Multi-arm robot has infinitive torque solution with a given motion and constructs closed system. Therefore, dynamic analysis and control of the multi-arm robot are not typical problems. Several researches are made for single-arm robot but are not directly available for multi-arm robot. Robot dynamic response analysis is an essential task to improve the performance and efficiently operate. In this dissertation, we propose a method of dynamic analysis of multi-arm robot and new performance index, and apply the proposed method for dynamic characteristic analysis and robot design.
Since task space analysis of robot's end-effector is important, equations of motion are derived based on the working space. To represent available accelerations due to actuators and loads due to acceleration and velocity of object and gravity, set theory is introduced. Available acceleration due to actuators constructs polyhedron, and facets of polyhedron can be represented by column vectors of transformation matrix to map actuator torque into acceleration. Using the information, number and equations of facets of available acceleration polyhedron can be found. It is insufficient to quantify robot performance using one index, and it's difficult to consider acceleration and velocity capabilities together among the performances. Therefore, we propose two local performance indices, isotropic acceleration radius (IAR) and isotropic velocity radius (IVR), to quantify acceleration and velocity capabilities separately and analyze robot overall performance. Using the characteristics of available acceleration polyhedron, we propose an algorithm to obtain a compact and analytic solution by linear transformation of polyhedron facets onto normal hyperplane to the axes. To apply the proposed indices to improve the dynamic performance, optimization problem is formulated to determine the minimum actuator size and working points with more than desired values of IAR and IVR for overall workspace. Since this problem includes nonlinear terms, discrete design parameters, and non-differential functions, we employ genetic algorithm to solve the problem.
The proposed construction method of available acceleration polyhedron is easily applicable to robot and helpful to analyze robot overall performance. Available acceleration polyhedron of multi-arm robot is more isotropic than that of single-arm robot and not cross area of available acceleration polyhedrons of single-arm robots constructing multi-arm robot, which results are obtained by the proposed method. We can analyze effects of the single-arm robots for the multi-arm robot using the method as well. Since available acceleration polyhedron of multi-arm robot is more isotropic, IAR can represent the polyhedron better and is superior to the other proposed indices. Using two indices, IAR and IVR, robot dynamic performance can be more clearly analyzed. Although the indices are local, dynamic analysis over workspace can be easily done due to short computation time. By the application of genetic algorithm, the complicate optimization problem can be easily solved. It is found that the discrete variables such as actuator size need to be handled as discrete variables.