高速、大变位姿绳悬挂并联机器人动力学轨迹插值的解析方法研究

Cable-suspended parallel robots (CSPRs) have promising potentials in the field of motion simulation that requires high velocities and large workspace. Due to the unilateral tension property of cables, dynamic constraints that cable tensions are positive must be taken into account in planning trajectories with high velocities, namely planning dynamic trajectories. Previous researches focus on trajectory planning of the end-effector’s position. Symbolic expressions of cable forces are first obtained by solving the inverse dynamics, and the boundary conditions that satisfy positive global minimum values of the forces are then determined using an analytical approach. However, the above reasoning has some limitations when applied to six-DOF CSPRs. The symbolic expressions of cable tensions become complex and this complexity increases after the substitution of the functions of the trajectory, which prevents from determining their boundary conditions analytically. Therefore, the main questions to the dynamic trajectory planning are the development of a new method to find the boundary conditions that satisfy positive cable tensions, and the investigation of appropriate trajectories to alleviate analytical process...This proposal presents an analytical approach to develop dynamic trajectory interpolation for fully-actuated CSPRs in a case that target points are located outside the static workspace. The boundary expressions that correspond to feasible cable forces with one zero value are first obtained. Then, pose interpolation trajectories with continuous second derivatives using spherical interpolation of quaternions and basis functions are designed. The conditions that satisfy cable tension boundaries for the parameters of a point-to-point trajectory are found. Finally, an experimental implementation is presented using a six-DOF prototype to validate the feasibility of the trajectories. This project will provide a new theoretical foundation and approach for dynamic trajectory planning of cable-driven parallel mechanisms.

绳悬挂并联机器人在高速、大工作空间的运动模拟任务中的应用前景广阔。因绳索的单向受力性，规划高速轨迹时必须考虑绳拉力大于零的动力学约束，即必须规划动力学轨迹。但目前主要是位置轨迹规划，往往先求绳拉力表达式，再解析绳拉力全局最小值大于零的边界条件。而对于六自由度绳悬挂机器人，按此思路，因绳拉力表达式复杂，且位姿轨迹又增加了表达式的复杂度，阻碍了边界条件的解析工作。因此，如何转变边界条件的求解思路，设计有利于解析的轨迹，降低解析的难度，是当前动力学轨迹规划亟需回答的重要问题。本项申请针对目标点在静力学工作空间以外的情况，研究全驱动绳悬挂并联机器人的动力学轨迹插值的解析方法。首先求解绳拉力有零解的边界表达式，设计基于四元数球面插值以及基函数的二阶导数连续的位姿轨迹，再解析满足可行绳拉力边界值的轨迹参数条件，完成轨迹插值，并以实验验证。研究成果将为绳牵引并联机构动力学轨迹规划提供新的理论依据和方法。

绳悬挂并联机器人在高速、大工作空间的运动模拟任务中的应用前景广阔。因绳索的单向受力性，规划高速轨迹时必须考虑绳拉力大于零的动力学约束，即必须规划动力学轨迹。但目前主要是位置轨迹规划，往往先求绳拉力表达式，再解析绳拉力全局最小值大于零的边界条件，因绳拉力表达式复杂，且位姿轨迹又增加了表达式的复杂度，阻碍了边界条件的解析工作。本项申请运用凸包理论、矢量投影定理对绳牵引并联机器人的可行工作空间进行了分析，通过规划动态轨迹穿越驱动奇异姿态，有效地增大了机构的工作空间，提出最小二乘法求解的拉力分布作为轨迹跟踪控制中的动力学补偿，设计了点到点轨迹规划方法并通过仿真和实验验证了方法的有效性。相关研究成果目前在本领域国内外主流期刊上发表论文共3篇，申请发明专利3项，授权实用新型专利1项。项目研究成果为绳牵引并联机构动力学轨迹规划提供新的理论依据和方法。