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On the Surprising Robustness of Sequential Convex Optimization for Contact-Implicit Motion Planning

T0 review · 3 major / 5 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read A primal-only convex solver plans through contact from scratch

desk verdict Credible empirical robustness from all-zero initialization, but the convergence proof analyzes a different subproblem than the algorithm solves; the theory needs repair before the guarantee is taken at face value. read the letter →

arxiv 2502.01055 v3 pith:JC4ZFAGQ submitted 2025-02-03 math.OC cs.RO

Yulin Li , Haoyu Han , Shucheng Kang , Jun Ma , Heng Yang This is my paper · ORCID
classification math.OCcs.RO MSC 90C3390C5590C30
keywords contact-implicitmotionplanningmathematicalprogramwithcomplementarityconstraintssequentialconvexprogrammingtrust-regionmethodl1penaltymeritfunctionprimal-onlyoptimizationtrajectory
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 claims that contact-implicit motion planning, an optimization problem made notoriously hard by complementarity constraints that violate classical constraint qualifications, can be solved robustly by a primal-only sequential convex method. The proposed solver, CRISP, replaces the usual search for KKT primal-dual pairs with a sequence of convex trust-region quadratic programs, judging progress with a weighted $\ell^1$ penalty merit function. The paper proves sufficient conditions under which the iterates converge to a stationary point of that merit function, and shows that a feasible local minimizer of the merit function is a local minimizer of the original problem. On six planning tasks, CRISP is reported to discover usable contact sequences from naive and even all-zero initial guesses while established nonlinear solvers often fail or stall. If the method holds, contact-rich manipulation and locomotion planning would no longer need hand-specified contact modes or costly relaxation schemes.

What carries the argument

The load-bearing object is the weighted $\ell^1$ merit function $\varphi_1(x;\mu) = J(x) + \sum_{i\in E} \mu_i |c_i(x)| + \sum_{i\in I} \mu_i [c_i(x)]^-$, with a separate penalty weight for each constraint. CRISP minimizes it by repeatedly solving the convex trust-region quadratic program: a quadratic model of the convex objective, first-order linearizations of the constraints, slack variables that absorb the $\ell^1$ penalties, and an $\ell_\infty$ bound on the trial step. Each trial step is accepted or rejected according to the ratio of actual to predicted decrease in the merit function, and a second-order correction re-linearizes the constraints using the value already computed at the trial point, preserving the convex QP structure. The convergence proof works by passing to a subsequence on which the signs of the linearized constraint quantities are constant, then comparing directional derivatives of the subproblem model with those of the merit function.

What would settle it

Instrument the released implementation on the six benchmark tasks to log the trust-region radius and the merit function's directional derivative at termination; if any returned point has the radius below the stopping tolerance and a negative directional derivative in some direction, then the sufficient conditions of the main theorem are not satisfied.

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Extended reading notes

Core claim

The central discovery is that when the objective is convex, as quadratic tracking costs typically are, a method that never maintains dual variables and only drives down a weighted $\ell^1$ penalty merit function can still reach first-order stationary points. The main theorem states that if the sequence of convex trust-region subproblems converges to some point and the trust-region radius stays bounded below by a positive constant, then that limit is a stationary point of the merit function. The companion local-optimality result closes the loop: a feasible local minimizer of the merit function is a local minimizer of the original contact-implicit problem. The paper then demonstrates empirically that CRISP attains 100 percent success on the first four benchmark tasks and credible solutions on the hopper and waiter problems, all from naive or all-zero initializations, in contrast to the benchmarked primal-dual solvers.

Load-bearing premise

The theorem assumes the iterates converge while the trust-region radius stays bounded above zero, but Algorithm 1 stops when that radius falls below a tolerance and never verifies the assumed lower bound.

Editorial extensions

If this is right

  • If CRISP converges to a feasible local minimizer of the merit function, that point is also a local minimizer of the original contact-implicit problem, by Proposition 9.
  • On the four benchmark tasks, CRISP reports 100 percent success from naive or all-zero initial guesses, with the lowest median tracking error and constraint violation among the compared solvers.
  • On the hopper and waiter tasks, CRISP produces substantially lower objective values than the interior-point baseline, and in real-world push experiments it replans within about 80 milliseconds per cycle.
  • The convergence conditions of the main theorem are numerically checkable, so individual runs can be certified as reaching a stationary point of the merit function.
  • A mixed-integer reformulation of the Push T task becomes intractable beyond roughly four planning steps, whereas CRISP solves the same task in contact-implicit form.

Reading between the lines

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

  • If the robustness comes from convex objectives plus primal-only penalization, the same trust-region QP structure should transfer to other MPCC instances in robotics, such as legged locomotion with nonlinear friction cones, where the subproblem remains convex.
  • The paper leaves open whether the limit point of CRISP is feasible for the original problem; a testable extension is to add an outer feasibility-repair phase that projects the merit-function stationary point onto the nonlinear constraints and then restarts CRISP.
  • Because the subproblem uses the objective Hessian while Assumption 7 assumes only continuous differentiability, a more careful convergence proof could replace the Hessian with a bounded positive-definite approximation, aligning the certified regime with what the algorithm actually assumes.
  • The benchmarks count success by tracking error and constraint-violation thresholds; a natural further test is whether the discovered contact sequences remain valid under model mismatch, building on the real-world push experiments.
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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 / 5 minor

Summary. The paper proposes CRISP, a primal-only sequential convex programming solver for contact-implicit motion planning. At each iteration CRISP solves a trust-region convex QP that linearizes constraints and uses a quadratic model of the objective, with a weighted l1 penalty merit function to balance objective reduction and constraint satisfaction. The authors claim sufficient conditions for convergence of CRISP iterates to stationary points of the merit function (Theorem 8), a local-optimality correspondence (Proposition 9), an open-source C++ implementation, and benchmarks on six contact-implicit tasks showing 100% success for CRISP on the first four tasks, including all-zero initializations, plus a real-world push experiment with a Franka robot. The central theoretical proof in Appendix A is the main point of concern: it analyzes a different subproblem than the QP actually solved by the algorithm.

Significance. If the convergence guarantee is properly established, the paper makes a valuable practical contribution: a primal-only method that avoids the constraint-qualification failures of MPCC and shows surprising robustness from naive or zero initializations. The empirical core is substantial and credible: six planning problems, comparisons against SNOPT, IPOPT, PROXNLP, LCQpow, and Gurobi, a real-world MPC validation, and a released C++ implementation with reproducible benchmarks. These strengths are independent of the theoretical gap, and the open-source artifacts materially increase the paper's value. The theoretical claim, however, is load-bearing for the paper's abstract and Section II, and the proof as written does not connect the analyzed object to the implemented algorithm.

major comments (3)
  1. [Appendix A, Eq. (19)] The proof of Theorem 8 analyzes a subproblem that is not the one CRISP solves. Equation (19) defines x_{k+1} as the minimizer of J(x) plus l1 penalties on linearly approximated constraints, whereas Algorithm 1 solves the trust-region QP (10), whose objective is a quadratic Taylor model of J with a Hessian term and an explicit trust-region constraint. For a general convex C^1 objective, these two subproblems are not equivalent, and the proof's use of the first-order condition of the full-J subproblem, e.g. the appearance of grad J(x_{n_k+1}) in Eq. (24)-(26), is not justified for the QP. No argument is given that a solution of (10) is also a minimizer of (19), so the theorem's conclusion is not established for the actual algorithm.
  2. [Section II, Assumption 7 and Algorithm 1] The hypotheses of Theorem 8 do not match the algorithm's construction or termination criteria. Assumption 7 only requires J to be convex and continuously differentiable, but subproblem (10) uses the Hessian of J, which need not exist under this assumption. Additionally, Theorem 8 assumes the trust-region radius remains bounded below by some Delta_min > 0, yet Algorithm 1 declares convergence when Delta_{k+1} < epsilon_r (line 29) and contains no mechanism to enforce or verify a uniform lower bound. Thus the stated sufficient conditions are not verifiable from the algorithm's own data, contrary to the claim in Section II that the convergence conditions are numerically checkable. The theorem may be salvageable by assuming J is C^2 with bounded Hessian and by proving convergence directly from the KKT conditions of (10), or by adding a separate safeguard that prevents the trust region from shrinking below a positive threshold.
  3. [Theorem 8 and Proposition 9] The theorem's conclusion is about stationarity of the merit function (8), and Proposition 9 then states that a feasible local minimizer of the merit function is a local minimizer of the original problem. However, the paper explicitly acknowledges in Remark 3 and in the limitations section that the relationship between merit-function stationary points and local solutions of the original MPCC is not fully understood. That acknowledgment is appropriate, but it means the convergence theorem alone does not provide a guarantee about the quality of the contact-implicit solution unless an additional verification step is performed, which the paper does not provide. The empirical results remain informative, but the theoretical framing should be adjusted to reflect this gap.
minor comments (5)
  1. [Table I] The value of epsilon_c is listed as 1e6, which conflicts with the success criterion of constraint violation below 1e-5 stated in Section IV-C. This appears to be a typo, likely epsilon_c = 1e-6, and should be corrected.
  2. [Section III, user interface paragraph] The sentence beginning 'It is noteworthy to point that' is incomplete and should be finished or removed.
  3. [Table II] The header and row for PROXNLP are malformed: 'PROXNLP60' appears to merge the solver name with its success rate, and the success rate for PROXNLP in the cartpole task is unclear. The table formatting should be fixed.
  4. [Eq. (6e) and surrounding text] The explanation of the complementarity constraint says it should be interpreted as phi_i(x,lambda)*lambda_i = 0 or phi_i(x,lambda)*lambda_i <= 0 as suggested by [22]. The inequality form is not a standard complementarity condition; this phrasing should be clarified to avoid confusion.
  5. [Algorithm 1, line 29] The convergence check uses an OR condition between Delta_{k+1} < epsilon_r and ||p_k||_infty < epsilon_p, but Theorem 8 assumes a uniform lower bound Delta_min > 0. The stopping criterion based on a shrinking trust region is not covered by the theorem and should be discussed explicitly.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: CRISP's theoretical and empirical claims are not constructed from their own inputs; the Appendix A subproblem mismatch is a proof gap, not circularity.

full rationale

CRISP's derivation chain is not circular. The merit function (8) is an externally defined benchmark, independent of the algorithm's output, and the trust-region ratio (11) compares it against the quadratic model (9)/(10). No parameter is fitted to make Theorem 8 true, and the penalty weights are updated by constraint violation rather than tuned to force stationarity. Theorem 8 assumes, rather than proves, iterate convergence and a positive trust-region lower bound; assuming convergence is not the same as defining the stationarity conclusion into the assumptions, because the proof still needs to transfer subproblem optimality into nonnegative directional derivatives of the merit function. The genuine concern is that Appendix A analyzes subproblem (19), which minimizes the full objective J(x) with linearized penalties, while Algorithm 1 solves the trust-region QP (10); this is an incompleteness or correctness risk, not a reduction of the conclusion to the inputs. The single self-citation, [31], appears only in a future-work remark about possible GPU speedups and is not load-bearing. The central empirical claims are supported by released C++ code, comparisons against external solvers (SNOPT, IPOPT, PROXNLP, Gurobi, LCQPow), and real-world MPC experiments, so they are externally falsifiable rather than manufactured from the paper's own definitions.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on standard optimization assumptions plus several ad hoc conditions that are not guaranteed by the algorithm. No new physical entities are introduced. The most significant uncharged premises are the convergence and positive trust-region assumptions in Theorem 8 and the unproven equivalence between the analyzed subproblem and the implemented QP.

free parameters (3)
  • Solver hyperparameters = mu0=10, Delta0=1, Delta_max=10, eta_low=0.25, eta_high=0.75, gamma_shrink=0.25, gamma_expand=2, mu_max=1e6
    Hand-chosen in Table I. Robustness may depend on these values, and the paper provides no sensitivity study.
  • Stopping tolerances = kmax=1000, eps_p=1e-3, eps_r=1e-3, eps_c=1e6 (likely typo for 1e-6)
    These determine when Algorithm 1 declares convergence and success; Table I lists eps_c as 1e6, which is likely an error and affects the meaning of the reported success rates.
  • Benchmark success thresholds = violation <1e-5, translation error <0.1, velocity error <0.5, angular error <pi/6, angular velocity error <0.1pi
    Chosen by the authors to define 'success' in Section IV-C. The thresholds are arbitrary and directly determine the reported success rates.
assumptions (4)
  • domain assumption Assumption 7: objective J is convex and continuously differentiable; constraints are differentiable with Lipschitz gradients
    Used for Theorem 8, but it does not guarantee the twice-differentiability of J required by the Hessian in subproblem (10).
  • ad hoc to paper Theorem 8 suppositions: subproblems converge and the trust region radius stays bounded below by Delta_min > 0
    Algorithm 1 does not establish these conditions; its stopping check declares convergence when Delta drops below epsilon_r, so the guarantee may not apply to actual runs.
  • domain assumption Minimizing the weighted l1 penalty merit function is a valid proxy for solving the MPCC
    The authors acknowledge this is not fully established for MPCC without constraint qualifications and explicitly leave the precise relationship for future work (Remark 3 and Section VI).
  • ad hoc to paper The proof's subproblem (Eq. 19) can replace the implemented QP (Eq. 10)
    Appendix A uses the full objective J(x) in Eq. (19), while Algorithm 1 solves the quadratic model in Eq. (10); no equivalence proof is provided.

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Cite this review

Pith. "Pith review of On the Surprising Robustness of Sequential Convex Optimization for Contact-Implicit Motion Planning." pith.science (2026). https://pith.science/paper/JC4ZFAGQ

@misc{pith2026250201055,
  author       = {Pith},
  title        = {Pith review of: On the Surprising Robustness of Sequential Convex Optimization for Contact-Implicit Motion Planning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JC4ZFAGQ}},
  note         = {Machine review of arXiv:2502.01055}
}
read the original abstract

Contact-implicit motion planning-embedding contact sequencing as implicit complementarity constraints-holds the promise of leveraging continuous optimization to discover new contact patterns online. Nevertheless, the resulting optimization, being an instance of Mathematical Programming with Complementary Constraints, fails the classical constraint qualifications that are crucial for the convergence of popular numerical solvers. We present robust contact-implicit motion planning with sequential convex programming (CRISP), a solver that departs from the usual primal-dual algorithmic framework but instead only focuses on the primal problem. CRISP solves a convex quadratic program with an adaptive trust region radius at each iteration, and its convergence is evaluated by a merit function using weighted penalty. We (i) provide sufficient conditions on CRISP's convergence to first-order stationary points of the merit function; (ii) release a high-performance C++ implementation of CRISP with a generic nonlinear programming interface; and (iii) demonstrate CRISP's surprising robustness in solving contact-implicit planning with naive initialization. In fact, CRISP solves several contact-implicit problems with all-zero initialization.

Figures

Figures reproduced from arXiv: 2502.01055 by the authors.

Figure 1
Figure 1. CRISP computes entirely new contact sequences from naive and even all-zero initializations. For (a), (b), (c), and (d), the left side shows the initial trajectories and the right side displays the optimized trajectory from CRISP. For (e) the hopper problem, the initial guess is a free-fall motion released from the origin. The color gradient represents the progression of time (from blue to yellow). For (f), we implem… view at source ↗
Figure 2
Figure 2. Geometric intuition of MPCC through Example [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Depiction of the ℓ1 penalty merit function for Example 1 with different penalty parameters µ. Here, we absorb all other constraints into the general template c for simplicity. Primal-only merit function. From a primal￾only perspective, the core optimization challenge is to balance descent of the objective function with satisfaction of the constraints [46]. In CRISP, we adopt the following merit function with weighte… view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Schematic overview of the contact-implicit motion planning tasks considered in the experiments. Each task poses unique [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Box plots of benchmark metrics on three tasks: cartpole with soft walls, push box, transport, and push T. The plots [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 7
Figure 7. Figure 7: Comparison of optimized trajectories for the hopper [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 6
Figure 6. Figure 6: Visualization of some outlier cases in I [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 8
Figure 8. Figure 8: Key frames visualization of the real-world Push T experiments from various initial configurations (each row). Videos [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 9
Figure 9. Figure 9: Visualization of more trajectories solved by [PITH_FULL_IMAGE:figures/full_fig_p024_9.png]

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Reference graph

Works this paper leans on

63 extracted references · 58 canonical work pages · cited by 1 Pith paper

  1. [1]

    IFAC-PapersOnLine, 50(1):1463– 1469, 2017

    Sequential linear quadratic optimal control for nonlin- ear switched systems. IFAC-PapersOnLine, 50(1):1463– 1469, 2017. ISSN 2405-8963. 20th IFAC World Congress. 11

    work page 2017

  2. [2]

    Grieco, and Gerardo Fernández-López

    Bernardo Aceituno-Cabezas, Hongkai Dai, José Cappel- letto, Juan C. Grieco, and Gerardo Fernández-López. A mixed-integer convex optimization framework for robust multilegged robot locomotion planning over challenging terrain. In 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 4467–4472,

    work page 2017

  3. [3]

    Caldwell, José Cappelletto, Juan C

    Bernardo Aceituno-Cabezas, Carlos Mastalli, Hongkai Dai, Michele Focchi, Andreea Radulescu, Darwin G. Caldwell, José Cappelletto, Juan C. Grieco, Gerardo Fernández-López, and Claudio Semini. Simultaneous contact, gait, and motion planning for robust multilegged locomotion via mixed-integer convex optimization. IEEE Robotics and Automation Letters, 3(3):25...

    work page 2018

  4. [4]

    On using the elastic mode in nonlinear programming approaches to mathematical programs with complementarity constraints

    Mihai Anitescu. On using the elastic mode in nonlinear programming approaches to mathematical programs with complementarity constraints. SIAM Journal on Optimiza- tion, 15(4):1203–1236, 2005. 5

    work page 2005

  5. [5]

    Real-time multi- contact model predictive control via admm

    Alp Aydinoglu and Michael Posa. Real-time multi- contact model predictive control via admm. In 2022 International Conference on Robotics and Automation (ICRA), pages 3414–3421. IEEE, 2022. 3, 12

    work page 2022

  6. [6]

    PROX-QP: Yet another quadratic pro- gramming solver for robotics and beyond

    Antoine Bambade, Sarah ElKazdadi, Adrien Taylor, and Justin Carpentier. PROX-QP: Yet another quadratic pro- gramming solver for robotics and beyond. In Robotics: Science and Systems , 2022. 6

    work page 2022

  7. [7]

    Bradley M. Bell. CppAD: A package for C++ algo- rithmic differentiation (2024). https://github.com/coin-or/ CppAD. 6

    work page 2024

  8. [8]

    Powell, Benjamin Katz, Jared Di Carlo, Patrick M

    Gerardo Bledt, Matthew J. Powell, Benjamin Katz, Jared Di Carlo, Patrick M. Wensing, and Sangbae Kim. Mit cheetah 3: Design and control of a robust, dynamic quadruped robot. In 2018 IEEE/RSJ International Con- ference on Intelligent Robots and Systems (IROS) , pages 2245–2252, 2018. 11

    work page 2018

Show all 63 references
  1. [9]

    Blickhan

    R. Blickhan. The spring-mass model for running and hopping. Journal of Biomechanics , 22(11):1217–1227,

  2. [10]

    The Pinocchio C++ library – a fast and flexible implementation of rigid body dynamics algorithms and their analytical derivatives

    Justin Carpentier, Guilhem Saurel, Gabriele Buondonno, Joseph Mirabel, Florent Lamiraux, Olivier Stasse, and Nicolas Mansard. The Pinocchio C++ library – a fast and flexible implementation of rigid body dynamics algorithms and their analytical derivatives. In IEEE Internationa...

  3. [11]

    Xianyi Cheng, Eric Huang, Yifan Hou, and Matthew T. Mason. Contact mode guided motion planning for quasidynamic dexterous manipulation in 3d. In 2022 International Conference on Robotics and Automation (ICRA), pages 2730–2736, 2022. 11

    2022

  4. [12]

    Footstep planning on un- even terrain with mixed-integer convex optimization

    Robin Deits and Russ Tedrake. Footstep planning on un- even terrain with mixed-integer convex optimization. In 2014 IEEE-RAS International Conference on Humanoid Robots, pages 279–286, 2014. 12

    2014

  5. [13]

    Local convergence of generalized gauss-newton and sequential convex pro- gramming

    Moritz Diehl and Florian Messerer. Local convergence of generalized gauss-newton and sequential convex pro- gramming. In 2019 IEEE 58th Conference on Decision and Control (CDC) , pages 3942–3947, 2019. 4

    2019

  6. [14]

    Local convergence of sequential convex programming for nonconvex op- timization

    Quoc Tran Dinh and Moritz Diehl. Local convergence of sequential convex programming for nonconvex op- timization. In Recent Advances in Optimization and its Applications in Engineering , pages 93–102. Berlin, Germany: Springer, 2010. 4

    2010

  7. [15]

    A smoothing method for mathematical programs with equi- librium constraints

    Francisco Facchinei, Houyuan Jiang, and Liqun Qi. A smoothing method for mathematical programs with equi- librium constraints. Mathematical programming, 85(1): 107, 1999. 2

    1999

  8. [16]

    Real-time motion planning of legged robots: A model predictive control approach

    Farbod Farshidian, Edo Jelavic, Asutosh Satapathy, Markus Giftthaler, and Jonas Buchli. Real-time motion planning of legged robots: A model predictive control approach. In 2017 IEEE-RAS 17th International Confer- ence on Humanoid Robotics (Humanoids) , pages 577– 584, 2017. 11

    2017

  9. [17]

    OCS2: An open source library for optimal control of switched systems

    Farbod Farshidian et al. OCS2: An open source library for optimal control of switched systems. [Online]. Available: https://github.com/leggedrobotics/ocs2. 11, 12

  10. [18]

    Ferreau, C

    H.J. Ferreau, C. Kirches, A. Potschka, H.G. Bock, and M. Diehl. qpOASES: A parametric active-set algorithm for quadratic programming. Mathematical Programming Computation, 6(4):327–363, 2014. 6

    2014

  11. [19]

    Fletcher

    R. Fletcher. Penalty Functions, pages 87–114. Berlin, Germany: Springer, 1983. 4

    1983

  12. [20]

    Practical methods of optimization

    Roger Fletcher. Practical methods of optimization. Hobo- ken, NJ, USA: Wiley, 2013. 3, 4, 12

    2013

  13. [21]

    Solving mathematical programs with complementarity constraints as nonlinear programs

    Roger Fletcher and Sven Leyffer. Solving mathematical programs with complementarity constraints as nonlinear programs. Optimization Methods and Software , 19(1): 15–40, 2004. 3, 12

    2004

  14. [22]

    Local convergence of sqp methods for math- ematical programs with equilibrium constraints

    Roger Fletcher, Sven Leyffer, Danny Ralph, and Stefan Scholtes. Local convergence of sqp methods for math- ematical programs with equilibrium constraints. SIAM Journal on Optimization , 17(1):259–286, 2006. 3, 5, 12

    2006

  15. [23]

    Gill and Elizabeth Wong

    Philip E. Gill and Elizabeth Wong. Sequential quadratic programming methods. In Mixed Integer Nonlinear Programming, pages 147–224. New York, NY , USA: Springer, 2012. 4

    2012

  16. [24]

    Gill, Walter Murray, and Michael A

    Philip E. Gill, Walter Murray, and Michael A. Saunders. SNOPT: An sqp algorithm for large-scale constrained optimization. SIAM Journal on Optimization, 12(4):979– 1006, 2002. 2, 7

    2002

  17. [25]

    Sanfelice, and Andrew R

    Rafal Goebel, Ricardo G. Sanfelice, and Andrew R. Teel. Hybrid dynamical systems. IEEE Control Systems Magazine, 29(2):28–93, 2009. 11

    2009

  18. [26]

    Parrilo, and Russ Tedrake

    Bernhard Paus Graesdal, Shao Yuan Chew Chia, Tobia Marcucci, Savva Morozov, Alexandre Amice, Pablo A. Parrilo, and Russ Tedrake. Towards tight convex re- laxations for contact-rich manipulation, 2024. URL https://arxiv.org/abs/2402.10312. 18

    2024 arXiv

  19. [27]

    Gurobi Optimizer Reference Manual, 2024

    Gurobi Optimization, LLC. Gurobi Optimizer Reference Manual, 2024. URL https://www.gurobi.com. 7, 12

    2024

  20. [28]

    J. Hall, A. Nurkanovi ´c, F. Messerer, and M. Diehl. LCQPow: a solver for linear complementarity quadratic programs. Math. Prog. Comput. , 2024. 3, 7, 10

    2024

  21. [29]

    Constrained differential dynamic programming: A primal-dual augmented lagrangian ap- proach

    Wilson Jallet, Antoine Bambade, Nicolas Mansard, and Justin Carpentier. Constrained differential dynamic programming: A primal-dual augmented lagrangian ap- proach. In 2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) , pages 13371– 13378, 2022. 7

    2022

  22. [30]

    Stagewise implementations of sequential quadratic programming for model-predictive control

    Armand Jordana, Sébastien Kleff, Avadesh Meduri, Justin Carpentier, Nicolas Mansard, and Ludovic Righetti. Stagewise implementations of sequential quadratic programming for model-predictive control. Preprint, 2023. 4

    2023

  23. [31]

    Fast and certifiable trajectory optimiza- tion

    Shucheng Kang, Xiaoyang Xu, Jay Sarva, Ling Liang, and Heng Yang. Fast and certifiable trajectory optimiza- tion. arXiv preprint arXiv:2406.05846 , 2024. 12

    2024 arXiv

  24. [32]

    Tailoring so- lution accuracy for fast whole-body model predictive control of legged robots

    Charles Khazoom, Seungwoo Hong, Matthew Chignoli, Elijah Stanger-Jones, and Sangbae Kim. Tailoring so- lution accuracy for fast whole-body model predictive control of legged robots. IEEE Robotics and Automation Letters, 2024. 6

    2024

  25. [33]

    Fast contact-implicit model predictive control

    Simon Le Cleac’h, Taylor A Howell, Shuo Yang, Chi- Yen Lee, John Zhang, Arun Bishop, Mac Schwager, and Zachary Manchester. Fast contact-implicit model predictive control. IEEE Transactions on Robotics, 2024. 2, 3, 12

    2024

  26. [34]

    Contact models in robotics: A comparative analysis

    Quentin Le Lidec, Wilson Jallet, Louis Montaut, Ivan Laptev, Cordelia Schmid, and Justin Carpentier. Contact models in robotics: A comparative analysis. IEEE Transactions on Robotics , 40:3716–3733, 2024. doi: 10.1109/TRO.2024.3434208. 11

    2024

  27. [35]

    CppADCodeGen: About source code generation for automatic differentiation using oper- ator overloading (2024)

    Joao Rui Leal. CppADCodeGen: About source code generation for automatic differentiation using oper- ator overloading (2024). https://github.com/joaoleal/ CppADCodeGen. 6

    2024

  28. [36]

    Gabriel A. D. Lopes, Bart Kersbergen, Ton J. J. van den Boom, Bart De Schutter, and Robert Babuška. Modeling and control of legged locomotion via switching max-plus models. IEEE Transactions on Robotics, 30(3):652–665,

  29. [37]

    A practical and optimal first-order method for large-scale convex quadratic pro- gramming

    Haihao Lu and Jinwen Yang. A practical and optimal first-order method for large-scale convex quadratic pro- gramming. arXiv preprint arXiv:2311.07710 , 2023. 6

    2023 arXiv

  30. [38]

    Successive convexification of non-convex optimal control problems and its convergence properties

    Yuanqi Mao, Michael Szmuk, and Behçet Açıkme¸ se. Successive convexification of non-convex optimal control problems and its convergence properties. In 2016 IEEE 55th Conference on Decision and Control (CDC) , pages 3636–3641, 2016. doi: 10.1109/CDC.2016.7798816. 4

    2016

  31. [39]

    Successive convexification: A superlinearly convergent algorithm for non-convex optimal control problems

    Yuanqi Mao, Michael Szmuk, Xiangru Xu, and Behçet Açikmese. Successive convexification: A superlinearly convergent algorithm for non-convex optimal control problems. arXiv preprint arXiv:1804.06539 , 2018. 4

    2018 arXiv

  32. [40]

    Warm start of mixed- integer programs for model predictive control of hybrid systems

    Tobia Marcucci and Russ Tedrake. Warm start of mixed- integer programs for model predictive control of hybrid systems. IEEE Transactions on Automatic Control , 66 (6):2433–2448, 2021. 12

    2021

  33. [41]

    Marhefka and D.E

    D.W. Marhefka and D.E. Orin. A compliant contact model with nonlinear damping for simulation of robotic systems. IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans , 29(6):566– 572, 1999. 11

    1999

  34. [42]

    Crocoddyl: An Efficient and Versatile Framework for Multi-Contact Optimal Control

    Carlos Mastalli, Rohan Budhiraja, Wolfgang Merkt, Guilhem Saurel, Bilal Hammoud, Maximilien Naveau, Justin Carpentier, Ludovic Righetti, Sethu Vijayakumar, and Nicolas Mansard. Crocoddyl: An Efficient and Versatile Framework for Multi-Contact Optimal Control. In IEEE Internati...

    2020

  35. [43]

    Determining the exact local convergence rate of sequential convex pro- gramming

    Florian Messerer and Moritz Diehl. Determining the exact local convergence rate of sequential convex pro- gramming. In 2020 European Control Conference (ECC), pages 1280–1285, 2020. 4

    2020

  36. [44]

    Win- kler, and Jonas Buchli

    Michael Neunert, Farbod Farshidian, Alexander W. Win- kler, and Jonas Buchli. Trajectory optimization through contacts and automatic gait discovery for quadrupeds. IEEE Robotics and Automation Letters , 2(3):1502–1509,

  37. [45]

    Bellicoso, Jan Carius, Christian Gehring, Marco Hutter, and Jonas Buchli

    Michael Neunert, Markus Stäuble, Markus Giftthaler, Carmine D. Bellicoso, Jan Carius, Christian Gehring, Marco Hutter, and Jonas Buchli. Whole-body non- linear model predictive control through contacts for quadrupeds. IEEE Robotics and Automation Letters , 3 (3):1458–1465, 2018. 11

    2018

  38. [46]

    Numerical opti- mization

    Jorge Nocedal and Stephen J Wright. Numerical opti- mization. New York, NY , USA: Springer, 2006. 2, 4, 5

    2006

  39. [47]

    A direct method for trajectory optimization of rigid bodies through contact

    Michael Posa, Cecilia Cantu, and Russ Tedrake. A direct method for trajectory optimization of rigid bodies through contact. The International Journal of Robotics Research, 33(1):69–81, 2014. 1, 12

    2014

  40. [48]

    Mathematical pro- grams with complementarity constraints: Stationarity, optimality, and sensitivity

    Holger Scheel and Stefan Scholtes. Mathematical pro- grams with complementarity constraints: Stationarity, optimality, and sensitivity. Mathematics of Operations Research, 25(1):1–22, 2000. 2

    2000

  41. [49]

    Convergence properties of a regular- ization scheme for mathematical programs with comple- mentarity constraints

    Stefan Scholtes. Convergence properties of a regular- ization scheme for mathematical programs with comple- mentarity constraints. SIAM Journal on Optimization, 11 (4):918–936, 2001. 2

    2001

  42. [50]

    How stringent is the linear independence assumption for mathematical pro- grams with complementarity constraints? Mathematics of Operations Research , 26(4):851–863, 2001

    Stefan Scholtes and Michael Stöhr. How stringent is the linear independence assumption for mathematical pro- grams with complementarity constraints? Mathematics of Operations Research , 26(4):851–863, 2001. 2

    2001

  43. [51]

    Finding locally optimal, collision-free trajectories with sequential convex optimization

    John Schulman, Jonathan Ho, Alex X Lee, Ibrahim Awwal, Henry Bradlow, and Pieter Abbeel. Finding locally optimal, collision-free trajectories with sequential convex optimization. In Robotics: science and systems , volume 9, pages 1–10. Berlin, Germany, 2013. 4

  44. [52]

    Roland Schwan, Yuning Jiang, Daniel Kuhn, and Colin N. Jones. PIQP: A proximal interior-point quadratic programming solver. In 2023 62nd IEEE Con- ference on Decision and Control (CDC) , pages 1088– 1093, 2023. 6

    2023

  45. [53]

    Jha, Arvind U

    Yuki Shirai, Devesh K. Jha, Arvind U. Raghunathan, and Diego Romeres. Chance-constrained optimization for contact-rich systems using mixed integer programming. Nonlinear Analysis: Hybrid Systems , 52:101466, 2024. ISSN 1751-570X. 12

    2024

  46. [54]

    Stellato, G

    B. Stellato, G. Banjac, P. Goulart, A. Bemporad, and S. Boyd. OSQP: an operator splitting solver for quadratic programs. Mathematical Programming Computation, 12 (4):637–672, 2020. 6

    2020

  47. [55]

    OSQP: An operator splitting solver for quadratic programs

    Bartolomeo Stellato, Goran Banjac, Paul Goulart, Al- berto Bemporad, and Stephen Boyd. OSQP: An operator splitting solver for quadratic programs. Mathematical Programming Computation, 12(4):637–672, 2020. 6

    2020

  48. [56]

    Mixed integer linear programming formulation techniques

    Juan Pablo Vielma. Mixed integer linear programming formulation techniques. SIAM Review, 57(1):3–57, 2015. 11

    2015

  49. [57]

    On the imple- mentation of an interior-point filter line-search algorithm for large-scale nonlinear programming

    Andreas Wächter and Lorenz T Biegler. On the imple- mentation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Mathematical programming, 106:25–57, 2006. 2, 7

    2006

  50. [58]

    Wensing, Michael Posa, Yue Hu, Adrien Escande, Nicolas Mansard, and Andrea Del Prete

    Patrick M. Wensing, Michael Posa, Yue Hu, Adrien Escande, Nicolas Mansard, and Andrea Del Prete. Optimization-based control for dynamic legged robots. IEEE Transactions on Robotics , 40:43–63, 2024. 11

    2024

  51. [59]

    Semi-implicit euler method — Wikipedia, the free encyclopedia, 2023

    Wikipedia contributors. Semi-implicit euler method — Wikipedia, the free encyclopedia, 2023. URL https://en. wikipedia.org/wiki/Semi-implicit_Euler_method. [On- line; accessed 24-May-2023]. 18

    2023

  52. [60]

    Dynamic on-palm manipulation via controlled sliding

    William Yang and Michael Posa. Dynamic on-palm manipulation via controlled sliding. arXiv preprint arXiv:2405.08731, 2024. 9, 12

    2024 arXiv

  53. [61]

    Ye and Jinchuan Zhou

    Jane J. Ye and Jinchuan Zhou. First-order optimality conditions for mathematical programs with second-order cone complementarity constraints. SIAM Journal on Optimization, 26(4):2820–2846, 2016. 2

    2016

  54. [62]

    Yunt and C

    K. Yunt and C. Glocker. Trajectory optimization of mechanical hybrid systems using sumt. In 9th IEEE International Workshop on Advanced Motion Control, 2006., pages 665–671, 2006. 1 APPENDIX A PROOF OF THEOREM 8 Proof: As xk converges to x⋆, we have ∥pk∥= ∥xk+1 − xk∥→ 0. By de...

    2006

  55. [63]

    Similarly, m1 + 1 ∼ m1 + m2,− are negative, while m1 + m2,− + 1 ∼ m1 + m2’s components of w⋆ become zero

    To fix this, we assume that, for the 1 ∼ m1 components of w⋆, 1 ∼ m1,+ are positive, while m1,+ + 1 ∼ m1’s components of w⋆ become zero. Similarly, m1 + 1 ∼ m1 + m2,− are negative, while m1 + m2,− + 1 ∼ m1 + m2’s components of w⋆ become zero. Thus, D(ϕ1(x⋆; µ); p) = lim t↓0 J(...

Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.