A Global Quasi-Dynamic Model for Contact-Trajectory Optimization in Manipulation

Given a desired object trajectory, how should a robot make contact to achieve it? This paper proposes a global optimization model for this problem with alternated-sticking contact, referred to as Contact-Trajectory Optimization. We achieve this by reasoning on simplified geometric environments with a quasi-dynamic relaxation of the physics. These relaxations are the result of approximating bilinear torque effects and deprecating high-order forces and impacts. Moreover, we apply convex approximations that retain the fundamental properties of rigid multi-contact interaction. As result, we derive a mixedinteger convex model that provides global optimality, infeasibility detection and convergence guarantees. This approach does not require seeding and accounts for the shapes of the object and environment. We validate this approach with extensive simulated and real-robot experiments, demonstrating its ability to quickly and reliably optimize multi-contact manipulation behaviors.