This paper concerns generation of motion for a redundant robot manipulator that shows stochastic behavior. Since a deterministic model is not sufficient to represent the motion of such manipulators, a stochastic model should be considered in the motion planning step. While classical approaches for robot control use the motion planning based on the deterministic model and then apply controls (e.g. the feedback control) to compensate the motion error, the new method developed in this paper considers the stochasticity of the system in the planning step for better results in terms of the motion error. This will lower the burden of the controller, resulting in more accurate control. This paper uses the stochastic model for the angle variables of robot joints. This gives the probability density function (pdf) for the position and the orientation of the robot end-effector. The goal of this paper is to find the optimal motion plan that enables the end-effector to follow a reference path with the minimized root-mean-square (RMS) error. To achieve this goal, the cost function that computes the RMS error is defined and then minimized with respect to the target angle values in the joint space. Using simulation of a 4DOF planar robot arm and a 7DOF spatial robot arm, we verify that the suggested method generates better motions than the classical inverse kinematics approach based on the deterministic model.

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