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REVIEW 4 major objections 6 minor 1 cited by

Local Reactive Control for Mobile Manipulators with Whole-Body Safety in Complex Environments

T0 review · 4 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A mobile manipulator can be controlled with whole-body safety in real time by recasting reactive control as a multi-step optimization along the kinematic chain, with per-link geometric collision constraints solved by AL-DDP.

desk verdict A genuinely new spatial-domain reformulation of reactive control for mobile manipulators, worth a close look, but the central real-time claim is unsupported by any timing data. read the letter →

arxiv 2501.02815 v1 pith:NLAXQA5Z submitted 2025-01-06 cs.RO cs.SYeess.SY

Chunxin Zheng , Yulin Li , Zhiyuan Song , Zhihai Bi , Jinni Zhou , Boyu Zhou , Jun Ma This is my paper · ORCID
classification cs.ROcs.SYeess.SY
keywords mobilemanipulatorsreactivecontrolwhole-bodysafetycollisionavoidancespatialtrajectoryoptimizationaugmentedLagrangianDDPsums-of-squaresprogrammingfreeregions
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

Mobile manipulators are hard to control reactively because every link's motion is coupled to all preceding joints, so whole-body collision safety is usually approximated with spheres or ignored. This paper tries to establish that the coupling is an artifact of solving the control problem in the time domain, and it reformulates the single-step reactive problem as a multi-step optimization along the spatial kinematic chain, treating each link as one step. In that form, each link gets its own constraints, including a geometry-accurate collision constraint that requires the link to stay inside a free region extracted from the local map. The resulting optimization is solved with augmented Lagrangian differential dynamic programming (AL-DDP), which propagates the spatial kinematics in the forward pass and handles all link-specific constraints simultaneously in the backward pass. If the method works as reported, high-degree-of-freedom articulated robots can react to unknown obstacles in real time while preserving whole-body safety and threading narrow gaps.

What carries the argument

The central object is the spatial multi-step trajectory optimization of Eq. (1), where the state of each link on the serial chain is $q_k = [p_k, r_k]$ and the objective runs over the chain instead of over time, with kinematic propagation $f_k$ linking consecutive states. The mechanism that carries the argument is the pairing of link-specific geometric containment constraints $W_k \subseteq F_k$ with AL-DDP, an optimal-control solver that pulls constraints into the cost and propagates dynamics forward and backward. The collision constraint is made differentiable by a sums-of-squares subproblem that outputs the minimum scaling factor $\alpha_k$ and its gradients, and the safety condition is $\alpha_k \le 1$ for every link. This machinery turns whole-body safety into a set of decoupled per-link constraints that can be evaluated simultaneously during the backward pass.

What would settle it

Run the controller toward a thin vertical pole placed between two consecutive links so that no single link's body enters the pole, while the pole still lies inside the 3 m perception range. If the optimizer reports $\alpha_k \le 1$ for every link and the pole nevertheless contacts the robot because the adjacent free regions leave an uncovered gap, the whole-body safety claim fails.

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Extended reading notes

Core claim

The paper's central claim is that reformulating the time-domain single-step reactive problem into a multi-step spatial trajectory optimization along the kinematic chain is what makes whole-body safety tractable. Each link becomes a step with its own state $q_k$ and control $u_k$, and the propagation $f_k$ between adjacent links is absorbed naturally in the solver's forward pass. Collision avoidance is expressed per link as a containment constraint $W_k \subseteq F_k$ between the link's exact geometric body and a polytopic free region, enforced by a sums-of-squares computed minimum scaling factor $\alpha_k \le 1$ with gradient information. The decoupled constraint structure lets the backward pass of AL-DDP process all link-specific constraints simultaneously, yielding real-time computation with improved safety, shorter paths, and higher task completion rates than the baselines tested.

Load-bearing premise

The safety claim rests on the assumption that each link can be enclosed in a free region generated along the robot's skeleton and that the sums-of-squares minimum scaling factor $\alpha_k \le 1$ is a reliable test for collision with everything inside the 3 m perception range.

Editorial extensions

If this is right

  • Mobile manipulators can be driven by a local reactive controller that checks every link's exact geometry against locally perceived obstacles at real-time rates, without waiting for a global replan.
  • Because each link is constrained separately, adding a new per-link objective or constraint does not entangle it with the other links' constraints, so task-specific costs, such as keeping the base or a chosen arm link on a desired path, become straightforward.
  • The reported experiments indicate higher task completion rates and shorter traveled paths in narrow, cluttered scenes compared with MPC, QP, and sampling baselines, while remaining online with only a rough global path as guidance.
  • The approach extends the known free-region plus sums-of-squares collision formulation from a single rigid body to a whole articulated robot, which is the step that lets the robot use its actual link shapes in tight spaces.

Reading between the lines

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

  • (Editorial inference) The spatial horizon idea is a general recipe for serial kinematic chains, so humanoid limbs, dual-arm systems, or snake-like robots could inherit the same decoupling, provided free regions can be generated along their skeletons.
  • (Editorial inference) The safety certificate is local: it covers only what the 3 m perception range sees and only when each link is separately contained in its own free region, so a fully safe guarantee under arbitrary unknown obstacles would need an argument about gaps between adjacent free regions.
  • (Editorial inference) A natural stress test is to move a thin obstacle into the space between two consecutive links; if the per-link scaling-factor constraints all stay below one and the robot still contacts the obstacle, the whole-body claim would need an inter-link condition in addition to the per-link one.
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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

4 major / 6 minor

Summary. This paper proposes a local reactive controller for mobile manipulators that reformulates the usual time-domain single-step reactive control problem as a multi-step optimization problem in the spatial domain along the kinematic chain. The state of each link is optimized over a spatial horizon using spatial kinematic propagation functions, link-specific costs, and collision-avoidance constraints defined by containment of each link's polytopic geometric model in a free region. The constraints are enforced via an SOS-derived minimum scaling factor, and the resulting problem is solved with AL-DDP (ALTRO). The authors evaluate the method in a simulated cluttered forest, a combined navigation-manipulation task, and real-world experiments with a mobile base and 6-DOF Kinova arm, comparing against RRT, SLQ-MPC, Coupled-MPC, and NEO. They report higher success rates and shorter path lengths for their method in the multifaceted task and a comparable success rate in the forest, along with real-world demonstrations.

Significance. The central idea—moving from a single-step time-domain reaction to a multi-step spatial-domain optimization along the serial chain—is a genuinely new way to decouple whole-body constraints in reactive control, and it is supported by a plausible forward-kinematics formulation for an omnidirectional base. The link-specific free-region/SOS collision representation is a promising alternative to sphere-based or ESDF-based safety constraints, and the authors provide an open-source repository, which increases reproducibility. If the real-time and robustness claims are substantiated with timing measurements and statistical reporting, the contribution would be useful to the mobile-manipulation community. At present, however, the paper's own evidence is incomplete: no solve-time data are given, safety is conditional on inherited SOS/free-region machinery, and Tables I–II report aggregate point estimates without variance.

major comments (4)
  1. [Section IV, Tables I–II] The paper's central claim is that the controller is real-time and efficient, but no timing measurement appears anywhere: no solve time, control period, or computation budget is reported, and the 'Real-time ✓' entries in Tables I and II have no threshold. This is load-bearing because Section IV.A.1 explicitly excludes NEO from the forest experiment due to 'extended solving time,' showing that solve time is a differentiator. Please report per-step and per-iteration solve times, control frequency, and hardware, including timing for failed or degraded runs, so the real-time claim can be checked.
  2. [Section III-D, Eqs. (3)–(4)] The whole-body safety guarantee is inherited from the free-region decomposition [15] and the SOS containment subproblem [18], and the paper does not analyze failure modes of those components (e.g., poor free regions, nonsmooth alpha_k gradients, or aggressive solutions with minimal clearance). The paper itself reports 'minor scratches' in failure cases in Section IV.A.1, which weakens any unconditional safety claim. Please state the precise safety property being guaranteed, analyze when the SOS/free-region constraints can fail, and report collision/clearance statistics rather than only success rates.
  3. [Tables I–II, Section IV.A.1] The experimental tables report success rates and path lengths over 20 repetitions with no error bars, standard deviations, or statistical tests, and NEO is omitted from the forest comparison with 'N/A' entries. Because success rates such as 0.9 versus 0.9 and path-length differences around 1–2 m may be within noise, these point estimates do not support the claimed 'significant improvements.' Report per-path or per-repetition distributions, define the success criterion explicitly, and include NEO's timing or justify why its omission does not bias the forest comparison.
  4. [Section III-A, Eqs. (1)–(2)] The spatial reformulation, which is the core contribution, would benefit from a more precise statement of decision variables and the receding-horizon update. Equation (1) minimizes over Q and U, but the constraints (1a)–(1d) are written for q^{t+1}_k with fixed t, and the relationship between the spatial sequence {q_k, u_k} and the next time step q^{t+1} is not explicit. Please clarify the horizon N̄, the link indexing for base and arm, and how the optimized sequence is applied at each control step.
minor comments (6)
  1. [Section I] There are typos such as 'challanges' in the introduction, and the two consecutive paragraphs beginning 'On the other hand' should be restructured for readability.
  2. [Tables I–II] The table captions should define the columns 'Real-time' and 'Reference Requirement,' and state the number of repetitions and the success criterion used to compute the success rate.
  3. [Section IV.A.1] The text says '20 repetitions for each path,' but the table aggregates over three start-goal pairs; reporting per-path results would make the effect of obstacle density and initial path quality visible.
  4. [Section III-D] The bounding-box limits for free-region generation (0.8 m x 0.8 m x 0.8 m for the base and 0.4 m x 0.3 m x 0.3 m for links) are introduced without explaining how the bounding boxes are incorporated into the decomposition; a sentence or figure reference would help.
  5. [Abstract and Section IV] The open-source repository link appears only in the abstract; a Data Availability or Code Availability statement should be added in the main text.
  6. [Section III-C] The phrase 'The original points of the virtual links q1, q2, and q3 are located at the center of the mobile base' should be 'origins,' and the notation for the base control inputs (v_base_x, v_base_y, phi_dot) should be introduced explicitly before Eq. (2).

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the spatial-domain reformulation is self-contained; self-citations to prior SOS work are minor and not load-bearing.

full rationale

The derivation chain is self-contained. The central spatial-domain reformulation (Sections III-A to III-C) reparameterizes the single-step reactive control problem into a multi-step problem along the kinematic chain, with link-specific costs and constraints defined from kinematics and geometry rather than from the experimental outcomes. The collision-avoidance constraint Wk ⊆ Fk and the scaling-factor condition αk ≤ 1 are imported from the authors' prior work [18] via an SOS subproblem, but that prior work is a published, externally checkable result used as a computational tool, and the current paper extends it to per-link constraints rather than refitting it to the presented data. The experiments compare against external baselines (RRT, SLQ-MPC, Coupled-MPC, NEO) and report success rates, path lengths, and task completion, so the claimed improvements are not defined in terms of the method's own outputs. The repeated self-citations ([17], [18], [19]) are to prior works with overlapping authors, but they do not forbid alternatives or carry the central spatial-propagation claim, which stands on the formulation and on the external ALTRO solver. The skeptical observation that no solve times or control periods are reported concerns the evidence for the 'real-time' claim, but that is an empirical support gap, not a circular reduction of the derivation to its inputs.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

No new physical entities are introduced. The virtual base links are a modeling device. The central assumptions are the serial-chain kinematic model, the omnidirectional base decomposition, polynomial link geometry, the validity of the SOS subproblem from prior work, and convergence of AL-DDP.

free parameters (5)
  • Cost weights Qphi, Qk, Rk = not reported
    Hand-tuned quadratic weights for terminal pose error, per-link pose error, and control effort; they shape the objective but are not fitted to a benchmark.
  • Perception range = 3 m
    Limited sensor horizon used in both simulation and real-world tests; affects which obstacles are considered.
  • Free region max ranges = 0.8 m base; 0.4x0.3x0.3 m links
    Bounds on the polytopic free regions generated around each link; influence maneuverability and conservativeness.
  • Control time step Delta t = not specified
    Discretization used in the kinematic propagation (2a)-(2e); value not reported, though it affects control resolution.
  • Number of virtual base links = 3
    Splits base motion into x, y, yaw stages; this is a design choice that may not generalize to non-omnidirectional bases.
assumptions (5)
  • domain assumption Serial kinematic chain model with rigid links
    The propagation functions (2a)-(2e) assume the mobile manipulator is a serial chain where each link's pose is determined by the previous link and joint control.
  • domain assumption Omnidirectional base with decoupled x-y-yaw motion
    The three virtual base links in (2a)-(2c) assume the base can move independently along x, y, and yaw; this is not justified for non-omnidirectional bases.
  • domain assumption Link geometry representable by polynomial inequalities
    Collision avoidance in Section III-D models each link as a set of polynomial inequalities; this restricts the geometry to shapes that can be described this way.
  • domain assumption SOS subproblem solution and its gradient are correct and differentiable
    The safety constraint alpha_k <= 1 relies on the SOS programming formulation from [18], which the present paper does not re-derive.
  • standard math AL-DDP converges to a locally optimal solution
    The solver's convergence is assumed; no convergence analysis is provided for the spatial-domain problem.

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Cite this review

Pith. "Pith review of Local Reactive Control for Mobile Manipulators with Whole-Body Safety in Complex Environments." pith.science (2026). https://pith.science/paper/NLAXQA5Z

@misc{pith2026250102815,
  author       = {Pith},
  title        = {Pith review of: Local Reactive Control for Mobile Manipulators with Whole-Body Safety in Complex Environments},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NLAXQA5Z}},
  note         = {Machine review of arXiv:2501.02815}
}
read the original abstract

Mobile manipulators typically encounter significant challenges in navigating narrow, cluttered environments due to their high-dimensional state spaces and complex kinematics. While reactive methods excel in dynamic settings, they struggle to efficiently incorporate complex, coupled constraints across the entire state space. In this work, we present a novel local reactive controller that reformulates the time-domain single-step problem into a multi-step optimization problem in the spatial domain, leveraging the propagation of a serial kinematic chain. This transformation facilitates the formulation of customized, decoupled link-specific constraints, which is further solved efficiently with augmented Lagrangian differential dynamic programming (AL-DDP). Our approach naturally absorbs spatial kinematic propagation in the forward pass and processes all link-specific constraints simultaneously during the backward pass, enhancing both constraint management and computational efficiency. Notably, in this framework, we formulate collision avoidance constraints for each link using accurate geometric models with extracted free regions, and this improves the maneuverability of the mobile manipulator in narrow, cluttered spaces. Experimental results showcase significant improvements in safety, efficiency, and task completion rates. These findings underscore the robustness of the proposed method, particularly in narrow, cluttered environments where conventional approaches could falter. The open-source project can be found at https://github.com/Chunx1nZHENG/MM-with-Whole-Body-Safety-Release.git.

Figures

Figures reproduced from arXiv: 2501.02815 by the authors.

Figure 1
Figure 1. Overview of the proposed local reactive controller design approach. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Illustration of spatial kinematic propagation of base and manipula [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. (a). The free region (depicted in blue) for each link is generated [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Navigation of the mobile manipulator in the random forest environment. Three trajectories of the base from different start points are represented [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Visualization of the manipulation task in the unstructured envi [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: Visualization of the overall trajectory in the real-world experiment. The robot is reactive to its environment, avoiding obstacles and passing through [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. N2M: Bridging Navigation and Manipulation by Learning Pose Preference from Rollout

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    N2M predicts preferable base poses for manipulation policies from ego-centric point clouds, learned from rollouts, lifting success from 3% to 54% in the PnPCounterToCab task.

Reference graph

Works this paper leans on

23 extracted references · 21 canonical work pages · cited by 1 Pith paper

  1. [18]

    Collision-free trajectory optimization in cluttered environments using sums-of-squares programming,

    Y . Li, C. Zheng, K. Chen, Y . Xie, X. Tang, M. Y . Wang, and J. Ma, “Collision-free trajectory optimization in cluttered environments using sums-of-squares programming,” IEEE Robotics and Automation Letters, vol. 9, no. 12, pp. 11 026–11 033, 2024

    work page 2024

  2. [15]

    Planning dynamically feasible trajectories for quadrotors using safe flight corridors in 3-d complex environments,

    S. Liu, M. Watterson, K. Mohta, K. Sun, S. Bhattacharya, C. J. Taylor, and V . Kumar, “Planning dynamically feasible trajectories for quadrotors using safe flight corridors in 3-d complex environments,” IEEE Robotics and Automation Letters , vol. 2, no. 3, pp. 1688–1695, 2017

    work page 2017

  3. [1]

    Perceptive model predictive control for continuous mobile manipulation,

    J. Pankert and M. Hutter, “Perceptive model predictive control for continuous mobile manipulation,” IEEE Robotics and Automation Letters, vol. 5, no. 4, pp. 6177–6184, 2020

    work page 2020

  4. [2]

    Asymptotically optimal sampling-based kinodynamic planning,

    Y . Li, Z. Littlefield, and K. E. Bekris, “Asymptotically optimal sampling-based kinodynamic planning,” The International Journal of Robotics Research, vol. 35, no. 5, pp. 528–564, 2016

    work page 2016

  5. [3]

    STOMP: Stochastic trajectory optimization for motion planning,

    M. Kalakrishnan, S. Chitta, E. Theodorou, P. Pastor, and S. Schaal, “STOMP: Stochastic trajectory optimization for motion planning,” in 2011 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2011, pp. 4569–4574

    work page 2011

  6. [4]

    NEO: A novel expeditious optimisation algorithm for reactive motion control of manipulators,

    J. Haviland and P. Corke, “NEO: A novel expeditious optimisation algorithm for reactive motion control of manipulators,” IEEE Robotics and Automation Letters , vol. 6, no. 2, pp. 1043–1050, 2021

    work page 2021

  7. [5]

    Bi2rrt*: An efficient sampling-based path planning framework for task-constrained mobile manipulation,

    F. Burget, M. Bennewitz, and W. Burgard, “Bi2rrt*: An efficient sampling-based path planning framework for task-constrained mobile manipulation,” in 2016 IEEE/RSJ International Conference on Intel- ligent Robots and Systems (IROS) , 2016, pp. 3714–3721

    work page 2016

  8. [6]

    Sampling-based optimal motion planning with smart exploration and exploitation,

    Z. Wang, Y . Li, H. Zhang, C. Liu, and Q. Chen, “Sampling-based optimal motion planning with smart exploration and exploitation,” IEEE/ASME Transactions on Mechatronics , vol. 25, no. 5, pp. 2376– 2386, 2020

    work page 2020

Show all 23 references
  1. [7]

    Ac- celerating bi-directional sampling-based search for motion planning of non-holonomic mobile manipulators,

    S. Thakar, P. Rajendran, H. Kim, A. M. Kabir, and S. K. Gupta, “Ac- celerating bi-directional sampling-based search for motion planning of non-holonomic mobile manipulators,” in 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) , 2020, pp. 6711– 6717

    2020

  2. [8]

    CHOMP: Gradient optimization techniques for efficient motion planning,

    N. Ratliff, M. Zucker, J. A. Bagnell, and S. Srinivasa, “CHOMP: Gradient optimization techniques for efficient motion planning,” in 2009 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2009, pp. 489–494

    2009

  3. [9]

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

    J. Schulman, J. Ho, A. X. Lee, I. Awwal, H. Bradlow, and P. Abbeel, “Finding locally optimal, collision-free trajectories with sequential convex optimization.” in Robotics: science and systems , vol. 9, no. 1. Berlin, Germany, 2013, pp. 1–10

    2013

  4. [10]

    A holistic approach to reactive mobile manipulation,

    J. Haviland, N. S ¨underhauf, and P. Corke, “A holistic approach to reactive mobile manipulation,” IEEE Robotics and Automation Letters , vol. 7, no. 2, pp. 3122–3129, 2022

    2022

  5. [11]

    Visibility maximization controller for robotic manipulation,

    K. He, R. Newbury, T. Tran, J. Haviland, B. Burgess-Limerick, D. Kuli´c, P. Corke, and A. Cosgun, “Visibility maximization controller for robotic manipulation,” IEEE Robotics and Automation Letters , vol. 7, no. 3, pp. 8479–8486, 2022

    2022

  6. [12]

    OctoMap: An efficient probabilistic 3D mapping framework based on octrees,

    A. Hornung, K. M. Wurm, M. Bennewitz, C. Stachniss, and W. Bur- gard, “OctoMap: An efficient probabilistic 3D mapping framework based on octrees,” Autonomous Robots , 2013

    2013

  7. [13]

    FIESTA: Fast incremental Euclidean distance fields for online motion planning of aerial robots,

    L. Han, F. Gao, B. Zhou, and S. Shen, “FIESTA: Fast incremental Euclidean distance fields for online motion planning of aerial robots,” in 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2019, pp. 4423–4430

    2019

  8. [14]

    Real- time whole-body motion planning for mobile manipulators using environment-adaptive search and spatial-temporal optimization,

    C. Wu, R. Wang, M. Song, F. Gao, J. Mei, and B. Zhou, “Real- time whole-body motion planning for mobile manipulators using environment-adaptive search and spatial-temporal optimization,” in 2024 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2024, pp. 1369–1375

    2024

  9. [16]

    Coupled mobile manip- ulation via trajectory optimization with free space decomposition,

    M. Spahn, B. Brito, and J. Alonso-Mora, “Coupled mobile manip- ulation via trajectory optimization with free space decomposition,” in 2021 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2021, pp. 12 759–12 765

    2021

  10. [17]

    Geometry- aware safety-critical local reactive controller for robot navigation in unknown and cluttered environments,

    Y . Li, X. Tang, K. Chen, C. Zheng, H. Liu, and J. Ma, “Geometry- aware safety-critical local reactive controller for robot navigation in unknown and cluttered environments,” IEEE Robotics and Automation Letters, vol. 9, no. 4, pp. 3419–3426, 2024

    2024

  11. [19]

    FRTree Planner: Robot Navigation in Cluttered and Unknown Environments with Tree of Free Regions,

    Y . Li, Z. Song, C. Zheng, Z. Bi, K. Chen, M. Y . Wang, and J. Ma, “FRTree Planner: Robot Navigation in Cluttered and Unknown Environments with Tree of Free Regions,” 2024. [Online]. Available: https://arxiv.org/abs/2410.20230

    2024 arXiv

  12. [20]

    Differentiable collision detection for a set of convex primitives,

    K. Tracy, T. A. Howell, and Z. Manchester, “Differentiable collision detection for a set of convex primitives,” in 2023 IEEE International Conference on Robotics and Automation (ICRA) . IEEE, 2023, pp. 3663–3670

    2023

  13. [21]

    Siciliano, Ed., Robotics: Modelling, Planning and Control , ser

    B. Siciliano, Ed., Robotics: Modelling, Planning and Control , ser. Advanced Textbooks in Control and Signal Processing. Berlin, Germany: Springer, 2009

    2009

  14. [22]

    ALTRO: A fast solver for constrained trajectory optimization,

    T. A. Howell, B. E. Jackson, and Z. Manchester, “ALTRO: A fast solver for constrained trajectory optimization,” in 2019 IEEE Interna- tional Conference on Intelligent Robots and Systems (IROS) . IEEE, 2019, pp. 7674–7679

    2019

  15. [23]

    Cardinal Optimizer (COPT) user guide,

    D. Ge, Q. Huangfu, Z. Wang, J. Wu, and Y . Ye, “Cardinal Optimizer (COPT) user guide,” https://guide.coap.online/copt/en-doc, 2023

    2023

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Reviewed August 10, 2026 · model on record in the stance chip above.