Non-convex constrained optimizations are ubiquitous in robotic applications such as multi-agent navigation, UAV trajectory optimization, and soft robot simulation. As a common feature in these problems, the associated non-convex constraints, including collision constraints, inversion-free constraints, and strain limits, are also non-smooth with ill-defined gradients. It is well-known that such constraints are notoriously difficult to handle, for which off-the-shelf optimizers can fail catastrophically. Instead, prior works tend to design problem-specific optimizers that trade performance for robustness. To efficiently solve this problem class in a unified manner, we propose a variant of alternating direction method of multiplier (ADMM), called BC-ADMM. Over the past decade, ADMM has achieved great success in efficiently solving many large-scale (constrained) optimization problems by decoupling them into subproblems that can be solved in parallel. However, prior ADMM algorithms lack a convergence guarantee when handling a large number of non-convex constraints with loopy constraint graphs. Instead, our BC-ADMM relaxes each non-convex constraint into a bi-convex function, further breaking the constraint into two subproblems. We show that such relaxation leads to a variant of ADMM with convergence speed guarantees under appropriate parameter choices. We further provide a practical algorithm under much milder assumptions on the parameter choices, with convergence guarantees without a speed bound. Through numerical experiments in a row of four robotic applications, we show that BC-ADMM has faster convergence than conventional gradient descent and Newton’s method in terms of wall clock time.
Zherong Pan, Kui Wu· The international journal of...· 0 citations
Over the past decade, the Lattice Boltzmann Method (LBM) has matured into a leading framework for high-performance fluid simulation across research and industry alike. Its appeal rests on a set of properties that align unusually well with the demands of modern computing: collision and streaming operators that are strictly local, mapping naturally onto massively parallel architectures; an intrinsic ability to handle complex geometries through simple boundary rules; and a level of physical fidelity that has proven sufficient across a widening range of applications — from real-time simulation and visual effects to large-scale industrial tools such as virtual wind tunnels. The growing body of LBM-based work at SIGGRAPH and SIGGRAPH Asia reflects this trajectory directly: the method has moved from occasional appearance to recurring presence as a core computational framework. Despite this prominence, LBM has never been the subject of a dedicated SIGGRAPH course. To date, it has only been mentioned peripherally, most notably as a small component of the Real-Time Physics course at SIGGRAPH 2004. As a result, there remains a significant gap between the method’s practical importance and its formal coverage within the SIGGRAPH educational program. This lack of structured exposure has made it difficult for practitioners and researchers to fully understand the method’s foundations, strengths, limitations, and best practices for deployment on contemporary hardware. These course notes are an attempt to close that gap. Written by authors with direct experience across multiple LBM publications at SIGGRAPH over the past six years, they aim to provide something the existing literature rarely offers in a single place: a coherent path from first principles to production-oriented practice. The intent is not to survey recent work, but to equip attendees with the concepts, implementation details, and the critical perspective needed to start working with LBM solvers.
Wei Li, Chaoyang Lyu, Mengyun Liu et al.· Proceedings of the Special I...· 0 citations
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