Waveform based Inverse Kinematics Algorithm of Kinematically Redundant 3-DOF Manipulator

Abstract

This paper presents a new approach to the problem of inverse kinematics by modelling robot arm movements as signals generated from algebra-based solutions. The inverse kinematics of point P(x_P,y_P) are modelled as sinusoidal functions with mechanical constraints. Unique wave forms occur at each point in the workspace. There are four types of inverse kinematic waves depending on how sinusoidal waves cross the value of mechanical constraints. In terms of tracking the path, the robot's arm produces complex waves that produce the desired movement. Due to mechanical constraints, many points in the workspace have the bandwidth where the signal is produced only at limited intervals from the angular domain. Tracks must be stored at these appropriate intervals, which build bandwidth tunnels, completely from the initial configuration to the final configuration. Simulations will be carried out using 3-DOF series planar robots to track highly complex mathematical curves. With a wave-based approach, the solution of the IK problem can benefit from wave characteristics such as the superposition principle.