Inverse Kinematics Solution of Articulated Robots Using a Heuristic Approach for Optimizing Joint Displacement

In this work, a new constrained numerical optimization approach is proposed for solving offline the Inverse Kinematics Problem (IKP) of articulated robots, which consists on optimizing the joint displacement while the end effector is positioned and oriented in a desired pose. The novelty of this approach is in the formulation of the optimization problem, where the objective function calculates the minimum joint displacement, with the position and orientation errors handled as equality constraints. This formulation may avoid configurations containing singularities. The IKP is solved for a defined trajectory in the dexterous workspace of the robot by using two versions of the Differential Evolution algorithm and considering two stages. First, DE/rand/1/bin is used for positioning and orienting the end effector at the first point of the trajectory regardless of its initial position. The second stage applies DE/best/1/bin in order to emphasize the exploitation process and minimize the computational time to obtain the inverse kinematics due to the closeness that exists between the consecutive points that make up the trajectory. This combination of DE versions is another contribution of the proposed approach that speeds up considerably the search process by first prioritizing the exploration and then the exploitation, and this sequential application can be used to the solution of diverse constrained numerical optimization problems. Finally, the IKP for the IRB-1600 robot was solved as a case study considering two trajectories in its dexterous workspace, circular and Lissajous. The results generated by the proposed approach for the case study were simulated in the RoboDK® industrial robot simulator.