Division-merge based inverse kinematics for multi-DOFs humanoid robots in unstructured environments

A Two-step Division-Merge (TDM) based inverse kinematics (IK) mechanism is proposed for robots with multiple degrees of freedom (multi-DOFs) in unstructured environments. For any robot with n-DOFs (n>6), a division point is selected first to divide it into a lower part subsystem from its base to the division point, together with an upper part one from the point to its end-effector. Once a collision-free configuration is found for the upper part subsystem to match with the target, the lower part subsystem is then planned to merge with the upper part subsystem at the division point. Specifically, the division point is selected such that the lower part subsystem has 6-DOFs, while the upper part subsystem has (n-6)-DOFs. Furthermore, a Reverse & Random Rotation (RRR) algorithm is also proposed to solve the IK of the upper part subsystem in unstructured environments, while the IK of the lower part subsystem is solved analytically. The proposed TDM based mechanism is verified via experiments using a lab-customized humanoid apple harvesting robot with 11- and 13-DOFs, respectively. Under the various scenarios with different target and obstacle configurations, errors in position coordinates and orientation angles between the target pose and those of the end-effector obtained with forward kinematics (FK) are calculated. Results show that the errors in position and orientation are less than 0.005 mm and 0.007°, respectively, and the average computational time is less than 2 s for the IK solution of the entire robot. Such results indicate that the proposed mechanism is reliable and capable of reducing the complexity of IK for multi-DOFs humanoid robots. With the proposed algorithm, the apple harvesting success rate of a lab-customized 11-DOFs robot reaches 89.2%, which can be further increased up to 93.3% with error compensation, while the average time starting from the robot action to the end-effector reaching the target pose of the apple is around 12.3 s.