Motion Planning with Metric Temporal Logic Using Reachability Analysis and Hybrid Zonotopes

• URL: http://arxiv.org/abs/2602.00325v1
• Date: Fri, 30 Jan 2026 21:25:26 GMT
• Title: Motion Planning with Metric Temporal Logic Using Reachability Analysis and Hybrid Zonotopes
• Abstract summary: This article presents a method that uses reachability analysis to implicitly express the set of states satisfying an MTL specification and then optimize to find a motion plan.<n>A numerical benchmark highlights the proposed method's computational advantages as compared to existing methods in the literature.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Metric temporal logic (MTL) provides a formal framework for defining time-dependent mission requirements on autonomous vehicles. However, optimizing control decisions subject to these constraints is often computationally expensive. This article presents a method that uses reachability analysis to implicitly express the set of states satisfying an MTL specification and then optimizes to find a motion plan. The hybrid zonotope set representation is used to efficiently and conveniently encode MTL specifications into reachable sets. A numerical benchmark highlights the proposed method's computational advantages as compared to existing methods in the literature. Further numerical examples and an experimental application demonstrate the ability to address time-varying environments, region-dependent disturbances, and multi-agent coordination.

Related papers

• Signal Temporal Logic Motion Planning via Graphs of Convex Sets [8.443328067924298]
  This paper investigates continuous-time motion planning under Signal Temporal Logic (STL) specifications.<n>We propose a framework that combines timed-automata reasoning with graphs of convex sets.<n> Numerical experiments on low-dimensional benchmarks, a $3$-Drotor, a $30$-DoF humanoid, and a hardware experiment on a UR-3 robot arm demonstrate that the proposed method efficiently solves complex STL motion-planning problems.
  arXiv  Detail & Related papers  (2026-05-22T05:19:43Z)
• Feedback Motion Planning for Stochastic Nonlinear Systems with Signal Temporal Logic Specifications [25.484834028091083]
  We study feedback motion planning for continuous-time nonlinear systems under signal temporal logic (STL) specifications.<n>We propose a framework that synthesizes control policies for chance-constrained STL trajectory optimization problems.
  arXiv  Detail & Related papers  (2026-05-04T09:02:16Z)
• Lexicographic Minimum-Violation Motion Planning using Signal Temporal Logic [9.646103797793614]
  Motion planning for autonomous vehicles often requires satisfying multiple conditionally conflicting specifications.<n>Signal temporal logic provides a formal language for rigorously defining these specifications.<n>A total ordering of specifications yields a lexicographic optimization problem.<n>We address this problem by transforming the multi-objective lexicographic optimization problem into a single-objective scalar optimization problem.
  arXiv  Detail & Related papers  (2026-04-22T10:49:09Z)
• SGA-MCTS: Decoupling Planning from Execution via Training-Free Atomic Experience Retrieval [74.1918709002557]
  We introduce textbfSGA-MCTS, a framework that casts LLM planning as non-parametric retrieval.<n>Online, a retrieval-augmented agent employs a hybrid symbolic-semantic mechanism to fetch relevant State-Goal-Action atoms.<n>By effectively amortizing the heavy computational cost of search, SGA-MCTS achieves System 2 reasoning depth at System 1 inference speeds, rendering autonomous planning both scalable and real-time feasible.
  arXiv  Detail & Related papers  (2026-04-16T07:22:36Z)
• Multi-Robot Trajectory Planning via Constrained Bayesian Optimization and Local Cost Map Learning with STL-Based Conflict Resolution [1.6243762297989983]
  We address multi-robot motion planning under Signal Temporal Logic (STL) specifications with kinodynamic constraints.<n>We propose a two-stage framework integrating sampling-based online learning with formal STL reasoning.
  arXiv  Detail & Related papers  (2026-03-06T00:03:18Z)
• Fast Near Time-Optimal Motion Planning for Holonomic Vehicles in Structured Environments [8.195916347194315]
  The approach aims to solve the problem of motion planning for planar motion systems using magnetic levitation.<n>The presented approach encodes the environment representation using free-space corridors and represents the motion of the vehicle through such a corridor using a motion primitive.<n>The method achieves significantly lower times compared to the state-of-the-art and is validated on a real-world Beckhoff XPlanar system.
  arXiv  Detail & Related papers  (2026-02-02T21:26:30Z)
• Dynamical Measure Transport and Neural PDE Solvers for Sampling [77.38204731939273]
  We tackle the task of sampling from a probability density as transporting a tractable density function to the target. We employ physics-informed neural networks (PINNs) to approximate the respective partial differential equations (PDEs) solutions. PINNs allow for simulation- and discretization-free optimization and can be trained very efficiently.
  arXiv  Detail & Related papers  (2024-07-10T17:39:50Z)
• Synthesizing Efficiently Monitorable Formulas in Metric Temporal Logic [4.60607942851373]
  We consider the problem of automatically synthesizing formal specifications from system executions. Most of the classical approaches for synthesizing temporal logic formulas aim at minimizing the size of the formula. We formalize this notion and devise a learning algorithm that synthesizes concise formulas having bounded lookahead.
  arXiv  Detail & Related papers  (2023-10-26T14:13:15Z)
• Formal Controller Synthesis for Markov Jump Linear Systems with Uncertain Dynamics [64.72260320446158]
  We propose a method for synthesising controllers for Markov jump linear systems. Our method is based on a finite-state abstraction that captures both the discrete (mode-jumping) and continuous (stochastic linear) behaviour of the MJLS. We apply our method to multiple realistic benchmark problems, in particular, a temperature control and an aerial vehicle delivery problem.
  arXiv  Detail & Related papers  (2022-12-01T17:36:30Z)
• Spectral Representation Learning for Conditional Moment Models [33.34244475589745]
  We propose a procedure that automatically learns representations with controlled measures of ill-posedness. Our method approximates a linear representation defined by the spectral decomposition of a conditional expectation operator. We show this representation can be efficiently estimated from data, and establish L2 consistency for the resulting estimator.
  arXiv  Detail & Related papers  (2022-10-29T07:48:29Z)
• Linear Temporal Logic Modulo Theories over Finite Traces (Extended Version) [72.38188258853155]
  This paper studies Linear Temporal Logic over Finite Traces (LTLf) proposition letters are replaced with first-order formulas interpreted over arbitrary theories. The resulting logic, called Satisfiability Modulo Theories (LTLfMT), is semi-decidable.
  arXiv  Detail & Related papers  (2022-04-28T17:57:33Z)
• Policy Analysis using Synthetic Controls in Continuous-Time [101.35070661471124]
  Counterfactual estimation using synthetic controls is one of the most successful recent methodological developments in causal inference. We propose a continuous-time alternative that models the latent counterfactual path explicitly using the formalism of controlled differential equations.
  arXiv  Detail & Related papers  (2021-02-02T16:07:39Z)
• DynaMiTe: A Dynamic Local Motion Model with Temporal Constraints for Robust Real-Time Feature Matching [47.72468932196169]
  We present the lightweight pipeline DynaMiTe, which is agnostic to the descriptor input and leverages spatial-temporal cues with efficient statistical measures. DynaMiTe achieves superior results both in terms of matching accuracy and camera pose estimation with high frame rates, outperforming state-of-the-art matching methods.
  arXiv  Detail & Related papers  (2020-07-31T12:18:18Z)
• Stochastic Finite State Control of POMDPs with LTL Specifications [14.163899014007647]
  Partially observable Markov decision processes (POMDPs) provide a modeling framework for autonomous decision making under uncertainty. This paper considers the quantitative problem of synthesizing sub-optimal finite state controllers (sFSCs) for POMDPs. We propose a bounded policy algorithm, leading to a controlled growth in sFSC size and an any time algorithm, where the performance of the controller improves with successive iterations.
  arXiv  Detail & Related papers  (2020-01-21T18:10:47Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.