MIT professor and Toyota Research Institute vice president Russ Tedrake explains how graphs of convex sets can combine trajectory optimization and discrete search for robot planning at the MIT Robotics Seminar.
Tedrake argues that learning and planning complement each other: learned policies bring prior experience, while planning can strengthen decisions by looking ahead. He points to AlphaGo’s combination of imitation learning, reinforcement learning, and tree search, then describes diffusion policies trained on robot demonstrations, including T-shaped object pushing and shirt folding.
Tedrake separates motion planning into a combinatorial choice, such as which side of an obstacle to pass, and continuous optimization over a feasible trajectory. Graphs of convex sets represent regions of configuration space as graph vertices, leaving room to optimize continuous curves and constraints. He shows examples including a quadrotor in a maze, jointly planned bimanual arms, and Spot.
The approach grows collision-free convex regions around samples and connects overlapping regions, allowing trajectories to move continuously between them. IRIS and related methods generate useful convex covers of configuration space; Bézier curves and continuity constraints describe motion within and between regions. Tedrake says the method often finds strong plans by solving a convex relaxation and rounding, while branch and bound can certify solutions.
Contact planning adds choices such as which side to push from or whether to pick an object up. Tedrake describes representing contact modes with convex sets built from semidefinite relaxations of the nonlinear dynamics, then using GCS to choose a mode sequence and optimize motion. He presents planar T-pushing as an example and says the resulting plans can also supply physically meaningful training data for diffusion policies.
Tedrake connects GCS dual solutions to lower bounds on the value function, which can support planning from multiple starting states and reasoning about uncertainty. In the discussion, he suggests using a generalist policy to identify promising graph regions, then applying GCS to a smaller search. He sees a trade-off between finer region decompositions, which may tighten relaxations, and the extra work they require.
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MIT robotics professor Russ Tedrake discusses physical AI, robot learning, deployment, and the human impact of automation with Automated host Bryant Heater in Boston.
Russ Tedrake, MIT associate professor and Toyota Research Institute vice president of robotics research, discusses feedback control and manipulation at a University of Toronto Robotics Institute seminar hosted by Florian.
