exoskeleton in closed loop. This energetic control approach, known as energy shaping, controls the system energy to a speciﬁc analytical function of the system state in order to induce different dynamics via the Euler-Lagrange equations. By explicitly modeling holonomic contact constraints in the dynamics, we transform the conventional Lagrangian dynamics into the equivalent constrained dynamics that have fewer (or possibly zero) unactuated coordinates. Based on these constrained dynamics, the matching conditions, which determine what energetic properties of the human body can be shaped, become easier to satisfy. By satisfying matching conditions for human-robot systems with arbitrary system dimension and degrees of actuation, we are therefore able to present a complete theoretical framework for underactuated energy shaping that incorporates both environmental and human interaction. Simulation results on a human-like biped model and experimental results with able-bodied subjects across a variety of locomotor tasks have demonstrated the potential clinical beneﬁts of the proposed control approach.