This article presents a quadratic programming (QP) based approach to local kinematic motion planning of general multibody robotic systems. Given kinematic constraints and targets such as desired positions and orientations in Cartesian space, we find locally optimal joint velocities toward the targets at every time step by formulating the problem into a constrained optimization with a quadratic objective function and linear constraints in terms of the joint velocities. The solution is integrated to obtain the joint displacements at the next time step, and this process is repeated until reaching the targets or converging to a certain configuration. Our formulation based on relative Jacobian is particularly useful in handling constraints on relative motions, which arises in many practical problems such as dual-arm manipulation and self-collision avoidance, in a concise manner. A brief overview of our software implementation and its applications to manipulation and mobility planning of a simulated multi-limbed robot are also presented.
