Inverse Kinematics Solution of Deformable Manipulator for Point Touching Task

For the human-robot interaction in home environment, a 4-joint deformable manipulator is designed, whose links can deform to perform specific tasks. Compared with traditional rigid ones, the deformable manipulator is more dexterous, lower-cost and intrinsically safe. However, the arbitrary arm-shape brings extra difficulties into the manipulator inverse kinematics solution. For the the spatial touching task of the deformable manipulator, the concept of "touching angle" is introduced to relax the orientation constraint of end-effector. Therefore the original inverse kinematics problem with the underactuation constraint is converted into an inverse optimization problem of redundant manipulator to minimizes the touching angle under the constraint of the touching position. For the solving time and touching accuracy of the problem, an improved sequential quadratic programming (SQP) and the particle swarm optimization and Paden-Kahan subproblems (PSO-PK) hybrid algorithm are proposed respectively based on the screw model. The SQP algorithm solves the nonlinear optimization problem directly at position level, and the results show that the time consumption won't increase as the arm-shape changes from a special one to an arbitrary one. It's suitable for online real-time control due to its high solving efficiency. The layered search method is used to decrease the possibility of local minimum through initial value setting. In the PSO-PK algorithm, the analytical inverse solution of Paden-Kahan subproblems is utilized to reduce the dimension of particle swarm optimization (PSO) algorithm. The experiment results demonstrate that the method can obtain the stable minimum touching angle without error in touching position and improve the touching performance.