本研究以上肢復健為例，建立一個基於微分動態程序之復健最佳路徑的規劃方法。此方法考慮患者關節所受扭矩的極限，以及肢體運動的拘束。在參考復健師規劃之標準路徑的情況下，經由微分動態程序，計算出最適合患者之上肢復健運動路徑及最佳關節扭矩。在復健師規劃路徑方面，為使復健師方便建立參考之復健路徑，我們藉由一多項式來模擬標準路徑。在扭矩拘束方面，藉由調整權重及設定上下限來使關節扭矩可以被拘束在一固定範圍內。至於肢體運動的拘束，將其表現在成本函數中，期望微分動態程序在使成本值變小的過程中，肢體運動路徑能逐漸滿足拘束。此外，我們經由模擬的方式建立復健機馬達驅動的輔助力，除了幫助患者達到最佳復健路徑外，也可藉由調整輔助程度來增加或減少復健強度。模擬結果顯示，成本值在疊代過程中越變越小，且增加成本函數中的追蹤誤差項權重時，最佳復健路徑的確和標準路徑相像。最佳關節扭矩滿足拘束，雖部分之肢體運動路徑超出拘束，但不違反人體正常運動姿態。

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.

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