In this paper, we present a method to initialize at a feasible point and unfailingly solve a non-convex optimization problem in which a set-point motion is planned for a multi-link manipulator under state and control constraints. We construct an initial feasible solution by analyzing the final time effect for feasibility problems of flatness based motion planning problems. More specifically, we first find a feasible time-optimal trajectory under state constraints without a control constraint by solving a linear programming problem. Then, we find a feasible trajectory under control constraints by scaling the trajectory. To evaluate the practical applicability of the proposed method, we did numerical experiments to solve a multi-link manipulator motion planning problem by combining the method with recursive inverse dynamics algorithms.
Their methods are based on the Lie group formulation of multi-link robot manipulator modeling and effective calculation of the inverse dynamics of a manipulator. The theory of the Lie group formulation of robot dynamics is described in detail elsewhere @cite_0 , @cite_6 . A recursive algorithm for the Lie group formulation of robot dynamics was developed @cite_6 and then analyzed more deeply and extended @cite_1 @cite_12 . Our method references Kim and Polland's implementation @cite_13 .
@cite_1 @cite_6 @cite_0 @cite_13 @cite_12
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In this article we present a unified geometric treatment of robot dynamics. Using standard ideas from Lie groups and Rieman nian geometry, we formulate the equations of motion for an open chain manipulator both recursively and in closed form. The recursive formulation leads to an O(n) algorithm that ex presses the dynamics entirely in terms of coordinate-free Lie algebraic operations. The Lagrangian formulation also ex presses the dynamics in terms of these Lie algebraic operations and leads to a particularly simple set of closed-form equations, in which the kinematic and inertial parameters appear explic itly and independently of each other. The geometric approach permits a high-level, coordinate-free view of robot dynamics that shows explicitly some of the connections with the larger body of work in mathematics and physics. At the same time the resulting equations are shown to be computationally ef fective and easily differentiated and factored with respect to any of the robot parameters. This latter fe... 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. > Considers the problem of robot motion planning using an approximate cell decomposition method for Cspace representation. By means of a hierarchical multilevel discretization the authors are able to reduce the complexity of the problem and to provide a practically feasible procedure for its solution. Hierarchical discretization is based on the use of a multisource distance field that is introduced and described in the paper. The developed procedure, used as an heuristic, systematically reduces the amount of memory needed for implementing the motion planning algorithm. Using such a procedure, several instances of the motion planning problem, involving for example two three-links manipulators acting in the same tridimensional environment, have been solved in a reasonable amount of time. > A new approach to solve the inverse kinematics problem of redundant robot manipulators in environments cluttered with obstacles is presented in this paper. The physical problem is formulated as an optimization problem under constraints, and solved via a modified genetic algorithm (mGA). The mGA searches for successive robot configurations in the entire free space so that the robot moves its end-effector from an initial placement to a final desired. The objective of this optimization is to simultaneously minimize the end-effector's positional error and the robot's joint displacements. The efficiency of the proposed approach is demonstrated through multiple experiments carried out on several redundant robot manipulators. Comparison with two other approaches, the well known Pseudoinverse method and a previous method based on a simple GA, shows that the accuracy of the present solution is substantially better.