柔性机器人协调操作的动力学分析与规划
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摘要
柔性机器人协调操作是机器人研究的前沿课题之一，由于难度较大，目前国内外在此方面的研究成果还十分有限。本文采用新的方法，建立了柔性臂机器人，考虑关节柔性和臂柔性的机器人及其协调操作系统的动力学模型。系统研究了柔性机器人及其协调操作的正动力学问题，逆动力学问题，轨迹跟踪，冗余驱动，内力和承载能力等，并将这些方法拓展到受限柔性机器人以及柔性机器人协调操作受限物体领域当中，取得了一系列研究成果。
首先，基于实际位移，采用Timoshenko梁理论和有限元法，由Lagrange方程建立了柔性臂机器人和考虑关节柔性和臂柔性的机器人动力学模型。由此推导出了对于给定的关节输入求解柔性机器人末端轨迹的动力学方程。通过采用与通常方法不同的边界条件，推导出了给定机器人末端任务求解机器人输入关节角和关节力矩的柔性机器人动力学方程。
然后，根据本文所建立的柔性机器人动力学模型，由柔性机器人协调操作的运动约束条件和动力约束条件，推导出了柔性机器人协调操作刚性负载的动力学方程。由此推导出了对于给定的关节输入求被协调操作物体质心轨迹的动力学方程。令被操作物体的实际质心位置，而不是由刚体运动分析所确定的名义位置为边界条件，并且令其满足期望的轨迹，由提出的载荷分配方法，推导出了给定被操作物体轨迹求解机器人关节输入的动力学方程。此动力学方程可以求出机器人理想的关节输入。文中对柔性机器人协调操作的正动力学问题，逆动力学问题，载荷分配，轨迹跟踪，内力和承载能力等方面进行了理论分析和数值仿真。
接着，首次对柔性机器人协调操作的动力规划问题进行了研究，提出了输入功率这一新的规划目标。与采用输入关节力矩最小和输入关节速度最小为目标时的动力规划结果相比，以关节输入功率最小为规划目标进行动力规划时，可降低系统的能耗，同时系统的运动学和动力学特性较好。
最后，首次利用有限元法，根据柔性机器人与作业环境的运动约束条件和动力约束条件，推导出了受限柔性机器人的动力学模型，以及柔性机器人协调操作受限物体的动力学模型。由于采用了系统变形后的实际位置为边界条件，本文所提出的受限柔性机器人的动力学模型和柔性机器人协调操作受限负载的动力学模型克服了通常方法不方便对受限柔性系统进行动力学分析的弱点。文中通过数值仿真讨论了逆动力学问题，轨迹跟踪，载荷分配和与作业环境的最
北京工业大学工学博士学位论文
大接触力等方面。
The cooperation of flexible manipulators is one of the advanced topics in the robotics research. A literature search reveals little results on the cooperation of flexible manipulators. The dynamic models of flexible-link manipulators, manipulators with joint and link flexibility and the cooperation of flexible manipulators are developed. The forward dynamics, inverse dynamics and trajectory tracking of the flexible robot arms and further the forward dynamics, inverse dynamics, trajectory tracking redundant actuation, internal forces and dynamic load-carrying capacity of cooperating manipulators have been systematically studied. The methods have been developed further and used for the constrained flexible manipulators and flexible manipulators cooperating constrained objects.
First of all, using the Timoshenko beam theory and the Finite Element Method, according to Lagrange equation, the dynamic models of flexible-link manipulators and those with joint and link flexibility are proposed base on actual displacement. The dynamic equations are derived, which can be used to obtain the trajectory of the end-effector for given input joint angles or input joint torques. With boundary conditions different from the conventional method, the dynamic equation is developed, which can be used to find input joint angles or input joint torques for the specified trajectory of the end-effector.
Then, according to the kinematic and dynamic constrains of the cooperation, the dynamic models of multiple flexible robot arms cooperating a rigid body are developed by the proposed dynamic models of flexible manipulators. The dynamic models of the cooperation of the flexible robot arms have been derived, which can be used to obtain the trajectory of the mass center of the cooperated object for given joint input. Assuming the actual mass center of the cooperated object, instead of the nominal rigid position determined by the kinematics of the rigid link counterpart, to be the boundary constraint and to satisfy the anticipated trajectory, the dynamic model is developed with the proposed load distribution method. The model can be used to find perfect input joint angles or input joint torques for specified trajectory of the mass center of the cooperated object. The inverse dynamics, forward dynamics, load distribution, trajectory tracking internal forces and allowable dynamic
load-carrying capacity of the cooperation of the flexible manipulators have been discussed through analyses and numerical simulations.
After that, the dynamic programming of cooperating flexible manipulators has been studied and a new measure, namely, the input power measure, has been proposed for the first time. Compared with the results of the other objective functions such as minimum input joint torques and minimum input joint angular velocity, the power consumption can be decreased and the kinematical and dynamical performances will be better by dynamic programming when taking the minimum joint input power as the objective function.
Finally, using the Finite Element Method, according to the kinematic and dynamic constrains between the operated object and the environment, the dynamic models have been developed for constrained flexible manipulators and flexible robot arms cooperating constrained objects by the proposed dynamic models of flexible manipulators for the first time. Because the actual position has been assumed to be the boundary constraint, the proposed dynamic models have overcome the weakness that the conventional method is not convenient for the dynamic analysis of the kind of constrained flexible systems. The issues, inverse dynamics, trajectory tracking, load distribution and maximum dynamic contact force exerted on the environment, have been discussed through numerical simulations.
首先，基于实际位移，采用Timoshenko梁理论和有限元法，由Lagrange方程建立了柔性臂机器人和考虑关节柔性和臂柔性的机器人动力学模型。由此推导出了对于给定的关节输入求解柔性机器人末端轨迹的动力学方程。通过采用与通常方法不同的边界条件，推导出了给定机器人末端任务求解机器人输入关节角和关节力矩的柔性机器人动力学方程。
然后，根据本文所建立的柔性机器人动力学模型，由柔性机器人协调操作的运动约束条件和动力约束条件，推导出了柔性机器人协调操作刚性负载的动力学方程。由此推导出了对于给定的关节输入求被协调操作物体质心轨迹的动力学方程。令被操作物体的实际质心位置，而不是由刚体运动分析所确定的名义位置为边界条件，并且令其满足期望的轨迹，由提出的载荷分配方法，推导出了给定被操作物体轨迹求解机器人关节输入的动力学方程。此动力学方程可以求出机器人理想的关节输入。文中对柔性机器人协调操作的正动力学问题，逆动力学问题，载荷分配，轨迹跟踪，内力和承载能力等方面进行了理论分析和数值仿真。
接着，首次对柔性机器人协调操作的动力规划问题进行了研究，提出了输入功率这一新的规划目标。与采用输入关节力矩最小和输入关节速度最小为目标时的动力规划结果相比，以关节输入功率最小为规划目标进行动力规划时，可降低系统的能耗，同时系统的运动学和动力学特性较好。
最后，首次利用有限元法，根据柔性机器人与作业环境的运动约束条件和动力约束条件，推导出了受限柔性机器人的动力学模型，以及柔性机器人协调操作受限物体的动力学模型。由于采用了系统变形后的实际位置为边界条件，本文所提出的受限柔性机器人的动力学模型和柔性机器人协调操作受限负载的动力学模型克服了通常方法不方便对受限柔性系统进行动力学分析的弱点。文中通过数值仿真讨论了逆动力学问题，轨迹跟踪，载荷分配和与作业环境的最
北京工业大学工学博士学位论文
大接触力等方面。
The cooperation of flexible manipulators is one of the advanced topics in the robotics research. A literature search reveals little results on the cooperation of flexible manipulators. The dynamic models of flexible-link manipulators, manipulators with joint and link flexibility and the cooperation of flexible manipulators are developed. The forward dynamics, inverse dynamics and trajectory tracking of the flexible robot arms and further the forward dynamics, inverse dynamics, trajectory tracking redundant actuation, internal forces and dynamic load-carrying capacity of cooperating manipulators have been systematically studied. The methods have been developed further and used for the constrained flexible manipulators and flexible manipulators cooperating constrained objects.
First of all, using the Timoshenko beam theory and the Finite Element Method, according to Lagrange equation, the dynamic models of flexible-link manipulators and those with joint and link flexibility are proposed base on actual displacement. The dynamic equations are derived, which can be used to obtain the trajectory of the end-effector for given input joint angles or input joint torques. With boundary conditions different from the conventional method, the dynamic equation is developed, which can be used to find input joint angles or input joint torques for the specified trajectory of the end-effector.
Then, according to the kinematic and dynamic constrains of the cooperation, the dynamic models of multiple flexible robot arms cooperating a rigid body are developed by the proposed dynamic models of flexible manipulators. The dynamic models of the cooperation of the flexible robot arms have been derived, which can be used to obtain the trajectory of the mass center of the cooperated object for given joint input. Assuming the actual mass center of the cooperated object, instead of the nominal rigid position determined by the kinematics of the rigid link counterpart, to be the boundary constraint and to satisfy the anticipated trajectory, the dynamic model is developed with the proposed load distribution method. The model can be used to find perfect input joint angles or input joint torques for specified trajectory of the mass center of the cooperated object. The inverse dynamics, forward dynamics, load distribution, trajectory tracking internal forces and allowable dynamic
load-carrying capacity of the cooperation of the flexible manipulators have been discussed through analyses and numerical simulations.
After that, the dynamic programming of cooperating flexible manipulators has been studied and a new measure, namely, the input power measure, has been proposed for the first time. Compared with the results of the other objective functions such as minimum input joint torques and minimum input joint angular velocity, the power consumption can be decreased and the kinematical and dynamical performances will be better by dynamic programming when taking the minimum joint input power as the objective function.
Finally, using the Finite Element Method, according to the kinematic and dynamic constrains between the operated object and the environment, the dynamic models have been developed for constrained flexible manipulators and flexible robot arms cooperating constrained objects by the proposed dynamic models of flexible manipulators for the first time. Because the actual position has been assumed to be the boundary constraint, the proposed dynamic models have overcome the weakness that the conventional method is not convenient for the dynamic analysis of the kind of constrained flexible systems. The issues, inverse dynamics, trajectory tracking, load distribution and maximum dynamic contact force exerted on the environment, have been discussed through numerical simulations.
引文
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