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2025-2026 Seminar Series

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Upcoming Seminar

Speaker: Heng Yang (Harvard University)

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Title: Semidefinite Relaxations for Robot Perception and Control: From Theory to Practice and Back

Abstract: Many problems in robot perception, control, and planning can be formulated as nonconvex polynomial optimization problems (POPs). The Moment–SOS (sums-of-squares) hierarchy provides a principled approach for global optimization by relaxing a nonconvex POP into a sequence of convex semidefinite programs (SDPs) whose optimal values converge to that of the original problem. Despite its theoretical elegance, the framework is often viewed as impractical due to the need to solve large-scale and ill-conditioned SDPs.

In the first part of this talk, I will show how problem-specific structure in robotics can be exploited to make Moment–SOS relaxations practical at scale. On the perception side, I will present XM, our structure-from-motion pipeline that leverages monocular depth prediction to cast bundle adjustment as a polynomial optimization problem. Using GPU-accelerated low-rank Riemannian optimization, XM solves bundle adjustment instances with thousands to tens of thousands of images. On the control side, I will introduce SPOT, a trajectory planning pipeline that exploits sparsity inherent in robot motion planning problems, such as Markov and kinematic chain structure. With a GPU-accelerated ADMM solver, SPOT is able to generate near–globally optimal trajectories within seconds, including contact-rich motions.

In the second part, I will turn to theory, briefly highlighting our recent work on understanding and accelerating the convergence of first-order methods for SDPs. This includes proving local linear convergence of ADMM, designing a composite polynomial filter for approximate projection onto the positive semidefinite cone, and analyzing the slow-convergence regions of ADMM.

Date: Thursday, December 11th, 2025

Time: 09:00-10:00 AM EST

Link: https://dartmouth.zoom.us/j/94765993258?pwd=aErnkjFBqQaOTEgonxZkeNTbojHRbp.1

Date Speaker Title YouTube
Dec. 11, 2025 Heng Yang Semidefinite Relaxations for Robot Perception and Control: From Theory to Practice and Back
Jan. 15, 2026 Anirudha Majumdar Topic coming soon
Jan. 26, 2026 Thomas Lew Topic coming soon
March 12, 2026 Yan Gu Topic coming soon
April 9, 2026 Somil Bansal Topic coming soon