A unified method for computing the dynamic load-carrying capacity (DLCC) and the inverse dynamics of multiple cooperating robotic manipulators is developed in this paper. In this method, the kinematic constraints and the governing dynamic equations of the multi-robot system are formulated in the joint space based on a coordinate partitioning technique and the generalized D'Alembert's principle. This approach not only gives the minimum number of equations but also allows separate computations of the dynamics of the robots and that of the payload. The upper limit of the DLCC at any points on a given trajectory is obtained by solving a small-size linear programming problem. An iterative algorithm for evaluating the maximum allowable DLCC of the trajectory is also developed. After the DLCC is determined, the optimum distribution of actuator torques are computed by using a quadratic programming technique. The proposed method is conceptually straightforward, and it is applicable to wide varieties of multi-robot systems as well as fully parallel robots with redundant actuators.>

A systematic two-part approach for the numerical kinematic analysis of general parallel robotic manipulators, is presented. The first part deals with structural analysis. Based on graph theory and the depth first search algorithm, a method for identifying and orienting the dependent kinematic loops of the robot is developed. This method not only facilitates the assignment of the local coordinate systems attached to the robot, but also arranges them in the correct order to allow efficient recursive coordinate transformation. The second part deals with displacement analysis. A set of recursion formulas is developed for computing the forward coordinate transformations, and these formulas are then adopted in a two-phase computational algorithm to obtain the numerical solutions to the direct and inverse kinematics problems. The two-phase algorithm developed is not only insensitive to the initial approximation of the solution vector, but also converges rapidly. It is also useful for finding multiple solutions for the robot as well as for continuous trajectory planning, as shown by the numerical examples presented.>

A new method for computing numerical solutions to the inverse kinematics problem of robotic manipulators is developed. The method is based on a combination of two nonlinear programming techniques and the forward recursion formulas, with the joint limitations of the robot being handled implicitly as simple boundary constraints. This method is numerically stable since it converges to the correct answer with virtually any initial approximation, and it is not sensitive to the singular configuration of the manipulator. In addition, this method is computationally efficient and can be applied to serial manipulators having any number of degrees of freedom.>

Computational kinematics and dynamics of robot manipulators are dealt with. A recursive method based on the vector form of Rodrigues' equation is presented for the computation of the associated coordinate transformations. The method allows for forward, backward, and two-way recursions and is applied to the computations of the Jacobian matrices and dynamic equations for mechanical manipulators. The computational complexities of the resulting equations are also evaluated and compared to some of the existing methods in each case. It is shown that the algorithms presented have certain computational advantages over most of the existing methods.