Ensuring Viability: A QP-based Inverse Kinematics for Handling Joint Range, Velocity and Acceleration Limits, as Well as Whole-body Collision Avoidance

Abstract This paper proposes a new quadratic programming (QP) based inverse kinematics (IK) method to simultaneously handle physical joint limits and whole-body collision avoidance, including self-collision and collisions with static obstacles. These constraints may conflict with each other and result in infeasible solutions of IK, which can subsequently produce unpredictable motions. The proposed method incorporates an additional linear constraint to ensure that the robot state is viable , guaranteeing the existence of solutions that do not violate the given constraints. Our IK method consists of two stages: the offline construction stage and the online computation stage. In the offline construction stage, the parameters of the proposed constraint for ensuring viable states are calculated. In the online computation stage, the proposed constraints are updated in realtime based on the robot’s state, and the IK is solved as a QP problem. The proposed method can effectively handle most robots with DOFs below 10 and can also accommodate some robots with higher DOFs under simpler constraints. This marks a significant advancement compared to previous studies. The validity of the proposed method is illustrated through some simulation results.