Study on Optimal Motion Trajectory of Multi-Degree-of Freedom Articulated Mechanism

为了开发通用的最优运动规划方法，并研究铰接机构最优运动的特点，提出了一种基于五阶Hermite多项式和非线性数值最优规划方法的近似数值方法。利用该方法，根据Kuhn-Tucker定理推导出了直接驱动机器人在平均发热量约束下的最短时间运动轨迹，并通过实验验证了该方法的有效性。为了显著减少计算时间，我们还开发了一种准最小时间运动规划方法，该方法总是可以导致严格最优解的良好近似解。为了研究铰接机构的更复杂的运动，我们开发了一种数值方法，以获得最佳的人的手臂运动，可以在最大速度扔球，并发现最佳的运动分为两组。作为非完整约束运动的一个典型例子，我们还研究了巨摆最优运动的数值求解方法。采用罚函数法可以得到第一轴输入力矩为零的近似解。通过引入手与杆件之间的摩擦力矩和手臂运动的允许范围，得到了与真实的人体大秋千运动相似的解

In order to develop a generic optimal motion planning method and to investigate features of the optimal motion of articulated mechanisms, we formulated an approximated numerical method based on the fifth-order Hermite polynomial and nonlinear numerical optimal planning methods. By using this method we derived the minimum time motion trajectory of direct drive robotic manipulators under average heat generation constraint in terms of Kuhn-Tucker theorem and verified the effectiveness of the solution by experiments. In order to markedly reduce the computing time, we also developed a quazi-minimum time motion planning method that can always leads to a good approximated solution to the strictly optimum solution. For investigation of more complex motion of articulated mechanisms, we developed a numerical method to get an optimal human arm motion that can throw a ball at maximum speed and found that the optimal motions are classified into two groups. We also studied a numerical method to obtain the optimal otion of giant swing as a typical example of the non-holonomic constraint motion. An approximated solution with zero input torque at the first axis could be obtained by using the penalty method. By introducing friction torque between hand and bar and allowable region of arm motion, we could get a solution that is similar to a real human body motion of the giant swing