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REVIEW 3 major objections 4 minor 51 references

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

T0 review · 3 major / 4 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read This paper shows that robot missions expressed in Signal Temporal Logic can be planned and controlled by translating each task into a time-varying convex set, making the planning problem a graph shortest-path search and the control problem

desk verdict A solid GCS planner for dc-STL with an honest but unresolved control-layer guarantee—worth refereeing, needs revision. read the letter →

arxiv 2607.19196 v1 pith:QRLWDQIC submitted 2026-07-21 eess.SY cs.ROcs.SY

Nicola De Carli , Gregorio Marchesini , Dimos V. Dimarogonas This is my paper · ORCID
classification eess.SYcs.ROcs.SY
keywords SignalTemporalLogicGraphsofConvexSetsControlBarrierFunctionsMotionplanningForwardinvarianceTime-varyingB-splinetrajectoryFormalmethodsforrobotics
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper claims that the hard problem of generating and executing robot trajectories that satisfy Signal Temporal Logic (STL) specifications—tasks with explicit time windows like 'reach the goal within 10 seconds while always avoiding obstacles'—can be recast as a convex optimization problem. The key move is to replace the STL formula with a time-varying convex set: if the robot stays inside this set, the specification is guaranteed to be met with some robustness margin. The same set is then used twice: first, as the constraint regions in a Graphs-of-Convex-Sets planner that finds a short collision-free path; second, as the safety constraint in a Control-Barrier-Function filter that keeps the closed-loop system inside the set during execution. If correct, this provides a way to preserve task satisfaction during closed-loop execution rather than only planning an open-loop trajectory.

What carries the argument

The central object is the STL-induced time-varying set B_ψ(t), with its spatio-temporal lift B̄_ψ. It is constructed via a piecewise-linear shrinking funnel (parameter κ_k(t)) that drives the configuration into a robustified predicate set within the task's time window. The set turns STL satisfaction into a forward-invariance condition (Eq. 15); its convex pieces populate the product graph that makes planning a GCS shortest-path problem, and the same set feeds the CBF-based safety filter during execution.

What would settle it

For a quadrotor with position constraints (relative degree 2), compute the lifted set C_lift(t) at a task-switching time when the active predicate changes; if C_lift(t_s^-) ⊈ C_lift(t_s^+) for every choice of the funnel slope and HOCBF gains, then the paper's guarantee of closed-loop STL satisfaction under high-order CBFs cannot hold as stated.

Watch

Extended reading notes

Core claim

The paper establishes a sufficient condition: for every STL formula ψ in the proposed dc-STL fragment, there exists a time-varying set B_ψ(t) such that for all t≥0, q(t)∈B_ψ(t) implies (q,0)⊨ψ (Eq. 15). The construction uses a piecewise-linear shrinking funnel that drives the set into a robustified predicate set within the task's time window. The paper then lifts this to the joint time–configuration space, organizes the convex pieces into a task graph, combines it with a collision-free graph into a product graph, and formulates the trajectory planning problem as a GCS shortest-path problem with B-spline parameterization. At the control layer, the same sets are used to design a CBF-based quad

Load-bearing premise

The framework's closed-loop guarantee rests on the assumption that the admissible sets only expand (never shrink) at every task-switching instant, including after lifting to higher-order barrier-function state spaces; the paper leaves the high-order case as a design premise rather than a proof.

Editorial extensions

If this is right

  • STL planning in cluttered environments reduces to solving a (relaxed) convex shortest-path problem, avoiding mixed-integer encodings and their exponential worst-case complexity.
  • The planned trajectory and the online controller share the same admissible sets, so the controller does not need to reconstruct the specification at execution time.
  • Satisfaction becomes a closed-loop property: the CBF filter actively drives the robot back into the set when tracking errors appear, rather than merely following a nominal path.
  • The framework applies to a rich fragment (dc-STL) including conjunctions and disjunctions of bounded-time temporal operators with convex predicates.
  • The same sets can be used with high-order CBFs and backstepping for higher-relative-degree systems, provided the lifted switching compatibility condition holds.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If Eq. (15) is indeed the right sufficient condition, then the framework shifts the burden of STL satisfaction from proving a temporal-logic property to checking set invariance—an established systems-theoretic notion that may scale to multi-agent or networked settings.
  • The lifted compatibility issue (Eq. 56) suggests that for high-relative-degree systems, the planner should optimize not only the configuration-level funnels but also their first derivatives across switching times; this could be a constructive next step to guarantee the closed-loop guarantee in the HOCBF case.
  • The disjunction handling via a union of sets implies that the planner may choose among alternative task branches, but the controller does not switch branches online; a natural extension is to use the robustness margin to trigger branch switching if the selected branch becomes infeasible during execution.
  • The real-world validation on a free-flyer platform suggests the approach may transfer to spacecraft docking or on-orbit servicing, where STL specifications with time windows are natural.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper proposes a combined planning-and-control framework for a fragment of Signal Temporal Logic (STL), called dc-STL, defined over convex predicates. In the planning layer, each elementary STL task is encoded as a time-varying convex set whose forward invariance is a sufficient condition for satisfaction with a prescribed robustness margin; these sets are lifted to the joint time–configuration space and embedded into a Graphs of Convex Sets (GCS) shortest-path formulation via a task graph, a collision-free graph, and their product graph. Trajectories are represented as concatenated B-spline segments with set-containment, velocity, and smoothness constraints. In the control layer, a CBF-based safety filter renders the active STL-induced sets forward invariant during execution, using high-order or backstepping CBFs when the configuration-level barrier has relative degree greater than one. The framework is validated on a planar free-flyer hardware experiment and a 3D quadrotor simulation.

Significance. If fully established, the paper would make a useful contribution: it connects STL mission planning to the scalable GCS framework while retaining a forward-invariance-based certificate that is reusable by a low-level CBF controller. The core planning construction is coherent and has several genuine strengths: the superlevel sets are convex because predicates and the time-varying perturbation are piecewise affine; the B-spline control-point containment is a valid sufficient condition via the convex-hull property; and the product-graph path is a legitimate discrete abstraction for the considered fragment. The real-world free-flyer experiment is a concrete asset. However, the paper's central closed-loop claim—that the controller preserves STL satisfaction during execution with a prescribed robustness margin—currently rests on a switching-compatibility condition, Eq. (56), that is explicitly stated but not proved, and the validation metric is the paper's own set-membership barrier rather than the STL robustness measure. These issues are load-bearing and require major revision.

major comments (3)
  1. [Sec. VI-B1, Eqs. (54)-(56) and Prop. 7] The exact closed-loop STL preservation claim is not established for the systems used in validation. In both the planar free-flyer and the 3D quadrotor, the planning model has p>=2 integrators, so the configuration-level barriers b(q,t) have relative degree at least 2 and the implemented filter necessarily relies on HOCBF/backstepping barriers of the form (54)-(55). The paper itself states that configuration-level expansion (28) does not, in general, imply expansion of the lifted set C_lift(t), and it gives no proof, algorithm, or verification that Eq. (56), C_lift(t_s^-) subset of C_lift(t_s^+), can be enforced. The following sentence concedes that if (56) is not guaranteed, forward invariance across the switch is lost and 'exact closed-loop preservation of the STL-induced set' is 'temporarily lost.' Since the abstract claims the controller preserves STL satisfaction during execution wit
  2. [Sec. III-B1 and Appendix A] The switching set-expansion condition (28) is central to the control layer, because Proposition 7 relies on the analogous condition (50) at every switching instant. However, the paper does not fully establish (28) for the claimed fragment. The parameter-selection paragraph says (28) can be enforced through convex optimization, but the only concrete construction provided in Appendix A treats two consecutive polytopic single-task funnels; overlapping-task groups are deferred to [28, Sec. IV.C/V.C], and for general convex sets the paper notes that exact containment requires an infinite-dimensional check and instead proposes conservative polytopic inner/outer approximations. Thus the closed-loop guarantee is conditional on a design step that is not fully specified for several cases in the dc-STL fragment. The manuscript should either supply the missing construction/verification for all cases
  3. [Sec. VII, Figs. 8 and 10] The metric reported as 'actual trajectory robustness' in the experiments is b_phi(q,t), a configuration-level barrier value whose nonnegativity certifies membership in the paper's own time-varying set. It is not the STL quantitative robustness rho_phi(q,t) defined in Eq. (11), and it is not an independent measure of the prescribed robustness margin r. While nonnegativity of b_phi is a valid certificate for the sufficient condition (15) if that condition is correctly constructed, the plots and wording overstate the empirical evidence: they do not demonstrate robustness in the STL semantics, and the validation is therefore partly self-referential. I recommend computing rho_phi on the executed trajectory and reporting its minimum value, and at minimum relabeling the figures and any related text to say 'set-membership certificate' rather than 'actual trajectory robustness.'
minor comments (4)
  1. [Sec. III-B, Eq. (24)] There is a likely typo in the definition of the until components: both the funnel and the predicate component are written as B̄^P_{k1} ∩ B̄^F_{k2}. The predicate component should presumably intersect with the predicate set of h_{k2} (e.g., B̄^P_{k1} ∩ B̄^P_{k2}). Please correct.
  2. [Table II] The total planning time is reported as '58,4177 s', which should be '58.4177 s'.
  3. [Figs. 8 and 10] The axis label 'Operator a/b' is unclear. It should say which operator (Always/Eventually) and predicate are associated with each interval, or be expanded in the caption.
  4. [Throughout] The manuscript relies heavily on [28] for two load-bearing ingredients: the handling of overlapping task groups in the set construction and the claimed constructive approach to the lifted compatibility condition (56). Since these ingredients are not merely background but support the closed-loop guarantee, the authors should either include the essential arguments in this manuscript or clearly mark those guarantees as inherited from [28] with the precise statements reproduced.

Circularity Check

2 steps flagged · score 4.0 of 10

No definitional reduction in the GCS derivation, but the closed-loop STL guarantee leans on an unproven same-author condition and the validation metric is self-referential.

  1. self citation load bearing [Section VI-B1, around Eqs. (54)-(56)]
    "Consequently, when HOCBFs or backstepping CBFs are used, the switching compatibility condition should be imposed or verified directly on the lifted set, namely Clift(t−s) ⊆ Clift(t+s), ∀ts ∈ Ts. (56) This condition may be enforced conservatively through the choice of the funnel parameters and of the HOCBF/backstepping design. For polytopic predicates, a constructive approach similar to [28, Sec. V .C] can be used to define the parameters of the barrier such that (56) holds."

    The paper's control contribution is to render the STL-induced sets forward invariant during execution, thereby preserving STL satisfaction. For planning models with p≥2 integrators, this guarantee requires the HOCBF lifted-set compatibility condition (56). The manuscript does not prove or algorithmically verify (56); it delegates the constructive design to [28, Sec. V.C], whose authors overlap with the present paper. The paper itself concedes that if (56) is not guaranteed, 'forward invariance across the switching instant is not guaranteed, and the closed-loop STL satisfaction guarantee is temporarily lost.' Thus the load-bearing step of the closed-loop claim reduces to a same-author citation rather than a derivation in this manuscript.

  2. other [Section VII, experimental validation paragraph]
    "In both studies, we report the STL-induced satisfaction margin b_phi(q,t) associated with the selected branch ϕ. Its nonnegativity certifies membership in the active STL-induced time-varying set and, by construction, satisfaction of the selected branch."

    The reported validation metric is the paper's own set-membership certificate: b_phi(q,t)≥0 means q(t)∈B_phi(t), and Eq. (15) defines STL satisfaction by construction as containment in B_phi(t). Thus the experimental evidence confirms that the controller keeps the trajectory inside the paper's constructed sets, rather than providing an independent computation of STL robustness. This makes the empirical validation partly self-referential, though it does not taint the planning-side derivation.

full rationale

The planning-side derivation is not circular. Eq. (15) is explicitly a sufficient condition, and Section III constructs B_k(t) via b_k(q,t)=h_k(q)+κ_k(t); for G and F operators the implication q(t)∈B_k(t) ⇒ STL satisfaction is proved directly from the funnel timing and the robustness margin. The GCS layer does not fit any parameter to measured STL robustness: funnel slopes are computed from containment LPs in Appendix A, and B-spline containment relies on the convex-hull property. The controller is a standard CBF QP, and the forward-invariance argument is standard. The main circularity-adjacent weaknesses are two. First, for p≥2 planning models the closed-loop STL-preservation claim depends on the HOCBF lifted-set compatibility condition (56), which is not proved or verified in this manuscript; the text explicitly defers to [28, Sec. V.C], a same-author citation, and states that if (56) fails 'the closed-loop STL satisfaction guarantee is temporarily lost.' This is a load-bearing self-citation for the control contribution, though the GCS planning contribution remains independent. Second, the validation metric b_phi is the paper's own set-membership certificate, so the experiments confirm containment in the constructed sets rather than an independently computed STL robustness value. Neither issue reduces the GCS derivation to its inputs, so the score is 4 rather than higher.

Assumptions & free parameters 6 free parameters · 7 assumptions · 0 invented entities

No new physical or ontological entities are introduced; the time-varying sets B_k(t) are mathematical constructions from the task predicates. The main externally imposed inputs are the user-chosen robustness margin r, task timing parameters, objective weights, and barrier design functions, plus the chain-of-integrators planning model and free-space convex decomposition.

free parameters (6)
  • robustness margin r = r = 0.1 in quadrotor simulation; not stated for planar experiment
    Defines the robustified predicate sets H^r_k (Eq. 19) and controls how much the funnel shrinks; chosen by the user rather than derived.
  • F-task completion time t' (alpha_k = tf_k = t') = not stated how selected within [a,b]
    For eventually tasks, the funnel reaches the robustified set at t', which determines feasibility and the resulting trajectory; the selection procedure is not specified.
  • B-spline degree and number of control points = not stated
    The spline degree p and control-point count J appear in Eqs. (36)-(37) and the continuity constraints (41), but their values in the experiments are not reported.
  • objective weights w1, w2 = not stated
    Trade off final time versus trajectory length in (35a) and (43a); hand-tuned parameters.
  • extended class-K functions alpha_k, alpha_l and HOCBF alpha_j = not stated
    Design functions in the CBF conditions (46), (53), and (54); their concrete forms are not specified.
  • slack weight w_s = not stated
    Weights the minimum-violation slacks in the safety-filter QP (53); must be chosen sufficiently large.
assumptions (7)
  • standard math STL quantitative semantics positivity implies satisfaction
    rho_phi(q,t) > 0 =implies (q,t) |= phi, stated after Eq. (11) and used throughout as the basis of robustness margins.
  • domain assumption Restriction to dc-STL fragment with convex predicates
    The grammar (13) and the convex-predicate assumption define the scope; formulas outside this fragment, such as general negation or arbitrary nesting, are not handled.
  • domain assumption Existence of a chain-of-integrators planning model z = Pi(x) with q^(p) = v
    Section II-A assumes a flat/feedback-linearizable or reduced-order planning model; the planned trajectory is dynamically feasible only for this planning model, and the physical system must track it.
  • domain assumption Nonsmooth time-varying CBF forward-invariance theorem
    Section VI-A relies on [46], [47] for the claim that a feedback law satisfying (46) renders C(t) forward invariant; this is cited, not re-proved.
  • domain assumption GCS convex relaxation and rounding produce a feasible approximate solution
    The optimization in Section V-C uses the perspective relaxation and randomized rounding from [23], [24]; the paper does not prove optimality or feasibility of the rounded solution itself beyond citing the GCS framework.
  • domain assumption Convex decomposition of free space exists and is available
    Section IV-B assumes finitely many convex regions {F_l}; the experiments use IRIS [42], but the planner depends on this decomposition being provided.
  • ad hoc to paper Lifted HOCBF compatibility (56) can be enforced by parameter choice
    Section VI-B1 states condition (56) 'may be enforced conservatively through the choice of funnel parameters and of the HOCBF/backstepping design' and points to [28, Sec. V.C]; this premise is needed for exact closed-loop STL preservation and is not proven in this paper.

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Pith. "Pith review of STL-GCS: A Planner-Controller Framework for Signal Temporal Logic via Graphs of Time-varying Convex Sets." pith.science (2026). https://pith.science/paper/QRLWDQIC

@misc{pith2026260719196,
  author       = {Pith},
  title        = {Pith review of: STL-GCS: A Planner-Controller Framework for Signal Temporal Logic via Graphs of Time-varying Convex Sets},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QRLWDQIC}},
  note         = {Machine review of arXiv:2607.19196}
}
read the original abstract

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.

Figures

Figures reproduced from arXiv: 2607.19196 by the authors.

Figure 1
Figure 1. Trajectory q(t) of a quadrotor navigating through collision-free convex regions (dashed rectangles) while sat￾isfying an STL specification by ensuring forward invariance of convex time-varying sets. The evolution of these sets is illustrated by the zero-level set boundaries of their defining functions, shown with different shades of red and blue. Black dots mark the junctions between consecutive B-splines, while red… view at source ↗
Figure 2
Figure 2. Illustration of the GCS associated to a simple task [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Illustration of Example 1. The robot satisfies the [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Set representation of a formula φk induced by (17) and (18) for linear predicates. Left: spatio-temporal set B¯ k for a G operator (top) and an F operator (bottom). Top right: evolution of Bk(t) in the configuration space, shrinking toward the robustified predicate set…
Figure 5
Figure 5. Figure 5: Illustration of the grouping of tasks in the conjunc [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: Planar free-flyer robot used in the experiments. [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]
Figure 7
Figure 7. Figure 7: Planar free-flyer experiment. Left: laboratory [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]
Figure 8
Figure 8. Figure 8: Temporal evolution of the STL-induced satisfaction [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]
Figure 9
Figure 9. Figure 9: Executed 3D quadrotor trajectory satisfying the [PITH_FULL_IMAGE:figures/full_fig_p015_9.png]
Figure 10
Figure 10. Figure 10: Temporal evolution of bϕ2 (q, t) during the 3D quadrotor simulation. The nonnegative robustness confirms satisfaction of the selected STL branch ϕ2 along the executed trajectory. VIII. CONCLUSIONS We presented a unified planning and control framework for satisfying a …

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Reference graph

Works this paper leans on

51 extracted references · 6 linked inside Pith

  1. [29]

    Signal temporal logic motion planning via graphs of convex sets.arXiv preprint arXiv:2605.23240, 2026

    Yu Chen, Ancheng Hou, Mingyang Feng, Xiao Yu, and Xiang Yin. Signal temporal logic motion planning via graphs of convex sets.arXiv preprint arXiv:2605.23240, 2026

    arXiv 2026

  2. [28]

    Sampling-based planning under stl specifications: A forward invariance approach.IEEE Transactions on Automatic Control, 2026

    Gregorio Marchesini, Siyuan Liu, Lars Lindemann, and Dimos V Dimarogonas. Sampling-based planning under stl specifications: A forward invariance approach.IEEE Transactions on Automatic Control, 2026

    2026

  3. [1]

    MIT Press, 2025

    Lars Lindemann and Dimos V Dimarogonas.Formal Methods for Multi- Agent Feedback Control Systems. MIT Press, 2025

    2025

  4. [2]

    Motion planning with temporal-logic specifications: Progress and challenges.AI communications, 29(1):151– 162, 2015

    Erion Plaku and Sertac Karaman. Motion planning with temporal-logic specifications: Progress and challenges.AI communications, 29(1):151– 162, 2015

    2015

  5. [3]

    Syn- thesis for robots: Guarantees and feedback for robot behavior.Annual Review of Control, Robotics, and Autonomous Systems, 1(1):211–236, 2018

    Hadas Kress-Gazit, Morteza Lahijanian, and Vasumathi Raman. Syn- thesis for robots: Guarantees and feedback for robot behavior.Annual Review of Control, Robotics, and Autonomous Systems, 1(1):211–236, 2018

    2018

  6. [4]

    Power line inspection tasks with multi-aerial robot systems via signal temporal logic specifications.IEEE Robotics and Automation Letters, 6(2):4169–4176, 2021

    Giuseppe Silano, Tomas Baca, Robert Penicka, Davide Liuzza, and Martin Saska. Power line inspection tasks with multi-aerial robot systems via signal temporal logic specifications.IEEE Robotics and Automation Letters, 6(2):4169–4176, 2021

    2021

  7. [5]

    Temporal-logic-based reactive mission and motion planning.IEEE transactions on robotics, 25(6):1370–1381, 2009

    Hadas Kress-Gazit, Georgios E Fainekos, and George J Pappas. Temporal-logic-based reactive mission and motion planning.IEEE transactions on robotics, 25(6):1370–1381, 2009

    2009

  8. [6]

    Springer, 2017

    Calin Belta, Boyan Yordanov, and Ebru Aydin Gol.Formal methods for discrete-time dynamical systems, volume 89. Springer, 2017

    2017

Show all 51 references
  1. [7]

    Monitoring temporal properties of continuous signals

    Oded Maler and Dejan Nickovic. Monitoring temporal properties of continuous signals. InInternational symposium on formal techniques in real-time and fault-tolerant systems, pages 152–166. Springer, 2004

    2004

  2. [8]

    Formal methods for control synthesis: An optimization perspective.Annual Review of Control, Robotics, and Autonomous Systems, 2(1):115–140, 2019

    Calin Belta and Sadra Sadraddini. Formal methods for control synthesis: An optimization perspective.Annual Review of Control, Robotics, and Autonomous Systems, 2(1):115–140, 2019

    2019

  3. [9]

    Mixed-integer programming for signal temporal logic with fewer binary variables.IEEE Control Systems Letters, 6:2635–2640, 2022

    Vincent Kurtz and Hai Lin. Mixed-integer programming for signal temporal logic with fewer binary variables.IEEE Control Systems Letters, 6:2635–2640, 2022

    2022

  4. [10]

    Formal synthesis of control strategies for positive monotone systems.IEEE Transactions on Automatic Control, 64(2):480–495, 2018

    Sadra Sadraddini and Calin Belta. Formal synthesis of control strategies for positive monotone systems.IEEE Transactions on Automatic Control, 64(2):480–495, 2018

    2018

  5. [11]

    Reactive synthesis from signal temporal logic specifications

    Vasumathi Raman, Alexandre Donz ´e, Dorsa Sadigh, Richard M Murray, and Sanjit A Seshia. Reactive synthesis from signal temporal logic specifications. InProceedings of the 18th international conference on hybrid systems: Computation and control, pages 239–248, 2015

    2015

  6. [12]

    Control from signal temporal logic specifications with smooth cumula- tive quantitative semantics

    Iman Haghighi, Noushin Mehdipour, Ezio Bartocci, and Calin Belta. Control from signal temporal logic specifications with smooth cumula- tive quantitative semantics. In2019 IEEE 58th Conference on Decision and Control (CDC), pages 4361–4366. IEEE, 2019

    2019

  7. [13]

    Temporally robust multi-agent stl motion planning in continuous time

    Joris Verhagen, Lars Lindemann, and Jana Tumova. Temporally robust multi-agent stl motion planning in continuous time. In2024 American Control Conference (ACC), pages 251–258. IEEE, 2024

    2024

  8. [14]

    Stlccp: Efficient convex optimization-based framework for signal tem- poral logic specifications.IEEE Transactions on Automatic Control, 2025

    Yoshinari Takayama, Kazumune Hashimoto, and Toshiyuki Ohtsuka. Stlccp: Efficient convex optimization-based framework for signal tem- poral logic specifications.IEEE Transactions on Automatic Control, 2025

    2025

  9. [15]

    Successive convexification for tra- jectory optimization with continuous-time satisfaction of signal temporal logic specifications.arXiv preprint arXiv:2606.06896, 2026

    Samet Uzun and Behc ¸et Ac ¸ıkmes ¸e. Successive convexification for tra- jectory optimization with continuous-time satisfaction of signal temporal logic specifications.arXiv preprint arXiv:2606.06896, 2026

    2026 arXiv

  10. [16]

    Lexicographic minimum-violation motion planning using signal temporal logic.arXiv preprint arXiv:2604.20428, 2026

    Patrick Halder, Lothar Kiltz, Hannes Homburger, Johannes Reuter, and Matthias Althoff. Lexicographic minimum-violation motion planning using signal temporal logic.arXiv preprint arXiv:2604.20428, 2026

    2026 arXiv

  11. [17]

    Prescribed performance control for signal temporal logic specifications

    Lars Lindemann, Christos K Verginis, and Dimos V Dimarogonas. Prescribed performance control for signal temporal logic specifications. In2017 IEEE 56th Annual Conference on Decision and Control (CDC), pages 2997–3002. IEEE, 2017

    2017

  12. [18]

    Control barrier functions for signal temporal logic tasks.IEEE control systems letters, 3(1):96– 101, 2018

    Lars Lindemann and Dimos V Dimarogonas. Control barrier functions for signal temporal logic tasks.IEEE control systems letters, 3(1):96– 101, 2018

    2018

  13. [19]

    Sequen- tial control barrier functions for mobile robots with dynamic temporal logic specifications.Robotics and autonomous systems, 176:104681, 2024

    Ali Tevfik Buyukkocak, Derya Aksaray, and Yasin Yazıcıo ˘glu. Sequen- tial control barrier functions for mobile robots with dynamic temporal logic specifications.Robotics and autonomous systems, 176:104681, 2024

    2024

  14. [20]

    Resilient online planning for mobile robots with minimal relaxation of signal temporal logic specifications.IEEE Robotics and Automation Letters, 2025

    Ali Tevfik Buyukkocak and Derya Aksaray. Resilient online planning for mobile robots with minimal relaxation of signal temporal logic specifications.IEEE Robotics and Automation Letters, 2025

    2025

  15. [21]

    An operator-based approach to stl.arXiv preprint arXiv:2605.28092, 2026

    Panagiotis Rousseas and Dimos V Dimarogonas. An operator-based approach to stl.arXiv preprint arXiv:2605.28092, 2026

    2026 arXiv

  16. [22]

    Control barrier function based quadratic programs for safety critical systems.IEEE Transactions on Automatic Control, 62(8):3861–3876, 2016

    Aaron D Ames, Xiangru Xu, Jessy W Grizzle, and Paulo Tabuada. Control barrier function based quadratic programs for safety critical systems.IEEE Transactions on Automatic Control, 62(8):3861–3876, 2016

    2016

  17. [23]

    Shortest paths in graphs of convex sets.SIAM Journal on Optimization, 34(1):507–532, 2024

    Tobia Marcucci, Jack Umenberger, Pablo Parrilo, and Russ Tedrake. Shortest paths in graphs of convex sets.SIAM Journal on Optimization, 34(1):507–532, 2024

    2024

  18. [24]

    Motion planning around obstacles with convex optimization.Science robotics, 8(84):eadf7843, 2023

    Tobia Marcucci, Mark Petersen, David von Wrangel, and Russ Tedrake. Motion planning around obstacles with convex optimization.Science robotics, 8(84):eadf7843, 2023

    2023

  19. [25]

    Admm-based continuous trajectory optimization in graphs of convex sets.arXiv preprint arXiv:2603.11335, 2026

    Lukas Pries, Jon Arrizabalaga, Zachary Manchester, and Markus Ryll. Admm-based continuous trajectory optimization in graphs of convex sets.arXiv preprint arXiv:2603.11335, 2026

    2026

  20. [26]

    Temporal logic motion planning with convex optimization via graphs of convex sets.IEEE Transactions on Robotics, 39(5):3791–3804, 2023

    Vince Kurtz and Hai Lin. Temporal logic motion planning with convex optimization via graphs of convex sets.IEEE Transactions on Robotics, 39(5):3791–3804, 2023

    2023

  21. [27]

    Continuous-time control synthesis under nested signal temporal logic specifications.IEEE Transactions on Robotics, 40:2272–2286, 2024

    Pian Yu, Xiao Tan, and Dimos V Dimarogonas. Continuous-time control synthesis under nested signal temporal logic specifications.IEEE Transactions on Robotics, 40:2272–2286, 2024

    2024

  22. [30]

    A framework for motion planning with temporal logic precedence specifications via augmented graphs of convex sets.arXiv preprint arXiv:2606.00842, 2026

    Shilin You, Gael Luna, and Tyler H Summers. A framework for motion planning with temporal logic precedence specifications via augmented graphs of convex sets.arXiv preprint arXiv:2606.00842, 2026

    2026 arXiv

  23. [31]

    Discontinuous dynamical systems.IEEE Control systems magazine, 28(3):36–73, 2008

    Jorge Cortes. Discontinuous dynamical systems.IEEE Control systems magazine, 28(3):36–73, 2008

    2008

  24. [32]

    Differential flatness of mechanical control systems: A catalog of prototype systems

    Richard M Murray, Muruhan Rathinam, and Willem Sluis. Differential flatness of mechanical control systems: A catalog of prototype systems. InASME international mechanical engineering congress and exposition, pages 349–357. San Francisco CA, 1995

    1995

  25. [33]

    Flat- ness and defect of non-linear systems: introductory theory and examples

    Michel Fliess, Jean L ´evine, Philippe Martin, and Pierre Rouchon. Flat- ness and defect of non-linear systems: introductory theory and examples. International journal of control, 61(6):1327–1361, 1995

    1995

  26. [34]

    Bezier reachable polytopes: Efficient certificates for robust motion planning with layered architec- tures

    Noel Csomay-Shanklin and Aaron D Ames. Bezier reachable polytopes: Efficient certificates for robust motion planning with layered architec- tures. In2025 American Control Conference (ACC), pages 5052–5059. IEEE, 2025

    2025

  27. [35]

    Safety-critical control for autonomous systems: Control barrier functions via reduced- order models.Annual Reviews in Control, 57:100947, 2024

    Max H Cohen, Tamas G Molnar, and Aaron D Ames. Safety-critical control for autonomous systems: Control barrier functions via reduced- order models.Annual Reviews in Control, 57:100947, 2024

    2024

  28. [36]

    Convex programming for disjunctive convex optimization.Mathematical Programming, 86(3):595–614, 1999

    Sebasti ´an Ceria and Jo ˜ao Soares. Convex programming for disjunctive convex optimization.Mathematical Programming, 86(3):595–614, 1999. JOURNAL OF LATEX CLASS FILES, VOL. 18, NO. 9, SEPTEMBER 2020 17

    1999

  29. [37]

    A unified and scalable method for optimization over graphs of convex sets.arXiv preprint arXiv:2510.20184, 2025

    Tobia Marcucci. A unified and scalable method for optimization over graphs of convex sets.arXiv preprint arXiv:2510.20184, 2025

    2025

  30. [38]

    Trajectory planning

    Luigi Biagiotti and Claudio Melchiorri. Trajectory planning. In Trajectory Planning for Automatic Machines and Robots, pages 1–12. Springer, 2008

    2008

  31. [39]

    Barrier function-based model predictive control under signal temporal logic specifications

    Maria Charitidou and Dimos V Dimarogonas. Barrier function-based model predictive control under signal temporal logic specifications. In 2021 European Control Conference (ECC), pages 734–739. IEEE, 2021

    2021

  32. [40]

    Set containment characterization.Journal of Global Optimization, 24(4):473–480, 2002

    OL Mangasarian. Set containment characterization.Journal of Global Optimization, 24(4):473–480, 2002

    2002

  33. [41]

    Linear encodings for polytope containment problems

    Sadra Sadraddini and Russ Tedrake. Linear encodings for polytope containment problems. In2019 IEEE 58th conference on decision and control (CDC), pages 4367–4372. IEEE, 2019

    2019

  34. [42]

    Certified polyhedral decompositions of collision-free configuration space.The International Journal of Robotics Research, 43(9):1322–1341, 2024

    Hongkai Dai, Alexandre Amice, Peter Werner, Annan Zhang, and Russ Tedrake. Certified polyhedral decompositions of collision-free configuration space.The International Journal of Robotics Research, 43(9):1322–1341, 2024

    2024

  35. [43]

    Fast iterative region inflation for computing large 2-d/3-d convex regions of obstacle- free space.IEEE Transactions on Robotics, 2025

    Qianhao Wang, Zhepei Wang, Mingyang Wang, Jialin Ji, Zhichao Han, Tianyue Wu, Rui Jin, Yuman Gao, Chao Xu, and Fei Gao. Fast iterative region inflation for computing large 2-d/3-d convex regions of obstacle- free space.IEEE Transactions on Robotics, 2025

    2025

  36. [44]

    Superfast configuration-space convex set computation on gpus for online motion planning.arXiv preprint arXiv:2504.10783, 2025

    Peter Werner, Richard Cheng, Tom Stewart, Russ Tedrake, and Daniela Rus. Superfast configuration-space convex set computation on gpus for online motion planning.arXiv preprint arXiv:2504.10783, 2025

    2025 arXiv

  37. [45]

    Multi-rate planning and control of uncertain nonlinear systems: Model predictive control and control lyapunov functions

    Noel Csomay-Shanklin, Andrew J Taylor, Ugo Rosolia, and Aaron D Ames. Multi-rate planning and control of uncertain nonlinear systems: Model predictive control and control lyapunov functions. In2022 IEEE 61st Conference on Decision and Control (CDC), pages 3732–3739. IEEE, 2022

    2022

  38. [46]

    A nonsmooth approach to controller synthesis for boolean specifications.IEEE Transactions on Automatic Control, 66(11):5160–5174, 2020

    Paul Glotfelter, Jorge Cort ´es, and Magnus Egerstedt. A nonsmooth approach to controller synthesis for boolean specifications.IEEE Transactions on Automatic Control, 66(11):5160–5174, 2020

    2020

  39. [47]

    Safe and dy- namically feasible motion planning using control lyapunov and barrier functions.IEEE Transactions on Robotics, 41:6440–6459, 2025

    Pol Mestres, Carlos Nieto-Granda, and Jorge Cort ´es. Safe and dy- namically feasible motion planning using control lyapunov and barrier functions.IEEE Transactions on Robotics, 41:6440–6459, 2025

    2025

  40. [48]

    High- order barrier functions: Robustness, safety, and performance-critical control.IEEE Transactions on Automatic Control, 67(6):3021–3028, 2021

    Xiao Tan, Wenceslao Shaw Cortez, and Dimos V Dimarogonas. High- order barrier functions: Robustness, safety, and performance-critical control.IEEE Transactions on Automatic Control, 67(6):3021–3028, 2021

    2021

  41. [49]

    High-order control barrier functions.IEEE Transactions on Automatic Control, 67(7):3655–3662, 2021

    Wei Xiao and Calin Belta. High-order control barrier functions.IEEE Transactions on Automatic Control, 67(7):3655–3662, 2021

    2021

  42. [50]

    Safe backstepping with control barrier functions

    Andrew J Taylor, Pio Ong, Tamas G Molnar, and Aaron D Ames. Safe backstepping with control barrier functions. In2022 IEEE 61st Conference on Decision and Control (CDC), pages 5775–5782. IEEE, 2022

    2022

  43. [51]

    Cambridge university press, 2004

    Stephen P Boyd and Lieven Vandenberghe.Convex optimization. Cambridge university press, 2004

    2004

Pith tools

Reviewed August 1, 2026 · model on record in the stance chip above.