Applying differential dynamic program with inequality constraints for optimal rehabilitation trajectories planning

Abstract

In this study a method based on differential dynamic program is proposed for planning optimal rehabilitation trajectories and elaborated in an upper limb rehabilitation example This method considers the constraints of both patients' joint torques and limb movements Taking the standard path planned by a physical therapist as reference an optimal upper limb rehabilitation trajectory with optimal joint torques can be calculated by using differential dynamic program In terms of planning the standard path a rehabilitation path described by a polynomial was used to simplify the path-setting process for physical therapists In terms of torque constraints they can be con fined within a predefined upper and lower bounds by adjusting the torque-weighting in the cost function As for the constraints of limb movements they were considered and expressed in the cost function expecting that they could satisfy the constraints when cost value went down In addition the auxiliary force driven by the motor of the rehabilitation machine was set to be adjustable in simulation; therefore this hypothetic system can not only help the patients to achieve the optimal rehabilitation trajectories but also increase or decrease the assistant strength Simulation results show that (1) the cost value becomes smaller and smaller in the iterative process (2) the optimal rehabilitation trajectory is similar to the reference path when the weighting of tracking errors in the cost function increases (3) the optimal joint torque satisfies the constraints Although part of the limb movement exceeds the predefined constraints it does not violate the normal posture of human beings

Date of Award	2019
Original language	English
Supervisor	Szu-Chi Tien (Supervisor)