Towards Tight Convex Relaxations for Contact-Rich Manipulation
CoRR(2024)
摘要
We present a method for global motion planning of robotic systems that
interact with the environment through contacts. Our method directly handles the
hybrid nature of such tasks using tools from convex optimization. We formulate
the motion-planning problem as a shortest-path problem in a graph of convex
sets, where a path in the graph corresponds to a contact sequence and a convex
set models the quasi-static dynamics within a fixed contact mode. For each
contact mode, we use semidefinite programming to relax the nonconvex dynamics
that results from the simultaneous optimization of the object's pose, contact
locations, and contact forces. The result is a tight convex relaxation of the
overall planning problem, that can be efficiently solved and quickly rounded to
find a feasible contact-rich trajectory. As a first application of this
technique, we focus on the task of planar pushing. Exhaustive experiments show
that our convex-optimization method generates plans that are consistently
within a small percentage of the global optimum. We demonstrate the quality of
these plans on a real robotic system.
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