Atomic Functions and Motion Planning for a Welding Robot

The investigation deals with the kinematic level of a control system for a friction stir welding robot. We propose using U-splines, that is, infinitely differentiable spline functions based on atomic functions, to implement motion planning of the end effector in such a robot. We solved the problem of interpolating a function of a real variable by means of 3rd order U-splines, obtaining a system of equations in their coefficients, and proved its solvability for any step size ratio in the grid used. We present steps for planning the motion of the welding robot end effector employing U-splines and a kinematic analysis algorithm for the robot to determine its joint trajectories. The algorithm involves numerical integration of the kinematic equations describing the robot, repea-tedly solving velocity-based inverse kinematics problems. The paper also considers issues of software implementation of this algorithm

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