A trajectory optimization formulation for assistive robotic devices

Abstract

We present a trajectory optimization formulation for the design of a sit-to-stand assistive device for humans with motion impairments. We develop a constrained Lagrangian to derive the equations of motion for the trajectory optimization formulation. Such a Lagrangian enables us to impose constraints on joint reaction wrenches in the human, to simulate the motion impairment of human joints due to injury and infirmity. Using trajectory optimization, we compute the optimal sit-to-stand motions of a human as well as the actuation wrenches of the sit-to-stand device. The trajectory of the device as it follows and supports the human, and its actuation wrenches provide necessary inputs for the design of the assistive device. We propose an assistive device capable of following the natural trajectory of the human during sit-to-stand. We show by numerical simulation that the human requires less effort with the device that can follow its trajectory than with an assistive device restricted to only vertical motion to lift up a human. Our formulation provides a systematic approach for the design of such sit-to-stand assistive devices.