Shortest Paths in Graphs of Convex Sets

Marcucci, Tobia; Umenberger, Jack; Parrilo, Pablo A.; Tedrake, Russ

doi:10.48550/arxiv.2101.11565

Cited by 8 publications

(39 citation statements)

References 52 publications

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“…In this section, we exploit the fact that is often the tightness of convex relaxation, rather than the number of binary variables and constraints, that determines MICP scalability to propose a more efficient MICP encoding. Our main inspiration in this regard is [19], which presents a more efficient MICP for control of PWA systems by increasing the number of binary variables but tightening the convex relaxation.…”

Section: Resultsmentioning

confidence: 99%

“…Our basic idea is to introduce a binary variable for every edge in the graph (the standard encoding (9) introduces a binary variable for each node). This may seem counterintuitive, as there are many more edges than nodes, but similar formulations perform well for special cases of temporal-logic planning, including SPP [22], TSP [23], and PWA control [19].…”

Section: Resultsmentioning

confidence: 99%

“…In this work, we revisit MICP for timed temporal-logic, focusing in particular on MTL. Taking inspiration from recent work on trajectory-optimization for piecewise-affine systems [19], we note that while the worst-case complexity of MICP depends primarily on the number of binary variables, performance in practice often depends more heavily on the tightness of the convex relaxation (a convex program where the binary variables in the original MICP are allowed to take continuous values), since modern MICP solvers rely heavily on the branch-and-bound algorithm [20].…”

Section: Since the Worst-case Complexity Of Micp Is Exponential Inmentioning

confidence: 99%

“…Following [19], the basic idea behind our proposed encoding is to introduce binary variables for each possible transition at every timestep, rather than for each possible state. This results in more binary variables than a standard encoding, but a tighter convex relaxation and better performance in practice [21].…”

Section: Since the Worst-case Complexity Of Micp Is Exponential Inmentioning

confidence: 99%

“…This is the case for a number of interesting problems, including the SPP in graph theory [22] and a convex fragment of timed temporal logic [7, Theorem 1]. Even for nonconvex problems (e.g., MTL and the TSP), the relaxation gap plays an important role in determining solver performance [19], [21].…”

Section: B Mixed Integer Programmingmentioning

confidence: 99%

See 4 more Smart Citations

A More Scalable Mixed-Integer Encoding for Metric Temporal Logic

Kurtz¹,

Lin²

2021

Preprint

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The state-of-the-art in optimal control from timed temporal logic specifications, including Metric Temporal Logic (MTL) and Signal Temporal Logic (STL), is based on Mixed-Integer Convex Programming (MICP). The standard MICP approach is sound and complete, but struggles to scale to long and complex specifications. Drawing on recent advances in trajectory optimization for piecewise-affine systems, we propose a new MICP encoding for finite transition systems that significantly improves scalability to long and complex MTL specifications. Rather than seeking to reduce the number of variables in the MICP, we focus instead on designing an encoding with a tight convex relaxation. This leads to a larger optimization problem, but significantly improves branch-and-bound solver performance.In simulation experiments involving a mobile robot in a gridworld, the proposed encoding can reduce computation times by several orders of magnitude.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Since the Worst-case Complexity Of Micp Is Exponential Inmentioning

confidence: 99%

Section: Since the Worst-case Complexity Of Micp Is Exponential Inmentioning

confidence: 99%

Section: B Mixed Integer Programmingmentioning

confidence: 99%

See 3 more Smart Citations

A More Scalable Mixed-Integer Encoding for Metric Temporal Logic

Kurtz¹,

Lin²

2021

Preprint

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Sliding homoclinic orbits and bifurcations of three-dimensional piecewise affine systems

Huan

Liu

2023

Nonlinear Dyn

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Piecewise-affine (PWA) systems are widely used for modeling and control of robotics problems including modeling contact dynamics. A common approach is to encode the control problem of the PWA system as a Mixed-Integer Convex Program (MICP), which can be solved by general-purpose offthe-shelf MICP solvers. To mitigate the scalability challenge of solving these MICP problems, existing work focuses on devising efficient and strong formulations of the problems, while less effort has been spent on exploiting their specific structure to develop specialized solvers. The latter is the theme of our work. We focus on efficiently handling onehot constraints, which are particularly relevant when encoding PWA dynamics. We have implemented our techniques in a tool, Soy, which organically integrates logical reasoning, arithmetic reasoning, and stochastic local search. For a set of PWA control benchmarks, Soy solves more problems, faster, than two stateof-the-art MICP solvers.

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Multi-Rate Planning and Control of Uncertain Nonlinear Systems: Model Predictive Control and Control Lyapunov Functions

Csomay-Shanklin

Taylor

Rosolia

et al. 2022

2022 IEEE 61st Conference on Decision and Control (CDC)

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Modern control systems must operate in increasingly complex environments subject to safety constraints and input limits, and are often implemented in a hierarchical fashion with different controllers running at multiple time scales. Yet traditional constructive methods for nonlinear controller synthesis typically "flatten" this hierarchy, focusing on a single time scale, and thereby limited the ability to make rigorous guarantees on constraint satisfaction that hold for the entire system. In this work we seek to address the stabilization of constrained nonlinear systems through a multi-rate control architecture. This is accomplished by iteratively planning continuous reference trajectories for a nonlinear system using a linearized model and Model Predictive Control (MPC), and tracking said trajectories using the full-order nonlinear model and Control Lyapunov Functions (CLFs). Connecting these two levels of control design in a way that ensures constraint satisfaction is achieved through the use of Bézier curves, which enable planning continuous trajectories respecting constraints by planning a sequence of discrete points. Our framework is encoded via convex optimization problems which may be efficiently solved, as demonstrated in simulation.

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Shortest Paths in Graphs of Convex Sets

Cited by 8 publications

References 52 publications

A More Scalable Mixed-Integer Encoding for Metric Temporal Logic

A More Scalable Mixed-Integer Encoding for Metric Temporal Logic

Sliding homoclinic orbits and bifurcations of three-dimensional piecewise affine systems

Multi-Rate Planning and Control of Uncertain Nonlinear Systems: Model Predictive Control and Control Lyapunov Functions

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