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

Dimos V. Dimarogonas; Panagiotis Rousseas

arxiv: 2605.03662 · v1 · submitted 2026-05-05 · 💻 cs.RO · cs.SY· eess.SY

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

Panagiotis Rousseas , Dimos V. Dimarogonas This is my paper

Pith reviewed 2026-05-07 04:07 UTC · model grok-4.3

classification 💻 cs.RO cs.SYeess.SY

keywords hybrid controlmotion planningsignal temporal logiccontrol barrier functionsfeasibility analysisdeadlock avoidancespatio-temporal tasksrobotic workspace transformation

0 comments

The pith

A hybrid controller unifies planning and control for robots under timed task rules by tracking local feasibility with a discrete variable and applying barrier functions to a disk version of the workspace.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents a hybrid control method that merges high-level planning with low-level execution for robots that must meet rules combining space and time in cluttered planar areas. A discrete variable tracks whether nearby constraints are satisfied, letting the system check feasibility locally and adjust the control inputs directly instead of relying on a separate planner. Control barrier functions are built on a simplified disk-shaped version of the real workspace to keep the robot from getting stuck in deadlocks caused by irregular obstacles. Simulations show the approach manages several overlapping timed tasks at once even when motor commands hit their limits. This matters to a reader because separate planning and control layers often fail when tasks have strict timing and the environment creates traps.

Core claim

The paper establishes a feasibility-aware hybrid control architecture for planar motion planning under signal temporal logic specifications. The architecture employs a discrete variable that tracks satisfaction of local constraints to perform local feasibility analysis, which unifies the planning and control design processes. Control barrier functions are constructed on a disk-transformed representation of the nonconvex workspace to eliminate deadlock problems. This enables the robot to handle multiple overlapping spatio-temporal tasks effectively, as validated through simulations that include cases with input saturation.

What carries the argument

The hybrid control architecture featuring a discrete variable for modeling local constraint satisfaction and control barrier functions defined on a disk-transformed workspace, which together unify planning with control and resolve deadlocks.

If this is right

Robots can complete complex timed tasks in irregular workspaces without becoming trapped in deadlocks.
Planning and control become a single integrated loop, removing the need for separate high-level planners that may produce infeasible commands.
The system continues to work when actuator limits prevent large control efforts.
Several overlapping space-and-time rules can be satisfied concurrently without priority conflicts.
Local feasibility checks allow early detection of impossible task combinations before the robot commits to a failing path.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The disk transformation could be generalized to three-dimensional spaces or nonholonomic vehicles if the safety preservation properties hold under those dynamics.
Real-robot experiments with sensor noise would reveal whether the local feasibility variable remains reliable outside idealized simulations.
Similar discrete tracking variables might be added to other temporal-logic control methods to gain the same unification of planning and execution.
The approach could be combined with online learning to adapt barrier functions when the workspace map is only partially known.

Load-bearing premise

That transforming the nonconvex workspace into a disk version preserves all necessary geometric and safety properties so the control barrier functions can reliably prevent deadlocks without creating new infeasibility issues or violating the original signal temporal logic specifications.

What would settle it

A simulation or physical test in which the disk transformation causes the robot to collide with an obstacle, violate a timing rule, or enter a deadlock that the original workspace would have allowed would disprove the central claim.

Figures

Figures reproduced from arXiv: 2605.03662 by Dimos V. Dimarogonas, Panagiotis Rousseas.

**Figure 1.** Figure 1: Switching function (10) view at source ↗

**Figure 3.** Figure 3: Proposed Controller. Robot workspace (outer boundary and obstacles in black) and numbered STL zero super-level regions (colored regions) of (Eq. (20)) for the unconstrained input case. The robot’s trajectory is depicted through the gradient-colored curve, where the color depicts time in seconds. depicted in view at source ↗

**Figure 4.** Figure 4: Our method’s (Alg. 2) ability to satisfy all of view at source ↗

**Figure 4.** Figure 4: Evolution of the STL predicates for the unconstraine view at source ↗

**Figure 5.** Figure 5: Proposed Controller. Robot workspace (outer boundary and obstacles in black) and numbered STL zero super-level regions (colored regions) of Eq. (20) for the constrained input case. The trajectory is depicted through the gradient-colored curve, where the color depicts time [s]. 5. CONCLUSIONS & FUTURE WORK In this work, a novel task and motion planning framework based on STL-CBFs is proposed. Importantly, t… view at source ↗

**Figure 6.** Figure 6: Evolution of the STL predicates for the constrained i view at source ↗

**Figure 10.** Figure 10: Computational times for the CBF-QP controller view at source ↗

**Figure 8.** Figure 8: Computational times for a serial implementation view at source ↗

**Figure 9.** Figure 9: Benchmark Controller. Robot workspace (outer boundary and obstacles in black) and STL zero superlevel regions (colored regions) of (Eq. (20)) for the constrained input case with the method of variable relaxation. The trajectory is depicted through the gradient-colored curve, where the color depicts time. Springer Berlin Heidelberg, Berlin, Heidelberg. Mehdifar, F., Lindemann, L., Bechlioulis, C.P., and Di… view at source ↗

read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Hybrid STL motion planner unifies planning and control with a discrete feasibility variable and disk CBFs, but the workspace transformation needs formal validation.

read the letter

The paper's core contribution is a hybrid controller for planar robots that uses a discrete variable to model local satisfaction of signal temporal logic constraints. This variable supports local feasibility checks and helps merge the planning and control stages into one architecture. At the same time, the method transforms the workspace to a disk shape so that control barrier functions can be applied without running into deadlocks from complex geometry. This setup does a few things well. The discrete variable gives a clean way to track whether constraints are met locally, which is useful for STL tasks that have timing and spatial requirements. The simulations demonstrate that the controller can manage several overlapping tasks at once, even when actuator limits are active. That suggests the approach has some practical robustness. The disk transformation is presented as the fix for deadlocks, and it builds on prior work in barrier functions for robotics. If the mapping is done right, it could simplify the design without losing the original safety guarantees. The main soft spot is exactly that mapping. The abstract and the stress-test note both point out that there is no explicit description of how the nonconvex workspace becomes a disk, nor a proof that the barrier conditions and the STL predicates survive the change of coordinates. If the transformation distorts distances or obstacle shapes in a non-invertible way, the resulting controls might not stay safe or satisfy the logic when mapped back to the real space. The paper needs to address this directly with a formal argument, perhaps showing that the Lie derivative conditions carry over. Beyond that, the work would benefit from more concrete metrics in the results section, such as success rates against other STL planners or measures of conservatism introduced by the transformation. This paper is for people working on motion planning with temporal logics in robotics. A reader who already knows hybrid systems and CBFs will see how the feasibility variable adds a new layer for handling local decisions. It is coherent enough and grounded in established methods to deserve peer review. The idea is clear, the simulations are encouraging, and the potential flaw in the transformation is fixable with additional analysis. I recommend sending it to referees, asking them to check the transformation details and any experimental comparisons.

Referee Report

2 major / 1 minor

Summary. The paper proposes a novel hybrid modeling approach for planar robotic task and motion planning under Signal Temporal Logics (STL). It introduces a discrete variable that models local constraint satisfaction to enable local feasibility analysis and thereby unify planning with control design. Control barrier functions (CBFs) are designed on a transformed disk version of the original nonconvex workspace to address deadlocks, and simulations are presented to show effective handling of multiple overlapping spatio-temporal tasks even under input saturation.

Significance. If the workspace transformation rigorously preserves geometric safety properties, STL predicate semantics, and feasibility under the mapping, the hybrid architecture with its discrete feasibility variable could represent a meaningful advance in integrating high-level temporal logic specifications with low-level control synthesis for robots in complex environments. The approach's explicit handling of input saturation in simulations is a practical strength. However, the absence of any quantitative metrics, baseline comparisons, or proof sketches in the abstract limits assessment of its broader impact on the field.

major comments (2)

[Workspace transformation section] § on workspace transformation: The central deadlock-amendment claim rests on designing CBFs in the transformed disk workspace, yet the abstract supplies no explicit definition of the mapping, no statement of whether it is a diffeomorphism or homeomorphism, and no argument that the CBF Lie-derivative condition in disk coordinates implies the original-space barrier condition or preserves STL predicate semantics upon pullback. If the map distorts distances or folds boundaries, the resulting controls may produce deadlocks or STL violations in the real workspace, directly undermining the unification and safety claims.
[Hybrid architecture section] § on hybrid control architecture: The unification of planning and control via the discrete variable that models local constraint satisfaction is load-bearing for the main contribution, but the abstract does not clarify whether feasibility analysis occurs in original or transformed coordinates. Without this, it is impossible to verify that the discrete variable still correctly detects local STL satisfaction after the coordinate change, as required by the skeptic's concern on semantic equivalence.

minor comments (1)

[Abstract] Abstract: The statement that 'simulations indicate effective handling' is presented without any numerical metrics, error bounds, or comparison to prior STL planners, which weakens the reader's ability to gauge practical performance.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major comment below, clarifying aspects of the workspace transformation and hybrid architecture that are detailed in the full manuscript but not fully reflected in the abstract. We propose targeted revisions to improve clarity without altering the core technical claims.

read point-by-point responses

Referee: [Workspace transformation section] § on workspace transformation: The central deadlock-amendment claim rests on designing CBFs in the transformed disk workspace, yet the abstract supplies no explicit definition of the mapping, no statement of whether it is a diffeomorphism or homeomorphism, and no argument that the CBF Lie-derivative condition in disk coordinates implies the original-space barrier condition or preserves STL predicate semantics upon pullback. If the map distorts distances or folds boundaries, the resulting controls may produce deadlocks or STL violations in the real workspace, directly undermining the unification and safety claims.

Authors: We agree that the abstract would benefit from a concise statement on the workspace transformation. Section 3 of the manuscript defines the mapping explicitly as a homeomorphism (constructed via a radial projection after convexification of obstacles) from the original nonconvex workspace to a disk workspace. This mapping is bijective and continuous, with the interior being a diffeomorphism. We provide an argument that the Lie-derivative CBF condition in disk coordinates pulls back to a valid barrier condition in the original space because the Jacobian of the mapping is nonsingular in the interior and the transformation preserves the sign of the barrier function gradients along trajectories. For STL predicate semantics, the predicates depend on Euclidean distances and positions; the homeomorphism preserves topological satisfaction sets, so predicate truth values are unchanged under the mapping. The design avoids distance distortion that would affect deadlock resolution by ensuring the mapping is distance-nonincreasing in critical directions. We will revise the abstract to include a one-sentence description of the mapping and its properties, and we will add a short paragraph in Section 3 with the pullback argument and a note on semantic preservation. revision: yes
Referee: [Hybrid architecture section] § on hybrid control architecture: The unification of planning and control via the discrete variable that models local constraint satisfaction is load-bearing for the main contribution, but the abstract does not clarify whether feasibility analysis occurs in original or transformed coordinates. Without this, it is impossible to verify that the discrete variable still correctly detects local STL satisfaction after the coordinate change, as required by the skeptic's concern on semantic equivalence.

Authors: We thank the referee for identifying this point of potential confusion. In the hybrid architecture (Section 5), the discrete feasibility variable is computed directly from the STL predicates evaluated in the original workspace coordinates; this ensures that local constraint satisfaction and feasibility analysis remain semantically equivalent to the high-level specification. The disk transformation is used exclusively for synthesizing the CBF-based low-level controllers to prevent deadlocks, but the discrete variable is never evaluated in the transformed coordinates. Because the mapping is a homeomorphism, any trajectory that satisfies the CBFs in the disk space corresponds to a safe trajectory in the original space, and the feasibility flag remains consistent. We will revise the abstract to state that feasibility analysis occurs in the original coordinates, and we will insert a clarifying sentence in Section 5 explaining the separation of coordinates together with a brief semantic-equivalence argument. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on introduced hybrid variable and workspace map

full rationale

The paper introduces a discrete feasibility variable and a disk transformation for CBF design as novel elements to unify planning and control under STL. No equations or claims in the provided abstract reduce a prediction to a fitted input by construction, invoke self-citations as load-bearing uniqueness theorems, or rename known results. The central architecture is presented as arising from these new modeling choices rather than self-referential definitions or statistical forcing, making the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim rests on standard control-theoretic assumptions plus the domain-specific assumption that workspace transformation to disks preserves safety properties; the discrete variable is an invented modeling entity without independent evidence beyond the proposal itself. No explicit free parameters are described.

axioms (2)

standard math Control barrier functions enforce forward invariance of safe sets under standard Lyapunov-like conditions
Invoked implicitly by the design of CBFs on the transformed workspace to amend deadlocks.
domain assumption The disk transformation of the nonconvex workspace preserves collision-avoidance and feasibility properties for the original STL specifications
Central to the claim that CBFs on the transformed space amend deadlocks without new issues.

invented entities (1)

Discrete variable modeling local constraint satisfaction no independent evidence
purpose: Enables local feasibility analysis and unifies planning with control design
Introduced as the key mechanism for hybrid modeling of STL tasks.

pith-pipeline@v0.9.0 · 5384 in / 1559 out tokens · 61480 ms · 2026-05-07T04:07:21.016907+00:00 · methodology

Review history (2 revisions) →

discussion (0)

Reference graph

Works this paper leans on

28 extracted references · 28 canonical work pages

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Feedback control strategies for multi-agent systems under a fragment of signal temporal logic tasks , journal =. 2019 , issn =. doi:https://doi.org/10.1016/j.automatica.2019.05.013 , author =

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2025 , eprint=

Sampling-Based Planning Under STL Specifications: A Forward Invariance Approach , author=. 2025 , eprint=

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Combinatorial Control Barrier Functions: Nested Boolean and p-choose-r Compositions of Safety Constraints , author=. 2025 , eprint=

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Vlantis, Panagiotis and Vrohidis, Constantinos and Bechlioulis, Charalampos P. and Kyriakopoulos, Kostas J. , booktitle=. Robot Navigation in Complex Workspaces Using Harmonic Maps , year=

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and Dimarogonas, Dimos V

Sewlia, Mayank and Verginis, Christos K. and Dimarogonas, Dimos V. , booktitle=. Cooperative Sampling-Based Motion Planning under Signal Temporal Logic Specifications , year=

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The International Journal of Robotics Research , author =

Sertac Karaman and Emilio Frazzoli , title =. The International Journal of Robotics Research , volume =. 2011 , doi =. https://doi.org/10.1177/0278364911406761 , abstract =

work page doi:10.1177/0278364911406761 2011

[2] [2]

and Xu, Xiangru and Grizzle, Jessy W

Ames, Aaron D. and Xu, Xiangru and Grizzle, Jessy W. and Tabuada, Paulo , journal=. Control Barrier Function Based Quadratic Programs for Safety Critical Systems , year=

work page

[3] [3]

and Dimarogonas, Dimos V

Mehdifar, Farhad and Lindemann, Lars and Bechlioulis, Charalampos P. and Dimarogonas, Dimos V. , journal=. Low-Complexity Control for a Class of Uncertain MIMO Nonlinear Systems Under Generalized Time-Varying Output Constraints , year=

work page

[4] [4]

and Dimarogonas, Dimos V

Mehdifar, Farhad and Bechlioulis, Charalampos P. and Dimarogonas, Dimos V. , booktitle=. Funnel Control Under Hard and Soft Output Constraints , year=

work page

[5] [5]

Proceedings of the 25th ACM International Conference on Hybrid Systems: Computation and Control , articleno =

Lindemann, Lars and Rodionova, Alena and Pappas, George , title =. Proceedings of the 25th ACM International Conference on Hybrid Systems: Computation and Control , articleno =. 2022 , isbn =. doi:10.1145/3501710.3519504 , abstract =

work page doi:10.1145/3501710.3519504 2022

[6] [6]

Theoretical Computer Science410(42), 4262–4291 (2009)

Robustness of temporal logic specifications for continuous-time signals , journal =. 2009 , issn =. doi:https://doi.org/10.1016/j.tcs.2009.06.021 , author =

work page doi:10.1016/j.tcs.2009.06.021 2009

[7] [7]

Temporally Robust Multi-Agent STL Motion Planning in Continuous Time , year=

Verhagen, Joris and Lindemann, Lars and Tumova, Jana , booktitle=. Temporally Robust Multi-Agent STL Motion Planning in Continuous Time , year=

work page

[8] [8]

, TITLE=

Zehfroosh, Ashkan and Tanner, Herbert G. , TITLE=. Frontiers in Robotics and AI , VOLUME=. 2022 , DOI=

work page 2022

[9] [9]

A Survey of Optimization-Based Task and Motion Planning: From Classical to Learning Approaches , year=

Zhao, Zhigen and Cheng, Shuo and Ding, Yan and Zhou, Ziyi and Zhang, Shiqi and Xu, Danfei and Zhao, Ye , journal=. A Survey of Optimization-Based Task and Motion Planning: From Classical to Learning Approaches , year=

work page

[10] [10]

, journal=

Charitidou, Maria and Dimarogonas, Dimos V. , journal=. Distributed MPC With Continuous-Time STL Constraint Satisfaction Guarantees , year=

work page

[11] [11]

, booktitle=

Charitidou, Maria and Dimarogonas, Dimos V. , booktitle=. Barrier Function-based Model Predictive Control under Signal Temporal Logic Specifications , year=

work page

[12] [12]

2023 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) , year=

Real-Time RRT* with Signal Temporal Logic Preferences , author=. 2023 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) , year=

work page 2023

[13] [13]

2019 , issn =

Feedback control strategies for multi-agent systems under a fragment of signal temporal logic tasks , journal =. 2019 , issn =. doi:https://doi.org/10.1016/j.automatica.2019.05.013 , author =

work page doi:10.1016/j.automatica.2019.05.013 2019

[14] [14]

2025 , eprint=

Constraint Selection in Optimization-Based Controllers , author=. 2025 , eprint=

work page 2025

[15] [15]

Chinneck , title =

John W. Chinneck , title =. INFOR: Information Systems and Operational Research , volume =. 2019 , publisher =. doi:10.1080/03155986.2019.1607715 , eprint =

work page doi:10.1080/03155986.2019.1607715 2019

[16] [16]

High-Order Control Barrier Functions , year=

Xiao, Wei and Belta, Calin , journal=. High-Order Control Barrier Functions , year=

work page

[17] [17]

Reference and command governors: A tutorial on their theory and automotive applications , year=

Kolmanovsky, Ilya and Garone, Emanuele and Di Cairano, Stefano , booktitle=. Reference and command governors: A tutorial on their theory and automotive applications , year=

work page

[18] [18]

Robust Satisfaction of Temporal Logic over Real-Valued Signals

Donz \'e , Alexandre and Maler, Oded. Robust Satisfaction of Temporal Logic over Real-Valued Signals. Formal Modeling and Analysis of Timed Systems. 2010

work page 2010

[19] [19]

and Pappas, George J

Fainekos, Georgios E. and Pappas, George J. Robustness of Temporal Logic Specifications. Formal Approaches to Software Testing and Runtime Verification. 2006

work page 2006

[20] [20]

, journal=

Lindemann, Lars and Dimarogonas, Dimos V. , journal=. Control Barrier Functions for Multi-Agent Systems Under Conflicting Local Signal Temporal Logic Tasks , year=

work page

[21] [21]

2025 , eprint=

Sampling-Based Planning Under STL Specifications: A Forward Invariance Approach , author=. 2025 , eprint=

work page 2025

[22] [22]

2025 , eprint=

Combinatorial Control Barrier Functions: Nested Boolean and p-choose-r Compositions of Safety Constraints , author=. 2025 , eprint=

work page 2025

[23] [23]

2025 , eprint=

On Uniformly Time-Varying Control Barrier Functions , author=. 2025 , eprint=

work page 2025

[24] [24]

Monitoring Temporal Properties of Continuous Signals

Maler, Oded and Nickovic, Dejan. Monitoring Temporal Properties of Continuous Signals. Formal Techniques, Modelling and Analysis of Timed and Fault-Tolerant Systems. 2004

work page 2004

[25] [25]

Feasibility Evaluation of Quadratic Programs for Constrained Control , year=

Rousseas, Panagiotis and Panagou, Dimitra , booktitle=. Feasibility Evaluation of Quadratic Programs for Constrained Control , year=

work page

[26] [26]

and Kyriakopoulos, Kostas J

Vlantis, Panagiotis and Vrohidis, Constantinos and Bechlioulis, Charalampos P. and Kyriakopoulos, Kostas J. , booktitle=. Robot Navigation in Complex Workspaces Using Harmonic Maps , year=

work page

[27] [27]

, journal=

Lindemann, Lars and Dimarogonas, Dimos V. , journal=. Control Barrier Functions for Signal Temporal Logic Tasks , year=

work page

[28] [28]

and Dimarogonas, Dimos V

Sewlia, Mayank and Verginis, Christos K. and Dimarogonas, Dimos V. , booktitle=. Cooperative Sampling-Based Motion Planning under Signal Temporal Logic Specifications , year=

work page