Unifying Complementarity Constraints and Control Barrier Functions for Safe Whole-Body Robot Control

Florian T. Pokorny; Luis F.C. Figueredo; Nilanjan Chakraborty; Rafael I. Cabral Muchacho; Riddhiman Laha

REVIEW 2 major objections 5 minor 37 references

Unifying Complementarity Constraints and Control Barrier Functions for Safe Whole-Body Robot Control

T0 review · 2 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read This paper proves that complementarity-based and control-barrier-function quadratic programs produce the same joint-velocity commands for sampled-data first-order whole-body robot control when margins and linear barrier rates are matched.

desk verdict Correct core equivalence between LCQP and CBF-QP, but the paper asserts a false pseudoinverse identity that blurs which controller is actually being compared; needs a focused revision. read the letter →

arxiv 2504.17647 v2 pith:XIUGPAHP submitted 2025-04-24 cs.RO cs.SYeess.SY

Rafael I. Cabral Muchacho , Riddhiman Laha , Florian T. Pokorny , Luis F.C. Figueredo , Nilanjan Chakraborty This is my paper · ORCID

classification cs.ROcs.SYeess.SY

keywords complementarityconstraintscontrolbarrierfunctionswhole-bodyrobotcollisionavoidancequadraticprogrammingsampled-dataconvexoptimizationequivalenceproof

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

This paper proves that two established ways of making a velocity-controlled robot avoid obstacles—linear-complementarity constrained quadratic programs and control-barrier-function quadratic programs—produce the same joint-velocity command at every sample time, provided their safety margins are matched and the barrier decay rate is the linear function $\alpha(s)=s/\tau$. The two frameworks grew up separately, yet for sampled-data first-order systems they are not competing designs: each is a minimum-norm correction to a desired velocity, projected onto the same linear safety constraints. The proof goes through a general theorem about quadratic programs: minimizing $\tfrac{1}{2}\|x\|^2$ over $Ax-b\ge 0$ has the same optimum as minimizing it over the complementarity set $x=G(A)\lambda$, $0\le\lambda\perp AH\lambda-b\ge 0$, when the rows of $A$ are nonzero. A simulation of a 3-DoF planar arm confirms the two controllers trace identical paths to solver precision. If the proof holds, safety margins, sampling-time conditions, and algorithmic improvements can be transferred in both directions between the two frameworks.

What carries the argument

The load-bearing object is the row-to-column operator $G$, defined by $G(A)=[a_1^{\dagger}\ \dots\ a_m^{\dagger}]$, where $a_i^{\dagger}=a_i^T/\|a_i\|^2$ is the Moore–Penrose inverse of the $i$-th row of $A$. Because these row pseudo-inverses span the row space of $A$, the matrix $H=G(A)$ lets the complementarity variable $\lambda$ reproduce exactly the direction any KKT multiplier would take, turning the perpendicularity condition into the same complementary-slackness condition as the convex CBF QP. The equality of the two formulations is completed by the parameter mapping $\alpha_i(x)=x/\tau$ and $\delta_{\mathrm{LC}}=\delta_{\mathrm{CBF}}$, which makes the affine constraint $Ax-b\ge 0$ identical in both formulations; equation (41) states this condition.

What would settle it

Run the two controllers on a sampled-data velocity-controlled robot with a nonlinear class-$\kappa$ function, for instance $\alpha(s)=2s$; if the joint-velocity commands still coincide exactly, the linear-$\alpha$ condition is not actually necessary, while if they differ, the unification holds only inside the stated scope. A more direct check is to solve the two general QPs of Theorem 1 for a small matrix $A$ with nonzero rows, such as $A=\begin{bmatrix}1&1\\1&-1\end{bmatrix}$ and $b=[1,\,1]^T$, to machine precision and compare the minimizers, which the theorem predicts are identical.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is an exact equivalence theorem. For any matrix $A\in\mathbb{R}^{m\times n}$ with nonzero rows and any offset $b$, the convex QP $\min \tfrac{1}{2}\|x\|^2$ s.t. $Ax-b\ge 0$ and the complementarity-constrained QP $\min \tfrac{1}{2}\|x\|^2$ s.t. $x=H\lambda$, $0\le\lambda\perp AH\lambda-b\ge 0$, with $H=G(A)$ built from Moore–Penrose inverses of the rows of $A$, have the same optimal solutions. The proof shows $X_1\subseteq X_0$, then uses KKT stationarity to show every optimizer of the first problem lies in the row space of $A$, and since $H$ maps $\mathbb{R}^m$ onto that row space, that optimizer is feasible for the complementarity problem; the complementary-slackness condition lines up with the perpendicularity condition. When the CBF class-$\kappa$ function is chosen as $\alpha_i(s)=s/\tau$ and the margins are equal, the CBF-QP and the LCQP are exactly these two problems, so their solutions coincide. The paper frames the result as a unification: one geometric statement covers both methods, and the active multiplier in each formulation plays the role of the push needed to keep the control inside the safe polyhedron.

Load-bearing premise

The equivalence rests on the control-barrier 'class-$\kappa$' function—the function that sets how fast the safety margin is enforced—being exactly the linear map $\alpha(s)=s/\tau$, and on the two safety margins being equal; with the nonlinear decay functions common in CBF practice, the two QPs are no longer the same problem and the theorem does not cover their commands.

Editorial extensions

If this is right

A complementarity-based controller inherits the sampled-data safety guarantees and Lipschitz-based margin design developed for CBFs, so its physical safety margin and time step can be certified rather than tuned ad hoc.
A CBF-QP gains access to complementarity solvers and to planning formulations that treat avoidance as switched contact-like constraints, which may simplify whole-body planning.
In the matched-parameter setting the two controllers can be swapped freely in deployment: the numerical experiment shows command differences at solver tolerance, with a maximum error of $1.5\times10^{-6}$.
The convexity corollary means the linear complementarity safe-control problem is convex despite being stated with complementarity constraints, so uniqueness and sufficiency results carry over.
Both frameworks are minimum-norm projections onto one polyhedron, so any algorithmic acceleration for one projection formulation transfers to the other.

Reading between the lines

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

The KKT proof suggests an extension the paper leaves open: any monotone barrier decay function may correspond to a modified complementarity condition with $\lambda$ weighted by a nonlinearity, so the unification could survive beyond linear $\alpha$.
If the equivalence extends to acceleration-level control, complementarity formulations of contact-rich manipulation and higher-order CBFs may turn out to be the same projection with different constraint derivatives; a numerical comparison on a torque-controlled manipulator would test this.
The convexity result implies that reactive whole-body avoidance has a convex solution set under velocity control, which may simplify real-time implementations on resource-constrained robots, though the paper does not test deployment.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The main result is real but narrower than the packaging. The paper is the first, as far as the cited literature goes, to state the equivalence between the complementarity LCQP controller and the CBF-QP controller for first-order sampled-data systems, and the core theorem is correct. Theorem 1 is essentially the KKT/LCP duality for a convex QP, but the identification of the two controller families with the specific parameter mapping in Eq. (41) is new and useful. The proof is clean, and the small numerical check (max error 1.5e-6) matches what the theorem predicts. Credit where due: this gives two communities a concrete dictionary between solvers and robustness results.

The load-bearing problem is Eq. (15). It asserts J†_{c,i} n_i = (n_i^T J_{c,i})†, which is false in general (a 2x2 diagonal example shows it). The controller in Eq. (15) is therefore not the same as the controller in Eq. (17)-(18), whose columns are the row pseudoinverses. Theorem 1 analyzes the latter. The error is in the derivation, not in the theorem: you can define the complementarity controller directly with G(∂h/∂q), no pseudoinverse identity needed. But as written, the paper gives two different parametrizations and calls them equal. This has to be fixed, and the numerics need to state which one fmincon actually solved.

Other soft spots are minor. Corollary 1 says ALC G(ALC) is positive semi-definite; the matrix is nonsymmetric. It is PSD in the monotone-LCP sense (AG(A)=AA^T D with D positive), so the claim is salvageable, but needs a definition or reference. The scope restriction is more important than the prose admits: the mapping (41) only works for linear class-κ α(s)=s/τ with matched margins. They do state it, but the abstract and conclusion lean on 'unifying' the methodologies. For nonlinear class-κ the two QPs are not equivalent, and the paper should say that in the headline, not just in the proof.

My take: this deserves a serious referee and can be accepted after revision. The core equivalence is correct and useful; the fix is to remove the false identity, clarify which controller is being solved, and tighten the scope claims.

Referee Report

2 major / 5 minor

Summary. The manuscript studies two reactive safety filters for velocity-controlled manipulators: a complementarity-constrained QP, in which a nonnegative multiplier activates a correction when the predicted distance falls below a threshold, and a CBF-QP enforcing sampled-data barrier conditions. After rewriting both as abstract QPs over a variable x with data A and b, the paper proves (Theorem 1) that the problem min (1/2)||x||^2 subject to Ax-b >= 0 and the complementarity-parametrized problem min (1/2)||x||^2 subject to x = G(A)lambda, 0 <= lambda perp A G(A)lambda - b >= 0 have identical optimal solutions, where G(A) is the row-pseudoinverse operator. The proof uses KKT conditions and the row-space relation between A and H=G(A). A single-constraint version is given first, and a numerical example on a 3-DoF planar manipulator reports agreement between the two controllers to within solver tolerance.

Significance. The main theorem is a correct and clean equivalence between a linearly constrained QP and an LCP-parametrized QP under the row-pseudoinverse map H=G(A); the KKT proof is sound, and the numerical experiment with a 3-DoF planar robot supports the predicted agreement. If the scope restrictions are stated accurately, the result is a useful theoretical bridge between the complementarity and CBF communities, with concrete downstream benefits such as transferring sampled-data margin guarantees. The main caveats are that the equivalence is established only for the G-parametrized complementarity controller, not for the J† n parametrization introduced in Eq. (15), and only for the linear class-kappa function alpha(s)=s/tau with matched thresholds. The paper's broad title and framing should be tempered to reflect this scope.

major comments (2)

[Sec. IV.A, Eq. (15)] The asserted identity J†_{c,i} n_i = (n_i^T J_{c,i})† is false for a general contact Jacobian. For example, with J=diag(1,2) and n=(1,1)/sqrt(2), J† n=(0.707,0.354)^T while (n^T J)†=(0.283,0.566)^T. Consequently Eq. (15) and Eq. (17) define different control laws, and Theorem 1 applies to the G-parametrized set (18), not to the controller defined by Eq. (15). The problem statement (19) uses U_LC from (18), so the reported numerical experiment should be interpreted as validating the G-parametrized controller. The paper must either define the complementarity controller directly via G(partial h/partial q) and remove the false identity, or explicitly restrict the unification claim to that parametrization and state the limitation.
[Sec. V.A, Eqs. (28)-(32)] The reduction lambda* = argmin_lambda ||J†_{c} n lambda||^2 = argmin_lambda ||lambda||^2 is valid only when ||J†_{c} n||=1, which does not hold for a general full-row-rank contact Jacobian. For the G-parametrization x=(n^T J_c)† lambda used in Theorem 1, one has ||x||^2=lambda^2/||n^T J_c||^2, so minimizing over lambda is equivalent to minimizing lambda^2; this is the correct version of the single-constraint argument. As written, the single-constraint proof inherits the error from Eq. (15) and should be rewritten around the row-pseudoinverse parametrization.

minor comments (5)

[Sec. V.C, Corollary 1] The claimed convexity of U_LC does not follow from the statement that A_LC G(A_LC) is positive semidefinite: A G(A) is not symmetric in general and need not satisfy z^T A G(A) z >= 0 for all z. For example, A=[[1,0],[0.1,0.1]] gives A G(A)=[[1,5],[0.1,1]], and z=(1,-1) yields z^T A G(A) z = -3.1. The corollary needs a proof or should be removed.
[Sec. V, Theorem 1] The theorem statement should include the assumption that X0 is nonempty, since the KKT argument applies only to feasible problems; the control application presumably guarantees this, but it should be stated explicitly.
[Sec. IV.B, Eq. (23)] Please clarify the domain of the class-kappa function alpha_i when h_i - delta_CBF,i is negative, since class-kappa functions are usually defined on [0,a) and the sampled-data condition in Eq. (23) evaluates them at possibly negative arguments.
[Sec. VI.A] Please state explicitly whether fmincon solves the complementarity problem in the form (19)-(18) with G(partial h/partial q), or a formulation based on Eq. (15); the numerical result reported in Eq. (48) is otherwise not tied to the controller analyzed in Theorem 1.
[Throughout] There are minor language and reference typos, e.g., 'casted' in Sec. II and 'nommonotone' in Ref. [19]; these should be corrected in the final version.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: Theorem 1 is an independent convex-optimization result with explicit parameter matching, not a self-referential derivation.

full rationale

No significant circularity. Section V.B proves Theorem 1 for the general forms X0={x | Ax−b≥0} and X1={x=Hλ | 0≤λ⊥AHλ−b≥0}, with A=∂h/∂q, b=b_LC=b_CBF, and H=G(A). The equality b_CBF=b_LC is not a hidden fit; it is the explicit parameter choice α_i(x)=x/τ and δ_CBF=δ_LC stated in Eq. (41), and the paper flags that nonlinear class-κ functions are outside the equivalence. The proof is self-contained: it uses KKT conditions from [36] (external textbook) to show any X0-minimizer x*=A^Tλ* can be written as Hλ' with λ'_i=||a_i||^2λ*_i and satisfies complementary slackness in X1, and X1⊆X0 then gives equality of minima. No self-citation is load-bearing: [5]-[7] are background for complementarity methods, and the proof cites Boyd & Vandenberghe, not the authors' own results. Numerical validation is an external solver comparison. The only issue noticed is non-circular: Eq. (15) claims J†_{c,i}n_i=(n_i^T J_{c,i})†, which is false in general, so the controller parametrized in (15) is not automatically the one analyzed as (18)/(43); that is a correctness/math risk, not a reduction of the conclusion to its premises, and it does not raise the circularity score.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central proof rests on standard convex optimization (KKT conditions) and on the explicit domain assumptions of nonzero C^1 constraint gradients and feasible QPs. The only hand-chosen quantity is the linear class-κ function, which the paper explicitly states as the scope condition for the equivalence. No invented entities or fitted-to-data parameters appear.

free parameters (1)

CBF class-κ function α = α(s) = s/τ
Chosen so that the CBF constraint (23) becomes identical to the complementarity look-ahead constraint (13); the equivalence result depends on this specific linear choice.

assumptions (4)

standard math KKT conditions are necessary and sufficient for the convex QP (44).
Used in the proof of Theorem 1; holds because the objective is strictly convex and the constraints are linear.
domain assumption The feasible sets X0 and X1 are nonempty at each sample.
The theorem presupposes an optimal solution; the paper does not analyze infeasible states or collision-inevitable configurations.
domain assumption Constraint gradients satisfy ||∂h/∂q|| ≠ 0 and h is C^1_loc along trajectories.
Needed for the Moore-Penrose row inverses; Remark 1 handles non-convex geometry by ball decompositions.
domain assumption δ_CBF = δ_LC is an admissible margin for the sampled-data CBF guarantee of [10].
The equivalence proof only needs the same numerical margin; the paper's discussion of transferring robustness guarantees additionally assumes this margin satisfies the Lipschitz-based conditions of [10], which is not verified.

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Pith. "Pith review of Unifying Complementarity Constraints and Control Barrier Functions for Safe Whole-Body Robot Control." pith.science (2026). https://pith.science/paper/XIUGPAHP

@misc{pith2026250417647,
  author       = {Pith},
  title        = {Pith review of: Unifying Complementarity Constraints and Control Barrier Functions for Safe Whole-Body Robot Control},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XIUGPAHP}},
  note         = {Machine review of arXiv:2504.17647}
}

read the original abstract

Safety-critical whole-body robot control demands reactive methods that ensure collision avoidance in real-time. Complementarity constraints and control barrier functions (CBF) have emerged as core tools for ensuring such safety constraints, and each represents a well-developed field. Despite addressing similar problems, their connection remains largely unexplored. This paper bridges this gap by formally proving the equivalence between these two methodologies for sampled-data, first-order systems, considering both single and multiple constraint scenarios. By demonstrating this equivalence, we provide a unified perspective on these techniques. This unification has theoretical and practical implications, facilitating the cross-application of robustness guarantees and algorithmic improvements between complementarity and CBF frameworks. We discuss these synergistic benefits and motivate future work in the comparison of the methods in more general cases.

Figures

Figures reproduced from arXiv: 2504.17647 by the authors.

**Figure 2.** The safety constraint h ′ ≥ 0 (top) and the solution error e (bottom) are plotted at each time step of the simulation. We use quadprog to solve the CBF-QP formulation and fmincon to solve the complementarity problem in MATLAB (2024b), relying on standard parameters and convergence tolerances of the solvers. Since the obstacle is a single disk, three scalar constraints are introduced, each enforcing collision avoidan… view at source ↗

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Reference graph

Works this paper leans on

37 extracted references · 27 canonical work pages

[1]

A safety-aware kin- odynamic architecture for human-robot collaboration,

A. Pupa, M. Arrfou, G. Andreoni, and C. Secchi, “A safety-aware kin- odynamic architecture for human-robot collaboration,” IEEE Robotics and Automation Letters , vol. 6, no. 3, pp. 4465–4471, 2021

work page 2021
[2]

S*: On safe and time efficient robot motion planning,

R. Laha, W. Wu, R. Sun, N. Mansfeld, L. F. Figueredo, and S. Haddadin, “S*: On safe and time efficient robot motion planning,” in 2023 IEEE International Conference on Robotics and Automation (ICRA) . IEEE, 2023, pp. 12 758–12 764

work page 2023
[3]

Pro- mind*: Proximity and reactivity optimisation of robot motion to tune safety limits, human stress, and productivity in industrial settings,

M. Lagomarsino, M. Lorenzini, E. De Momi, and A. Ajoudani, “Pro- mind*: Proximity and reactivity optimisation of robot motion to tune safety limits, human stress, and productivity in industrial settings,” IEEE Transactions on Robotics , 2025

work page 2025
[4]

Complementarity-based dy- namic simulation for kinodynamic motion planning,

N. Chakraborty, S. Akella, and J. Trinkle, “Complementarity-based dy- namic simulation for kinodynamic motion planning,” in 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems . IEEE, 2009, pp. 787–794

work page 2009
[5]

Task space planning with complementarity constraint-based obstacle avoidance,

A. Sinha, A. Sarker, and N. Chakraborty, “Task space planning with complementarity constraint-based obstacle avoidance,” in International Design Engineering Technical Conferences and Computers and Infor- mation in Engineering Conference , vol. 85451. American Society of Mechanical Engineers, 2021, p. V08BT08A012

work page 2021
[6]

Oc3: A reactive velocity level motion planner with complementarity constraint-based obstacle avoid- ance for mobile robots,

A. Sinha, R. Laha, and N. Chakraborty, “Oc3: A reactive velocity level motion planner with complementarity constraint-based obstacle avoid- ance for mobile robots,” in 2023 IEEE 19th International Conference on Automation Science and Engineering (CASE) . IEEE, 2023, pp. 1–8

work page 2023
[7]

On the synthesis of reactive collision-free whole- body robot motions: A complementarity-based approach,

H. Yao, R. Laha, A. Sinha, J. Hall, L. F. Figueredo, N. Chakraborty, and S. Haddadin, “On the synthesis of reactive collision-free whole- body robot motions: A complementarity-based approach,” in IEEE International Conference on Robotics and Automation (ICRA) , 2025

work page 2025
[8]

Control barrier function based quadratic programs for safety critical systems,

A. D. Ames, X. Xu, J. W. Grizzle, and P. Tabuada, “Control barrier function based quadratic programs for safety critical systems,” IEEE Transactions on Automatic Control, vol. 62, no. 8, pp. 3861–3876, 2016

2016

Show all 37 references

[9]

Control barrier functions: Theory and applications,

A. D. Ames, S. Coogan, M. Egerstedt, G. Notomista, K. Sreenath, and P. Tabuada, “Control barrier functions: Theory and applications,” in2019 18th European control conference (ECC) . Ieee, 2019, pp. 3420–3431

2019
[10]

Control barrier functions in sampled-data systems,

J. Breeden, K. Garg, and D. Panagou, “Control barrier functions in sampled-data systems,” IEEE Control Systems Letters , vol. 6, pp. 367– 372, 2021

2021
[11]

Real-time obstacle avoidance for manipulators and mobile robots,

O. Khatib, “Real-time obstacle avoidance for manipulators and mobile robots,” The international journal of robotics research, vol. 5, no. 1, pp. 90–98, 1986

1986
[12]

Rimon, Exact robot navigation using artificial potential functions

E. Rimon, Exact robot navigation using artificial potential functions . Yale University, 1990

1990
[13]

Aubin, Viability Theory

J.-P. Aubin, Viability Theory . Cambridge, MA, USA: Birkh ¨auser Boston, 1991

1991
[14]

A direct method for trajectory optimization of rigid bodies through contact,

M. Posa, C. Cantu, and R. Tedrake, “A direct method for trajectory optimization of rigid bodies through contact,” The International Journal of Robotics Research , vol. 33, no. 1, pp. 69–81, 2014

2014
[15]

Simultaneous tra- jectory optimization and contact selection for multi-modal manipulation planning,

M. Zhang, D. Jha, A. Raghunathan, and K. Hauser, “Simultaneous tra- jectory optimization and contact selection for multi-modal manipulation planning,” in Robotics science and systems , 2023

2023
[16]

Simultaneous trajectory optimization and contact selection for contact-rich manipula- tion with high-fidelity geometry,

M. Zhang, D. K. Jha, A. U. Raghunathan, and K. Hauser, “Simultaneous trajectory optimization and contact selection for contact-rich manipula- tion with high-fidelity geometry,” IEEE Transactions on Robotics, 2025

2025
[17]

Contact models in robotics: a comparative analysis,

Q. Le Lidec, W. Jallet, L. Montaut, I. Laptev, C. Schmid, and J. Car- pentier, “Contact models in robotics: a comparative analysis,” IEEE Transactions on Robotics , 2024

2024
[18]

A contribution to the analysis of unilateral contact problems with friction,

E. Mitsopoulou and I. Doudoumis, “A contribution to the analysis of unilateral contact problems with friction,” Solid Mechanics Archives , vol. 12, no. 3, pp. 165–186, 1987

1987
[19]

The path solver: a nommonotone sta- bilization scheme for mixed complementarity problems,

S. P. Dirkse and M. C. Ferris, “The path solver: a nommonotone sta- bilization scheme for mixed complementarity problems,” Optimization methods and software , vol. 5, no. 2, pp. 123–156, 1995

1995
[20]

A gauss-seidel like algorithm to solve frictional contact problems,

F. Jourdan, P. Alart, and M. Jean, “A gauss-seidel like algorithm to solve frictional contact problems,” Computer methods in applied mechanics and engineering, vol. 155, no. 1-2, pp. 31–47, 1998

1998
[21]

Numerical methods for linear complementarity problems in physics-based animation,

K. Erleben, “Numerical methods for linear complementarity problems in physics-based animation,” in Acm Siggraph 2013 Courses , 2013, pp. 1–42

2013
[22]

Safety barrier functions for human-robot interaction with industrial manipula- tors,

C. T. Landi, F. Ferraguti, S. Costi, M. Bonf `e, and C. Secchi, “Safety barrier functions for human-robot interaction with industrial manipula- tors,” in 2019 18th European Control Conference (ECC) . IEEE, 2019, pp. 2565–2570

2019
[23]

Energy based control barrier functions for robotic manipulators with large safety constraints,

Y . Choudhary and S. Kolathaya, “Energy based control barrier functions for robotic manipulators with large safety constraints,” in2022 European Control Conference (ECC). IEEE, 2022, pp. 1328–1335

2022
[24]

Safety-critical manipulation for collision-free food preparation,

A. Singletary, W. Guffey, T. G. Molnar, R. Sinnet, and A. D. Ames, “Safety-critical manipulation for collision-free food preparation,” IEEE Robotics and Automation Letters, vol. 7, no. 4, pp. 10 954–10 961, 2022

2022
[25]

Dual-mode human-robot collaboration with guar- anteed safety using time-varying zeroing control barrier functions and quadratic program,

K. Shi and G. Hu, “Dual-mode human-robot collaboration with guar- anteed safety using time-varying zeroing control barrier functions and quadratic program,” IEEE Robotics and Automation Letters, vol. 8, no. 9, pp. 5902–5909, 2023

2023
[26]

Safety-guaranteed and task-consistent human-robot interaction using high-order time-varying control barrier functions and quadratic programs,

S. K and G. Hu, “Safety-guaranteed and task-consistent human-robot interaction using high-order time-varying control barrier functions and quadratic programs,” IEEE Robotics and Automation Letters , vol. 9, no. 1, pp. 547–554, 2023

2023
[27]

Real- time safety and control of robotic manipulators with torque saturation in operational space,

M. A. Murtaza, S. Aguilera, V . Azimi, and S. Hutchinson, “Real- time safety and control of robotic manipulators with torque saturation in operational space,” in 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) . IEEE, 2021, pp. 702–708

2021
[28]

Safety com- pliant control for robotic manipulator with task and input constraints,

M. A. Murtaza, S. Aguilera, M. Waqas, and S. Hutchinson, “Safety com- pliant control for robotic manipulator with task and input constraints,” IEEE Robotics and Automation Letters, vol. 7, no. 4, pp. 10 659–10 664, 2022

2022
[29]

Safety and efficiency in robotics: The control barrier functions approach,

F. Ferraguti, C. T. Landi, A. Singletary, H.-C. Lin, A. Ames, C. Secchi, and M. Bonfe, “Safety and efficiency in robotics: The control barrier functions approach,” IEEE Robotics & Automation Magazine , vol. 29, no. 3, pp. 139–151, 2022

2022
[30]

Representing robot geometry as distance fields: Applications to whole-body manipulation,

Y . Li, Y . Zhang, A. Razmjoo, and S. Calinon, “Representing robot geometry as distance fields: Applications to whole-body manipulation,” in Proc. IEEE Intl Conf. on Robotics and Automation (ICRA) , 2024, pp. 15 351–15 357

2024
[31]

Regularized deep signed distance fields for reactive motion generation,

P. Liu, K. Zhang, D. Tateo, S. Jauhri, J. Peters, and G. Chalvatzaki, “Regularized deep signed distance fields for reactive motion generation,” in 2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2022, pp. 6673–6680

2022
[32]

Adaptive distance functions via kelvin transformation,

R. I. C. Muchacho and F. T. Pokorny, “Adaptive distance functions via kelvin transformation,” arXiv preprint arXiv:2406.03200 , 2024

2024 arXiv
[33]

Complementarity problem formulation of three- dimensional frictional contact,

B. M. Kwak, “Complementarity problem formulation of three- dimensional frictional contact,” 1991

1991
[34]

Complementarity formulations and exis- tence of solutions of dynamic multi-rigid-body contact problems with coulomb friction,

J.-S. Pang and J. C. Trinkle, “Complementarity formulations and exis- tence of solutions of dynamic multi-rigid-body contact problems with coulomb friction,” Mathematical programming, vol. 73, no. 2, pp. 199– 226, 1996

1996
[35]

Active constraints using vector field inequalities for surgical robots,

M. M. Marinho, B. V . Adorno, K. Harada, and M. Mitsuishi, “Active constraints using vector field inequalities for surgical robots,” in 2018 IEEE International Conference on Robotics and Automation (ICRA) . IEEE, 2018, pp. 5364–5371

2018
[36]

S. P. Boyd and L. Vandenberghe, Convex optimization . Cambridge university press, 2004

2004
[37]

The linear complimentarity problem, sufficient matrices, and the criss-cross method,

D. den Hertog, C. Roos, and T. Terlaky, “The linear complimentarity problem, sufficient matrices, and the criss-cross method,”Linear Algebra and Its Applications , vol. 187, pp. 1–14, 1993

1993

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Reviewed August 16, 2026 · model on record in the stance chip above.

[1] [1]

A safety-aware kin- odynamic architecture for human-robot collaboration,

A. Pupa, M. Arrfou, G. Andreoni, and C. Secchi, “A safety-aware kin- odynamic architecture for human-robot collaboration,” IEEE Robotics and Automation Letters , vol. 6, no. 3, pp. 4465–4471, 2021

work page 2021

[2] [2]

S*: On safe and time efficient robot motion planning,

R. Laha, W. Wu, R. Sun, N. Mansfeld, L. F. Figueredo, and S. Haddadin, “S*: On safe and time efficient robot motion planning,” in 2023 IEEE International Conference on Robotics and Automation (ICRA) . IEEE, 2023, pp. 12 758–12 764

work page 2023

[3] [3]

Pro- mind*: Proximity and reactivity optimisation of robot motion to tune safety limits, human stress, and productivity in industrial settings,

M. Lagomarsino, M. Lorenzini, E. De Momi, and A. Ajoudani, “Pro- mind*: Proximity and reactivity optimisation of robot motion to tune safety limits, human stress, and productivity in industrial settings,” IEEE Transactions on Robotics , 2025

work page 2025

[4] [4]

Complementarity-based dy- namic simulation for kinodynamic motion planning,

N. Chakraborty, S. Akella, and J. Trinkle, “Complementarity-based dy- namic simulation for kinodynamic motion planning,” in 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems . IEEE, 2009, pp. 787–794

work page 2009

[5] [5]

Task space planning with complementarity constraint-based obstacle avoidance,

A. Sinha, A. Sarker, and N. Chakraborty, “Task space planning with complementarity constraint-based obstacle avoidance,” in International Design Engineering Technical Conferences and Computers and Infor- mation in Engineering Conference , vol. 85451. American Society of Mechanical Engineers, 2021, p. V08BT08A012

work page 2021

[6] [6]

Oc3: A reactive velocity level motion planner with complementarity constraint-based obstacle avoid- ance for mobile robots,

A. Sinha, R. Laha, and N. Chakraborty, “Oc3: A reactive velocity level motion planner with complementarity constraint-based obstacle avoid- ance for mobile robots,” in 2023 IEEE 19th International Conference on Automation Science and Engineering (CASE) . IEEE, 2023, pp. 1–8

work page 2023

[7] [7]

On the synthesis of reactive collision-free whole- body robot motions: A complementarity-based approach,

H. Yao, R. Laha, A. Sinha, J. Hall, L. F. Figueredo, N. Chakraborty, and S. Haddadin, “On the synthesis of reactive collision-free whole- body robot motions: A complementarity-based approach,” in IEEE International Conference on Robotics and Automation (ICRA) , 2025

work page 2025

[8] [8]

Control barrier function based quadratic programs for safety critical systems,

A. D. Ames, X. Xu, J. W. Grizzle, and P. Tabuada, “Control barrier function based quadratic programs for safety critical systems,” IEEE Transactions on Automatic Control, vol. 62, no. 8, pp. 3861–3876, 2016

2016