STL Motion Planning

STL: Signal Temporal Logic

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19 papers3 papers in the last four weeks, level with the four weeks before. 0.0% of all new papers.

Oct 16, 2026

SparseMax-dSTL: Sound Robustness with Horizon-Independent Gradient Allocation for Temporal Logic Trajectory Optimization

A gradient-based solver that enforces a Signal Temporal Logic (STL) specification uses a smooth approximation of its quantitative semantics, the robustness. In safety-critical trajectory optimization, this approximation must have two properties. First, it must be sound, that is, nonnegative only on trajectories that satisfy the specification. Second, at each temporal operator, the weight of its gradient on the violating samples must stay bounded away from zero, however long the horizon. The approximations in use, including the log-sum-exp, its sound variant, and the generalized-mean robustness, do not have both. We introduce lower approximations of the minimum and the maximum whose gradients are sparsemax projections, and we prove that the robustness built from them has both. It lies below the exact robustness and is therefore sound, and its error has a bound that is independent of the number of samples and known before optimization. The gradient of each approximation is exactly zero on every sample beyond a data-dependent threshold, so the weight on violating samples a gap beyond the others has a positive lower bound at every horizon. On a planar unicycle and on a seven-joint manipulator beside a person in simulation, the log-sum-exp approximation is positive on a violating trajectory. As the horizon of the manipulator's task grows from 10 to 80 s, the gradient weight of the sound variant on the violating samples falls from 0.22 to 0.04, while that of sparsemax stays at 1. In a constrained trajectory optimization of the unicycle, the constraint on the log-sum-exp robustness returns a violating trajectory, whereas the constraint on the sparsemax robustness returns a trajectory that satisfies the specification with the required margin.

Sai Sandeep Damera, Ryan Matheu, John S. Baras +1

The authors are with the University of Maryland, College Park, USA.

STL Motion Planning Signal Temporal Logic Trajectory Optimization

Oct 12, 2026

Belief Space Planning for Risk Signal Temporal Logic via Mixed-Integer Convex Programming

Signal Temporal Logic (STL) specifies robot tasks with spatio-temporal requirements, and its robustness semantics allow planning by trajectory optimization. In practice, robots estimate their state from noisy measurements, and when the information gained from a measurement depends on the state, the robot can actively reduce its uncertainty by planning in the belief space. The resulting problem is, however, generally non-convex, for which gradient-based methods are neither complete nor globally optimal. In this paper, we consider Risk STL (RiSTL) planning in Gaussian belief space and show that an information-form parameterization of the belief, together with a convex relaxation of the belief dynamics, yields a mixed-integer convex program (MICP). We prove that the MICP is sound and complete, and that the relaxation preserves the globally optimal input trajectories. We validate the effectiveness of our method in numerical simulations.

Shaohang Han, Joris Verhagen, Kaier Liang +1

Division of Robotics, Perception and Learning, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm, Sweden · Digital Futures

Belief-Space Planning STL Planning STL Motion Planning Robot Motion Planning

Oct 11, 2026

Efficient Hybrid Hard--Soft Signal Temporal Logic MPC for Driving under Multimodal Uncertainty

Motion planning for automated vehicles in interactive traffic has to simultaneously ensure safety, respect traffic rules, and maintain comfortable progress under multi-modal behavior uncertainty. Imposing all these requirements as hard constraints reduces feasibility, whereas treating them all as costs allows safety-critical requirements to be traded against progress. We propose a hybrid hard--soft Signal Temporal Logic (STL) MPC framework that optimizes a single shared ego trajectory against every retained behavior hypothesis: minimum-distance and speed predicates are imposed as explicit hard constraints, while soft STL robustness terms shape clearance, comfort, and interaction quality within the resulting feasible driving corridor. This retains robustness to discrete interaction modes without branch-specific contingent ego policies. We further identify substantial symbolic graph-construction overhead and introduce reachability-certified relevance screening and vectorized symbolic construction to reduce computational cost while preserving the feasible set and objective. Closed-loop Monte Carlo evaluation over six highway and intersection scenarios shows the highest strict success rate among the compared planners with no observed collisions or rule violations, at roughly a quarter of the planning latency of the unoptimized formulation. An ablation study separates the two layers: the hard constraints define the safety envelope, while the soft terms improve clearance and motion quality within it.

Kumar Manas, Adrian Paschke

Technical University Darmstadt, Germany · Freie Universität Berlin, Germany · Freie Universität Berlin and Fraunhofer FOKUS, Berlin, Germany

STL Planning Safe Motion Planning Autonomous Driving Planning STL Motion Planning Constrained Motion Planning Model Predictive Control+1

Sep 19, 2026

Fast and Robust Temporal Logic Planning via ADMM-based Trajectory Optimization

We present a fast numerical method for safe continuous-time motion planning under Temporal Logic (TL) specifications. The method generates smooth continuous trajectories that remain collision-free while robustly satisfying temporal and logical task requirements. A central component of our method is the formulation of nonconvex safety and logic constraints as unions of convex sets where associated discrete decisions are encoded in a joint feasibility graph. This graph representation allows Euclidean projection onto the feasible set and proximal robustness maximization to be reformulated as shortest- and widest-path problems, respectively. Building on this structure, we develop a nonconvex splitting method based on the Alternating Direction Method of Multipliers (ADMM), which decouples smooth spatio-temporal trajectory optimization from nonsmooth discrete constraint handling within the optimization. The resulting algorithm exhibits reliable convergence across benchmarks and scales to large-scale motion-planning problems, providing a 4.7x average speedup over the state of the art on discrete and continuous-time logic problems.

Lukas Pries, Joris Verhagen, Jon Arrizabalaga +3

Department of Aerospace and Geodesy, TU Munich, Germany · Division of Robotics, Perception, and Learning, KTH Royal Institute of Technology, Stockholm, Sweden · Department of Aeronautics and Astronautics, MIT, Cambridge, MA, USA

STL Motion Planning Safe Motion Planning Motion Planning Trajectory Optimization

Sep 19, 2026

A Geometric Decision Procedure for STL Feasibility and Repair

Feasibility of a Signal Temporal Logic (STL) specification asks whether, from a given initial state, an admissible control input can satisfy its continuous-time requirements under actuator limits. Establishing feasibility is essential for detecting unrealizable tasks and repairing specifications before execution. State-of-the-art Mixed-Integer Linear Programming (MILP) methods face growing model sizes as temporal horizons and formula complexity increase, and can accept control witnesses that violate continuous-time STL semantics between samples. We propose a geometric approach to STL feasibility and temporal repair that translates temporal requirements into spatial constraints evaluated at the initial state. Its compiled feasibility check is independent of horizon length for fixed compiled dimensions. We prove nonnegative continuous robustness under a joint controller assumption. On 6D UAV benchmarks, median geometric repair times are 0.265--1.510 ms; we show up to 1.68x10^4 speedup over MILP feasibility checker. All geometric runs pass continuous STL validation, whereas majority of completed MILP control witnesses violate continuous-time STL.

Avinash Malik

Department of Electrical, Computer, and Software Engineering, University of Auckland, Auckland, New Zealand

Reachability Analysis Signal Temporal Logic Formal Verification STL Planning Temporal Logic STL Motion Planning

Aug 25, 2026

Safety-aware Model Predictive Path Integral Control with Signal Temporal Logic

Safety-aware motion planning remains a challenge in robotics, especially when missions are time-critical and are under complex specifications. In this paper, we propose safety-aware-stl-mppi, a computationally efficient sampling-based receding-horizon planning framework designed to promote satisfaction of constraints expressed in Signal Temporal Logic (STL). Our approach encodes discrete-time STL formulas into candidate time-varying control barrier functions (CBF), which are integrated into a model predictive path integral (MPPI) controller. Our method inherits the benefits of low computational cost from an efficiently parallelizable sampling based planner and utilizes CBF for constraints expressed in STL. We compare against several MPPI baselines using four artificial Mars Rover planning case studies with a diverse environment and cost setups, where we show our method consistently achieving high safety and efficiency. We show a quadcopter planning experiment with NVIDIA Isaac Lab.

Yiqi Zhao, Taekyung Kim, Hideki Okamoto +4

Thomas Lord Department of Computer Science, University of Southern California, Los Angeles, CA 90089, USA · Department of Robotics, University of Michigan, Ann Arbor, MI 48109, USA · Toyota Motor North America R&D, Ann Arbor, MI 48105, USA +1

STL Motion Planning Safe Motion Planning Motion Planning Constrained Motion Planning STL Planning MPPI Control+1

Aug 21, 2026

OpenSCvx: An Open-Source Modular and Extensible Nonlinear Trajectory Planning Package

Trajectory optimization computes dynamically feasible motions that enable autonomous systems to accomplish complex tasks while satisfying operational and environmental constraints. This tutorial presents OpenSCvx, an open-source Python framework that bridges the gap between high-level problem specification and efficient numerical optimization. Rather than requiring users to derive solver-specific mathematical formulations, OpenSCvx provides a symbolic modeling interface that automatically constructs and solves trajectory optimization problems from modular descriptions of objectives, dynamics, and constraints. Beyond simplifying problem formulation, OpenSCvx supports (i) continuous-time constraint modeling, (ii) temporal and logical specifications, (iii) automatic vectorization for scalable and batched optimization, and (iv) a modular architecture that enables new algorithms, models, and solver backends to be incorporated with minimal effort. These capabilities allow researchers and practitioners to rapidly prototype, solve, and extend state-of-the-art trajectory optimization methods.

Christopher R. Hayner, Griffin J. Norris, Fabio Spada +4

Dept. of Aeronautics and Astronautics, University of Washington, Seattle, WA, USA. · General Robotics, Seattle, WA, USA. · Dept. of Mechanical Engineering, University of California, Berkeley, Berkley CA, USA. +2

STL Motion Planning Trajectory Optimization Motion Planning Constrained Motion Planning

Jul 21, 2026

STL-GCS: A Planner-Controller Framework for Signal Temporal Logic via Graphs of Time-varying Convex Sets

We present a unified trajectory planning and control framework for the satisfaction of Signal Temporal Logic (STL) specifications defined over convex predicates. At the planning layer, STL tasks are encoded as time-varying convex sets in configuration space, specifically designed so that forward invariance of the system with respect to these sets implies satisfaction of the specification with a prescribed robustness margin. This representation is then lifted to the joint time--configuration space and combined with the Graphs of Convex Sets (GCS) framework, yielding a shortest-path formulation of the planning problem over convex spatio-temporal sets. Trajectories are parameterized by B-splines, which enable continuous-time enforcement of STL satisfaction, collision avoidance, and smoothness constraints. At the control layer, the same time-varying sets used for planning are exploited to design a feedback controller that tracks the planned trajectory while prioritizing satisfaction of the STL specification during execution in the presence of tracking errors and model mismatch. We validate the proposed approach in simulation and in real-world experiments on space robotic platforms.

Nicola De Carli, Gregorio Marchesini, Dimos V. Dimarogonas

Robot Trajectory Tracking Constrained Motion Planning Signal Temporal Logic STL Planning Robot Motion Planning STL Motion Planning

Jun 18, 2026

Autonomous Driving with Priority-Ordered STL Specifications Under Multimodal Uncertainty

Autonomous vehicles must plan trajectories that satisfy a multitude of requirements on safety, passenger comfort, and compliance with traffic rules. However, in safety-critical scenarios, it is not always possible to satisfy all requirements simultaneously, necessitating their prioritization based on importance. At the same time, in these safety-critical scenarios, the uncertainty in trajectory predictions of the surrounding traffic, such as other vehicles and pedestrians, should be explicitly accounted for. In this work, we propose an uncertainty-aware trajectory planning framework that incorporates a predefined lexicographic ordering over Signal Temporal Logic (STL) specifications that stays valid under uncertainty. We implement this formulation with Model Predictive Path Integral (MPPI) control and we demonstrate the effectiveness of our method on simulation scenarios, showing that our framework efficiently handles conflicting objectives under realistic multi-modal uncertainty.

Taha Bouzid, Shuhao Qi, Mircea Lazar +1

Control Systems Group, Department of Electrical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

STL Motion Planning Motion Planning Autonomous Driving Planning

May 22, 2026

Signal Temporal Logic Motion Planning via Graphs of Convex Sets

This paper investigates continuous-time motion planning under Signal Temporal Logic (STL) specifications. The goal is to generate smooth robot trajectories that satisfy high-level logical and timing requirements while respecting low-level motion constraints. To this end, we propose an efficient framework that combines timed-automata reasoning with graphs of convex sets (GCS). An STL specification is first represented by a timed automaton, which is then coupled with a convex decomposition of the configuration space to form a joint transition system encoding both task progress and region occupancy. Based on this joint transition system, the STL motion-planning problem is reformulated as a shortest-path problem over a GCS, whose solution induces a smooth Bézier-spline trajectory satisfying the STL specification, smoothness requirements, and velocity bounds. We establish the soundness of the proposed formulation and analyze its computational complexity, showing that, once the timed automaton and convex decomposition are fixed, the convex relaxation scales polynomially with the configuration-space dimension and the Bézier degree. We further develop a compact timed-automaton construction for an expressive STL fragment using dedicated templates and Boolean composition. Numerical experiments on low-dimensional benchmarks, a

3

-D quadrotor, 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 and produces smooth executable trajectories.

Yu Chen, Ancheng Hou, Mingyang Feng +2

School of Automation & Intelligent Sensing, Shanghai Jiao Tong University, Shanghai 200240, China · Institute of Artificial Intelligence, Xiamen University, Xiamen, China

Constrained Motion Planning Trajectory Generation STL Motion Planning Motion Planning Robot Motion Planning STL Planning

May 5, 2026

Feasibility-aware Hybrid Control for Motion Planning under Signal Temporal Logics

In this work, a novel method for planar task and motion planning based on hybrid modeling is proposed. By virtue of a discrete variable which models local constraint satisfaction and enables local feasibility analysis, the proposed control architecture unifies planning with control design. Concurrently, control barrier functions are designed on a transformed disk version of the original nonconvex and geometrically complex robotic workspace, thus amending the issue of deadlocks. Simulations of the proposed method indicate effective handling of multiple overlapping spatio-temporal tasks even in the face of input saturation.

Panagiotis Rousseas, Dimos V. Dimarogonas

∗KTH Royal Institute of Technology, School of Electrical Engineering and Computer Science, Division of Decision and Control Systems

Constrained Motion Planning Signal Temporal Logic STL Planning Feedback Control Robot Motion Planning Safe Motion Planning+2

May 4, 2026

Feedback Motion Planning for Stochastic Nonlinear Systems with Signal Temporal Logic Specifications

We study feedback motion planning for continuous-time stochastic nonlinear systems under signal temporal logic (STL) specifications. We propose a framework that synthesizes control policies for chance-constrained STL trajectory optimization problems, with the goal of ensuring that the closed-loop stochastic system satisfies a given STL formula with high probability (e.g., 99.99%). Our approach is based on a predicate erosion strategy that transforms the intractable stochastic problem into a deterministic STL trajectory optimization problem with tightened STL formula constraints. The amount of erosion is determined by a probabilistic reachable tube (PRT) that bounds the deviation between the stochastic trajectory and an associated nominal trajectory. To compute such bounds, we leverage contraction theory and feedback design, and develop several tracking controllers. This yields a complete feedback motion planning pipeline which can be implemented by numerical optimizations. We demonstrate the efficacy and versatility of the proposed framework through simulations on several robotic systems and through experiments on a real-world quadrupedal robot, and show that it is less conservative and achieves higher specification satisfaction probability than representative baselines.

Liqian Ma, Zishun Liu, Glen Chou +1

Georgia Institute of Technology, Atlanta, GA 30332

Constrained Motion Planning Trajectory Optimization Contraction Theory Stochastic Optimal Control Robot Motion Planning STL Motion Planning+2

Apr 27, 2026

Logic of Fuzzy Paths

We introduce a new family of temporal logics intended for specifications in motion planning (MP). It builds upon the signal temporal logic (STL), which is a linear-time logic over real-valued signals that possess quantitative semantics and thus became popular in the areas of cyber-physical systems, robotics, and specifically robot MP. However, in contrast to STL, the proposed logic works with paths as first-class citizens, separating the concerns of geometry and of logic. This in turn leads to simpler and more understandable formulae, and a more refined notion of satisfaction being able to reflect also preferences over behaviours. Technically, the logic is built on fuzzy, time-varying signal constraints. As a consequence of this expressivity, it is (i) more usable for human-given specifications in MP and (ii) more amenable to learning specifications from demonstrations than other logics. The former is important for the traditional style of verification in robot MP; the latter is becoming recognized as crucial for mining data-given tasks and controller synthesis in human-aware MP. We expose the advantages of our proposed logic on examples and show the versatility and flexibility of the framework on a number of scenarios. Finally, we give a learning algorithm with a prototype implementation and discuss the possibilities of model checking and monitoring.

Kush Grover, Pratham Gupta, Jan Křetínský

Fondazione Bruno Kessler · Indian Institute of Science · Masaryk University

Temporal Reasoning Signal Temporal Logic Robot Motion Planning Temporal Logic STL Motion Planning

Apr 22, 2026

Lexicographic Minimum-Violation Motion Planning using Signal Temporal Logic

Motion planning for autonomous vehicles often requires satisfying multiple conditionally conflicting specifications. In situations where not all specifications can be met simultaneously, minimum-violation motion planning maintains system operation by minimizing violations of specifications in accordance with their priorities. Signal temporal logic (STL) provides a formal language for rigorously defining these specifications and enables the quantitative evaluation of their violations. However, a total ordering of specifications yields a lexicographic optimization problem, which is typically computationally expensive to solve using standard methods. We address this problem by transforming the multi-objective lexicographic optimization problem into a single-objective scalar optimization problem using non-uniform quantization and bit-shifting. Specifically, we extend a deterministic model predictive path integral (MPPI) solver to efficiently solve optimization problems without quadratic input cost. Additionally, a novel predicate-robustness measure that combines spatial and temporal violations is introduced. Our results show that the proposed method offers an interpretable and scalable solution for lexicographic STL minimum-violation motion planning within a single-objective solver framework.

Patrick Halder, Lothar Kiltz, Hannes Homburger +2

School of Computation, Information and Technology, Technical University of Munich, 85748 Garching, Germany · 2ZF Friedrichshafen AG, 88046 Friedrichshafen, Germany · Institute of System Dynamics, HTWG Konstanz, 78562 Konstanz, Germany

STL Motion Planning Motion Planning MPPI Control Autonomous Driving Planning Multi-Objective Optimization

Apr 20, 2026

DAG-STL: A Hierarchical Framework for Zero-Shot Trajectory Planning under Signal Temporal Logic Specifications

Signal Temporal Logic (STL) is a powerful language for specifying temporally structured robotic tasks. Planning executable trajectories under STL constraints remains difficult when system dynamics and environment structure are not analytically available. Existing methods typically either assume explicit models or learn task-specific behaviors, limiting zero-shot generalization to unseen STL tasks. In this work, we study offline STL planning under unknown dynamics using only task-agnostic trajectory data. Our central design philosophy is to separate logical reasoning from trajectory realization. We instantiate this idea in DAG-STL, a hierarchical framework that converts long-horizon STL planning into three stages. It first decomposes an STL formula into reachability and invariance progress conditions linked by shared timing constraints. It then allocates timed waypoints using learned reachability-time estimates. Finally, it synthesizes trajectories between these waypoints with a diffusion-based generator. This decomposition--allocation--generation pipeline reduces global planning to shorter, better-supported subproblems. To bridge the gap between planning-level correctness and execution-level feasibility, we further introduce a rollout-free dynamic consistency metric, an anytime refinement search procedure for improving multiple allocation hypotheses under finite budgets, and a hierarchical online replanning mechanism for execution-time recovery. Experiments in Maze2D, OGBench AntMaze, and the Cube domain show that DAG-STL substantially outperforms direct robustness-guided diffusion on complex long-horizon STL tasks and generalizes across navigation and manipulation settings. In a custom environment with an optimization-based reference, DAG-STL recovers most model-solvable tasks while retaining a clear computational advantage over direct optimization based on the explicit system model.

Ruijia Liu, Ancheng Hou, Xiao Yu +1

School of Automation and Intelligent Sensing, Shanghai Jiao Tong University, Shanghai, China. · Institute of Artificial Intelligence, Xiamen University, Xiamen, China.

Constrained Motion Planning Trajectory Generation STL Planning Robot Motion Planning STL Motion Planning

Mar 6, 2026

STL-SVPIO: Signal Temporal Logic guided Stein Variational Path Integral Optimization

Signal Temporal Logic (STL) enables formal specification of complex spatiotemporal constraints for robotic task planning. However, synthesizing long-horizon continuous control trajectories from complex STL specifications is fundamentally challenging due to the nested structure of STL robustness objectives. Existing solver-based methods, such as Mixed-Integer Linear Programming (MILP), suffer from exponential scaling, whereas sampling methods, such as Model-Predictive Path Integral control (MPPI), struggle with sparse, long-horizon costs. We introduce Signal Temporal Logic guided Stein Variational Path Integral Optimization (STL-SVPIO), which reframes STL as a globally informative, differentiable reward-shaping mechanism. By leveraging Stein Variational Gradient Descent and differentiable physics engines, STL-SVPIO transports a mutually repulsive swarm of control particles toward high robustness regions. Our method transforms sparse logical satisfaction into tractable variational inference, mitigating the severe local minima traps of standard gradient-based methods. We demonstrate that STL-SVPIO significantly outperforms existing methods in both robustness and efficiency for traditional STL tasks. Moreover, it solves complex long-horizon tasks, including multi-agent coordination with synchronization and queuing while baselines either fail to discover feasible solutions, or become computationally intractable. Finally, we use STL-SVPIO in agile robotic motion planning tasks with nonlinear dynamics, such as 7-DoF manipulation and half cheetah back flips to show the generalizability of our algorithm.

Hongrui Zheng, Zirui Zang, Ahmad Amine +2

Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA, USA. · Mechanical Engineering and Mechanics Department, Lehigh University, Bethlehem, PA, USA.

STL Motion Planning Trajectory Optimization Robot Task Planning Motion Planning

Mar 6, 2026

Multi-Robot Trajectory Planning via Constrained Bayesian Optimization and Local Cost Map Learning with STL-Based Conflict Resolution

We address multi-robot motion planning under Signal Temporal Logic (STL) specifications with kinodynamic constraints. Exact approaches face scalability bottlenecks and limited adaptability, while conventional sampling-based methods require excessive samples to construct optimal trajectories. We propose a two-stage framework integrating sampling-based online learning with formal STL reasoning. At the single-robot level, our constrained Bayesian Optimization-based Tree search (cBOT) planner uses a Gaussian process as a surrogate model to learn local cost maps and feasibility constraints, generating shorter collision-free trajectories with fewer samples. At the multi-robot level, our STL-enhanced Kinodynamic Conflict-Based Search (STL-KCBS) algorithm incorporates STL monitoring into conflict detection and resolution, ensuring specification satisfaction while maintaining scalability and probabilistic completeness. Benchmarking demonstrates improved trajectory efficiency and safety over existing methods. Real-world experiments with autonomous surface vehicles validate robustness and practical applicability in uncertain environments. The STLcBOT Planner will be released as an open-source package, and videos of real-world and simulated experiments are available at https://stlbot.github.io/.

Sourav Raxit, Abdullah Al Redwan Newaz, Jose Fuentes +3

Department of Computer Science, University of New Orleans, New Orleans, LA 70148, USA · Knight Foundation School of Computing and Information Sciences, Florida International University, Miami, FL 33199, USA · Providence College, Department of Mathematics & Computer Science, Providence, RI 02918, USA

STL Motion Planning Multi-Robot Motion Planning Constrained Motion Planning Kinodynamic Motion Planning Conflict-Based Search Bayesian Optimization

Feb 21, 2026

Temporal-Logic-Aware Frontier-Based Exploration

This paper addresses the problem of temporal logic motion planning for an autonomous robot operating in an unknown environment. The objective is to enable the robot to satisfy a syntactically co-safe Linear Temporal Logic (scLTL) specification when the exact locations of the desired labels are not known a priori. We introduce a new type of automaton state, referred to as commit states. These states capture intermediate task progress resulting from actions whose consequences are irreversible. In other words, certain future paths to satisfaction become not feasible after taking those actions that lead to the commit states. By leveraging commit states, we propose a sound and complete frontier-based exploration algorithm that strategically guides the robot to make progress toward the task while preserving all possible ways of satisfying it. The efficacy of the proposed method is validated through simulations.

Azizollah Taheri, Derya Aksaray

Department of Electrical and Computer Engineering at Northeastern University.

STL Motion Planning Motion Planning Robot Motion Planning Linear Temporal Logic Frontier-Based Exploration

Feb 18, 2026

RRT $^η$ : Sampling-based Motion Planning and Control from STL Specifications using Arithmetic-Geometric Mean Robustness

Sampling-based motion planning has emerged as a powerful approach for robotics, enabling exploration of complex, high-dimensional configuration spaces. When combined with Signal Temporal Logic (STL), a temporal logic widely used for formalizing interpretable robotic tasks, these methods can address complex spatiotemporal constraints. However, traditional approaches rely on min-max robustness measures that focus only on critical time points and subformulae, creating non-smooth optimization landscapes with sharp decision boundaries that hinder efficient tree exploration. We propose RRT

^η

, a sampling-based planning framework that integrates the Arithmetic-Geometric Mean (AGM) robustness measure to evaluate satisfaction across all time points and subformulae. Our key contributions include: (1) AGM robustness interval semantics for reasoning about partial trajectories during tree construction, (2) an efficient incremental monitoring algorithm computing these intervals, and (3) enhanced Direction of Increasing Satisfaction vectors leveraging Fulfillment Priority Logic (FPL) for principled objective composition. Our framework synthesizes dynamically feasible control sequences satisfying STL specifications with high robustness while maintaining the probabilistic completeness and asymptotic optimality of RRT

^\ast

. We validate our approach on three robotic systems. A double integrator point robot, a unicycle mobile robot, and a 7-DOF robot arm, demonstrating superior performance over traditional STL robustness-based planners in multi-constraint scenarios with limited guidance signals.

Ahmad Ahmad, Shuo Liu, Roberto Tron +1

Division of Systems Engineering, Boston University, Boston, MA, USA. · Department of Mechanical Engineering, Boston University, Boston, MA, USA. · Department of Electrical and Computer Engineering and the Department of Computer Science at the University of Maryland, College Park, MD, USA.

STL Motion Planning Motion Planning Sampling-Based Motion Planning Constrained Motion Planning