本文为美国海军研究生院（作者：Joseph A. Cascio）的硕士论文，共121页。

本文研究了机器人手臂的控制问题，旨在通过求解最优关节轨迹和相应的任务控制（如点对点定位）来达到给定的性能要求。由此产生的最优控制问题是高度非线性的，由于机械臂动力学和包括关节速度、执行器扭矩限制在内的动力学约束非线性而受到相关限制。

本文阐述了伪谱方法在解决多连杆多自由度机械臂系统最优路径规划问题中的应用。以标准形式定义了最优控制问题，并用DIDO软件包求解。利用庞特里亚金最小原理验证了所提解满足最优性的必要条件。一个特别具有挑战性的方面是多个手臂在有碰撞风险的情况下进行独立任务时的最佳运动。通过对适当的路径约束进行建模，可以实现碰撞避免。针对单自由度机械手进行点对点定位，提出了一种优化轨迹的规划方法，并将其扩展到双自由度机械手避撞策略的轨迹规划。结果表明，伪谱技术在解决机械臂的最小时间和最小控制机动问题上是适用的。碰撞避免技术的应用将有助于利用多臂系统中的最优控制标准继续进一步研究自主机器人的运动规划。

This work investigates the problem ofrobotic arm control with the goal of achieving given performance requirementsby solving for the optimal joint trajectories and corresponding controls fortasks, such as point-to-point positioning. The resulting optimal controlproblem is highly nonlinear and constrained due to the nonlinearities in therobotic arm dynamics and kinodynamic constraints including limits on jointvelocities and actuator torques. This thesis illustrates the applicability ofpseudospectral methods to solve the optimal path planning problem for a systemof multi-link, multi-degree of freedom robotic arms. The optimal controlproblem is defined in standard form and solved using the software package DIDO.Pontryagin’s Minimum Principle is used to verify that the proposed solutionsatisfies the necessary conditions for optimality. A particularly challengingaspect that is explored is the optimal motion of multiple arms conductingindependent tasks with the risk of collision. Collision avoidance can beachieved by modeling appropriate path constraints. The processes for optimaltrajectory planning are developed for a single two degree-of-freedommanipulator conducting point-to-point positioning and extended to include dualthree degree-of-freedom manipulator maneuvers employing collision avoidance.The results demonstrate the suitability of pseudospectral techniques to solvingthe minimum time and minimum control maneuvers for robotic arms. The employmentof collision avoidance techniques will facilitate continued research inautonomous robotic motion planning using optimal control criteria in multiplearm systems.

1 引言

2 最优轨迹规划

3 障碍规避

4 基于PS方法的协作规划

5 结论与建议

附录 2自由度机械臂的动力学计算

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