Multicontact Locomotion on Transfemoral Prostheses via Hybrid System Models and Optimization-Based Control

Lower-limb prostheses provide a prime example of cyber-physical systems (CPSs) requiring the synergistic development of sensing, algorithms, and controllers. With a view towards better understanding CPSs of this form, this paper presents a systematic methodology using multidomain hybrid system models and optimization-based controllers to achieve human-like multicontact prosthetic walking on a custom-built prosthesis: AMPRO. To achieve this goal, unimpaired human locomotion data is collected and the nominal multicontact human gait is studied. Inspired by previous work which realized multicontact locomotion on the bipedal robot AMBER2, a hybrid system-based optimization problem utilizing the collected reference human gait as reference is utilized to formally design stable multicontact prosthetic gaits that can be implemented on the prosthesis directly. Leveraging control methods that stabilize bipedal walking robots-control Lyapunov function-based quadratic programs coupled with variable impedance control-an online optimization-based controller is formulated to realize the designed gait in both simulation and experimentally on AMPRO. Improved tracking and energy efficiency are seen when this methodology is implemented experimentally. Importantly, the resulting multicontact prosthetic walking captures the essentials of natural human walking both kinematically and kinetically. Note to Practitioners-Variable impedance control, as one of the most popular prosthetic controllers, has been used widely on powered prostheses with notable success. However, due to the passivity of this controller, heuristic feedback is required to adjust the control parameters for different subjects and motion modes. The end result is extensive testing time for users, coupled with non-optimal performance of prostheses. Motivated by the shortcomings in the current state-of-the-art, this work proposes a novel systematic methodology-including gait generation and optimization-based control based on a multidomain hybrid system-to achieve prosthetic walking for a given subject. This method also aims to improve control optimality and efficiency while potentially reducing clinical tuning. The overarching technology utilized in this paper is the use of nominal human trajectories coupled with formal models and controllers that circumvent the need for excessive hand-tuning. In particular, rather than using a prerecorded trajectory (as is common), this work takes a different approach by using a human-inspired optimization problem to design a human-like gait for the amputee automatically. The proposed optimization framework uses the trajectory of a healthy subject as the reference and is subject to specific constraints (to ensure smooth transitions, torque and angle limitations) such that the output gait is applicable for implementation on the prosthetic device directly. The results of the offline optimization are then utilized to synthesize an online real-time optimization-based feedback controller that allows for pointwise optimal tracking on the prosthesis, thereby improving overall efficiency. The experimental results in this work suggest that this approach is able to achieve stable human-like multicontact prosthetic walking and also guarantees a more balanced performance compared to other traditional controllers (such as PD).