Computing Invariant Reachable Sets through Sum-of-Squares Programming
Computing Invariant Reachable Sets through Sum-of-Squares Programming
This research paper introduces a self-contained approach to computing invariant reachable sets using sum-of-Squares (SOS) programming, implemented in the open-source package computeSOSFunnels. The authors propose a minimum-volume formulation with inlet and outlet constraints that allows funnels with coinciding nominal endpoints to compose by construction. Numerical experiments on a unicycle, timing studies on a cart-pole, and a 12-state quadrotor characterize the pipeline, showing that infeasible initial guesses can be partly decidable before solving, certificates show no violations among 39,000 boundary samples per funnel under true dynamics, and constructing the semidefinite program—not solving it—dominates computation time.
Source: arXiv Robotics — research abstracts · Read original article ↗
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Publisher-reported claims, with original evidence. These results have not been independently verified by RoboSignal.
Reported numbers
boundary samples
39,000
View original evidence
dies on a cart-pole and a 12-state quadrotor, characterize the pipeline: infeasible initial guesses are partly decidable before solving, the certificate shows no violations among 39,000 boundary samples per funnel under the true dynamics, and constructing the semidefinite program, not solving it, dominates computation time.
Open source S4
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- code: not_reported
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dies on a cart-pole and a 12-state quadrotor, characterize the pipeline: infeasible initial guesses are partly decidable before solving, the certificate shows no violations among 39,000 boundary samples per funnel under the true dynamics, and constructing the semidefinite program, not solving it, dominates computation time.
Open source S4
lization, and termination rule, which the literature documents only briefly. This paper presents a self-contained treatment of SOS-based funnel computation, implemented in the open-source package computeSOSFunnels. We propose a minimum-volume formulation with inlet and outlet constraints under which funnels with coinciding nominal endpoints compose by construction. Numerical experiments on a unicycle, with timing stu
Open source S3
Source：arXiv Robotics — research abstracts · arxiv.org