Optimal Mixed Tracking/Impedance Control with Application to Transfemoral Prostheses with Energy Regeneration

Objective: We design an optimal passivity-based tracking/impedance control system for a robotic manipulator with energy regenerative electronics, where the manipulator has both actively and semi-Actively controlled joints. The semi-Active joints are driven by a regenerative actuator that includes an energy-storing element. Method: External forces can have a large influence on energy regeneration characteristics. Impedance control is used to impose a desired relationship between external forces and deviation from reference trajectories. Multi-objective optimization (MOO) is used to obtain optimal impedance parameters and control gains to compromise between the two conflicting objectives of trajectory tracking and energy regeneration. We solve the MOO problem under two different scenarios: 1) constant impedance; and 2) time-varying impedance. Results: The methods are applied to a transfemoral prosthesis simulation with a semi-Active knee joint. Normalized hypervolume and relative coverage are used to compare Pareto fronts, and these two metrics show that time-varying impedance provides better performance than constant impedance. The solution with time-varying impedance with minimum tracking error (0.0008 rad) fails to regenerate energy (loses 9.53 J), while a solution with degradation in tracking (0.0452 rad) regenerates energy (gains 270.3 J). A tradeoff solution results in fair tracking (0.0178 rad) and fair energy regeneration (131.2 J). Conclusion: Our experimental results support the possibility of net energy regeneration at the semi-Active knee joint with human-like tracking performance. Significance: The results indicate that advanced control and optimization of ultracapacitor-based systems can significantly reduce power requirements in transfemoral prostheses.