A GJK-based approach to contact force feasibility and distribution for multi-contact robots

This paper presents a new approach to two fundamental problems concerning the equilibrium of a multi-contact robot: the contact force feasibility (CFF) and the contact force distribution (CFD). The CFF is to determine if there exist feasible contact forces to maintain a robot in equilibrium without breaking its contacts with the environment, while the CFD is to compute the minimum contact forces if a feasible solution exists. A general measure of overall contact force magnitude is defined, which includes the traditional measure (i.e., the sum of normal force components) and a more complex measure (i.e., the maximum of normal force components) as special cases. We first reduce the two problems into verifying the existence of nonnegative solutions and determining the nonnegative minimum one-norm solution to a system of linear equations, respectively. To obtain the explicit formulation of the linear system, it is required to compute the Minkowski sum of point sets, which usually is computationally expensive. Then, based on the GJK distance algorithm, we develop an iterative algorithm, which enables us to solve the linear system without calculating the Minkowski sum and compute the CFF and CFD in real time.

Research highlights
► We propose an algorithm to determine the contact force feasibility and distribution for multi-contact robotic systems.
► The proposed algorithm can compute optimal contact forces for balancing a robot and minimize the sum or maximum of normal contact forces.
► The algorithm is efficient and can be used in real time.