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arxiv: 2606.10579 · v1 · pith:DVUG6PAHnew · submitted 2026-06-09 · 💻 cs.RO · cs.SY· eess.SY

LieIPM: Lie Group Interior Point Method for Direct Trajectory Optimization of Rigid Bodies

Sangli Teng , Ruiqi Zhang , Tzu-Yuan Lin , William A Clark , Mark Mueller , Ram Vasudevan , Maani Ghaffari , Koushil Sreenath This is my paper

Pith reviewed 2026-06-27 13:31 UTC · model grok-4.3

classification 💻 cs.RO cs.SYeess.SY
keywords trajectory optimizationLie groupsrigid body dynamicsinterior point methodvariational integratorsmanifold optimizationrobot motion planning
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The pith

Lie group interior point method optimizes rigid body trajectories directly on manifolds while preserving rotation topology.

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

The paper develops a structure-aware framework for constrained trajectory optimization that works directly on matrix Lie groups instead of Euclidean space. It builds second-order rigid body models on these groups to support Newton-type updates that keep the manifold geometry intact. From this model the authors derive a line-search Lie Group Interior Point Method that enforces constraints on the manifolds. The method is instantiated with Lie group variational integrators and closed-form intrinsic derivatives that exploit group symmetries. Numerical experiments show the approach avoids singularities and reaches solutions more reliably and quickly than general-purpose or other structure-exploiting solvers.

Core claim

The LieIPM performs direct trajectory optimization on matrix Lie groups by using second-order rigid body models, Lie group variational integrators, and closed-form intrinsic derivatives. Because the updates stay on the manifold, the topology of rotation motions is preserved by construction and singularities are avoided. The resulting constrained optimizer exhibits faster convergence and greater robustness than general-purpose solvers and existing structure-exploiting optimal control methods.

What carries the argument

Lie Group Interior Point Method (LieIPM) that executes Newton-type updates on matrix Lie groups via variational integrators and intrinsic derivatives to enforce manifold constraints.

If this is right

  • Rotation motions remain topologically correct throughout the optimization without manual chart switching.
  • Constraints defined on the manifold can be handled directly by the interior-point line search.
  • Group symmetries yield closed-form derivatives that reduce the cost of each Newton step.
  • The same Lie-group model applies to any rigid-body system whose configuration lives on SE(3) or SO(3).

Where Pith is reading between the lines

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

  • The same interior-point construction could be applied to trajectory optimization on other matrix Lie groups such as the special Euclidean group in higher dimensions.
  • Hybrid planners that alternate between learned warm starts and LieIPM refinement might inherit the singularity-free property.
  • The framework offers a natural route to structure-preserving model-predictive control loops that stay on the manifold at every receding horizon.

Load-bearing premise

Second-order rigid body dynamics on Lie groups can be used for Newton updates without creating new instabilities or requiring extra problem-specific tuning.

What would settle it

A rigid-body motion planning problem with large rotations in which a Euclidean interior-point solver diverges or reaches a singular point while LieIPM produces a dynamically feasible trajectory.

Figures

Figures reproduced from arXiv: 2606.10579 by Koushil Sreenath, Maani Ghaffari, Mark Mueller, Ram Vasudevan, Ruiqi Zhang, Sangli Teng, Tzu-Yuan Lin, William A Clark.

Figure 1
Figure 1. Figure 1: We develop Lie Group Interior Point Method (LIEIPM) for direct trajectory optimization of rigid bodies on matrix Lie groups. We compare the landscape of minR ∥R − I∥ 2 F , s.t R ∈ SO(3), using different parameterizations. For the Euler angle with the yaw angle fixed, we see repeated degenerate directions as a limit of the 3 DOF parameterization of SO(3). The equivalent quaternion version has two distinct s… view at source ↗
Figure 2
Figure 2. Figure 2: The hardware used in the experiment and the corresponding thrust force. We use a motion capture system for localization. 7.1.2. Software setup We implemented Algorithm 1 in C++. We apply the sparse linear solver MUMPS (Amestoy et al. 2019) to solve the modified symmetric indefinite KKT systems as in Appendix Section B.2. We use CasADi (Andersson et al. 2019) to evaluate the second￾order models in [PITH_FU… view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of the solutions of LIEIPM on SE(3) and SO(3) × R3 for steering a fully actuated rigid body with initial rotation around z−axis at location [1, 1, 0] to the identity pose. We find that LIEIPM is capable of generating discontinuous solutions as expected for rotation groups (Kalabic´ et al. 2017; Bhat and Bernstein 2000) [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The convergence of the four cases in [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Snapshots of the in-place flip experiments. The quadrotor was initialized at the hovering pose and then moved upward, followed by a back flip motion, and then recovered to the hovering pose. This motion traverses the singular pose where the pitch angle equals ±90◦. -1 -0.5 0 0.5 1 Quaternion (Restricted to One Branch) qw qx qy qz -1 -0.5 0 0.5 1 Quaternion (Double Cover) qw qx qy qz 19 19.2 19.4 19.6 19.8 … view at source ↗
Figure 6
Figure 6. Figure 6: The orientation of the in-place flip motion. Though a quaternion is a singularity-free representation, the representation can still be discontinuous if the branch of the quaternion is not chosen properly. Due to the double cover of the quaternion, the terminal pose moves to another branch after a full circle of rotation. The Euler angle exhibits a singularity when the pitch angle across the 90 deg. The rot… view at source ↗
Figure 7
Figure 7. Figure 7: Snapshots of the power loop experiments. The quadrotor is commanded to rotate about the y−axis for a full circle while tracking motions in the x − z plane. The quadrotor starts to flip from the bottom￾center to the bottom-right of the picture. as each iteration includes repeated interval integration, sensitivity propagation, condensing, and QP solves. For the CROCODDYL, we note that the performance degrade… view at source ↗
Figure 8
Figure 8. Figure 8: The orientation of the power-loop motion. Due to the translational motion, the rotation has more oscillation compared to the in-place motion. The trajectories of orientation represented by the rotation matrix remain continuous along the trajectory. 19.2 19.4 19.6 19.8 20 20.2 20.4 20.6 20.8 21 0 5 10 Tim e (m s) Computation Time (Flip) 14.8 15 15.2 15.4 15.6 15.8 16 16.2 16.4 0 5 10 Computation Time (Power… view at source ↗
Figure 9
Figure 9. Figure 9: The computational time and KKT residual in the runtime. The rate of MPC control loop is set to be 100Hz. We find that in the power-loop case, LIEIPM only takes half of 0.01s to finish the computation. In the flip case, the solver only reaches the time budget when the desired roll angle changes abruptly. of reference pitch angle consumes more time. For both motions, the KKT violation in most of the cases co… view at source ↗
read the original abstract

Designing dynamically feasible trajectories for rigid bodies is a fundamental problem in robotics. While direct methods are widely used, the existing constrained optimizers typically operate in Euclidean space and ignore the manifold structure of rigid body motions. This mismatch may introduce singularities or lead to poorly conditioned optimization problems. To bridge this gap, we develop a structure-aware framework for constrained trajectory optimization directly on matrix Lie groups. Our approach is based on the second-order rigid body models utilizing Lie group structures, which enables efficient Newton-type updates while preserving the underlying geometry. Building on this model, we propose a line-search Lie Group Interior Point Method (LieIPM) to handle constraints on the manifolds. We instantiate the framework for rigid body motion planning using Lie group variational integrators and derive closed-form intrinsic derivatives that exploit group symmetries. The LieIPM preserves the topology of rotation motions by construction and avoids singularities. Numerical results demonstrate superior robustness and faster convergence compared to general-purpose solvers and structure-exploiting optimal control methods.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

1 major / 1 minor

Summary. The paper claims to develop a structure-aware framework called LieIPM for constrained trajectory optimization directly on matrix Lie groups for rigid body motions. It is based on second-order rigid body models utilizing Lie group structures for efficient Newton-type updates, uses Lie group variational integrators, and derives closed-form intrinsic derivatives. The method preserves the topology of rotation motions by construction, avoids singularities, and numerical results show superior robustness and faster convergence compared to other solvers.

Significance. If the results hold, this provides a geometrically consistent approach to trajectory optimization that could improve performance in robotics by avoiding singularities and preserving manifold structure. The closed-form derivatives exploiting group symmetries are a strength for efficiency.

major comments (1)
  1. Numerical results section: The claims of superior robustness and faster convergence require more detailed description of the experimental setup, including specific baseline implementations, statistical controls, and error analysis to support the central performance claims.
minor comments (1)
  1. The abstract is dense; consider breaking down the contributions more clearly.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed review and constructive suggestion. We agree that the numerical results section requires expanded description to strengthen the performance claims, and we will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: Numerical results section: The claims of superior robustness and faster convergence require more detailed description of the experimental setup, including specific baseline implementations, statistical controls, and error analysis to support the central performance claims.

    Authors: We agree with this assessment. In the revised manuscript, we will expand the numerical results section to include: (1) explicit descriptions of baseline implementations (e.g., the specific general-purpose solvers such as IPOPT and CasADi-based methods, along with structure-exploiting optimal control approaches used for comparison); (2) statistical controls such as the number of independent trials, variation in initial conditions, and random seeds; and (3) quantitative error analysis including success rates, convergence tolerances, iteration counts with standard deviations, and failure modes. These additions will be supported by updated tables and figures. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's central construction—optimizing trajectories directly on matrix Lie groups using Lie-group variational integrators and intrinsic derivatives—defines the topology preservation and singularity avoidance as direct consequences of the manifold choice rather than deriving them from fitted data or self-referential premises. No load-bearing step reduces a claimed prediction or uniqueness result to an input parameter, self-citation chain, or ansatz smuggled from prior author work; the method is presented as an application of established Lie-group structures to interior-point optimization, with performance claims left to numerical comparison against external solvers. The derivation chain remains self-contained against the stated geometric assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only; no explicit free parameters, axioms, or invented entities are stated. The framework implicitly assumes that Lie-group variational integrators exist and can be differentiated in closed form without additional fitting.

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discussion (0)

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Reference graph

Works this paper leans on

254 extracted references · 1 canonical work pages

  1. [1]

    Advances in Neural Information Processing Systems , volume=

    Max entropy moment kalman filter for polynomial systems with arbitrary noise , author=. Advances in Neural Information Processing Systems , volume=

  2. [2]

    arXiv preprint arXiv:2603.09458 , year=

    Stein Variational Ergodic Surface Coverage with SE (3) Constraints , author=. arXiv preprint arXiv:2603.09458 , year=

    Pith/arXiv arXiv

  3. [3]

    arXiv preprint arXiv:2602.17832 , year=

    MePoly: Max Entropy Polynomial Policy Optimization , author=. arXiv preprint arXiv:2602.17832 , year=

    arXiv

  4. [4]

    arXiv preprint arXiv:2511.18683 , year=

    Online Learning-Enhanced Lie Algebraic MPC for Robust Trajectory Tracking of Autonomous Surface Vehicles , author=. arXiv preprint arXiv:2511.18683 , year=

    arXiv

  5. [5]

    arXiv preprint arXiv:2509.24157 , year=

    Learning hybrid dynamics via convex optimizations , author=. arXiv preprint arXiv:2509.24157 , year=

    arXiv

  6. [6]

    IEEE/ASME Transactions on Mechatronics , year=

    Invariant Filtering for Full-State Estimation of Ground Robots in Noninertial Environments , author=. IEEE/ASME Transactions on Mechatronics , year=

  7. [7]

    arXiv preprint arXiv:2604.20990 , year=

    A Survey of Legged Robotics in Non-Inertial Environments: Past, Present, and Future , author=. arXiv preprint arXiv:2604.20990 , year=

    Pith/arXiv arXiv

  8. [8]

    arXiv preprint arXiv:2510.11682 , year=

    Ego-Vision World Model for Humanoid Contact Planning , author=. arXiv preprint arXiv:2510.11682 , year=

    arXiv

  9. [9]

    SIAM review , volume=

    On the parametrization of the three-dimensional rotation group , author=. SIAM review , volume=. 1964 , publisher=

    1964

  10. [10]

    arXiv preprint arXiv:2512.10117 , year=

    CHyLL: Learning Continuous Neural Representations of Hybrid Systems , author=. arXiv preprint arXiv:2512.10117 , year=

    arXiv

  11. [11]

    IEEE Transactions on Robotics , volume=

    Port-Hamiltonian neural ODE networks on Lie groups for robot dynamics learning and control , author=. IEEE Transactions on Robotics , volume=. 2024 , publisher=

    2024

  12. [12]

    IEEE Control Systems Letters , volume=

    Adaptive control of SE (3) Hamiltonian dynamics with learned disturbance features , author=. IEEE Control Systems Letters , volume=. 2022 , publisher=

    2022

  13. [13]

    Quantum Theory for Mathematicians , pages=

    Lie groups, Lie algebras, and representations , author=. Quantum Theory for Mathematicians , pages=. 2013 , publisher=

    2013

  14. [14]

    2012 , publisher=

    Differential topology , author=. 2012 , publisher=

    2012

  15. [15]

    2024 , publisher=

    State estimation for robotics , author=. 2024 , publisher=

    2024

  16. [16]

    Science Robotics , volume=

    Agile and cooperative aerial manipulation of a cable-suspended load , author=. Science Robotics , volume=. 2025 , publisher=

    2025

  17. [17]

    IEEE Robotics and Automation Letters , volume=

    Nonlinear MPC for quadrotor fault-tolerant control , author=. IEEE Robotics and Automation Letters , volume=. 2022 , publisher=

    2022

  18. [18]

    Systems & control letters , volume=

    A topological obstruction to continuous global stabilization of rotational motion and the unwinding phenomenon , author=. Systems & control letters , volume=. 2000 , publisher=

    2000

  19. [19]

    Optimization-based Robot Control and State Estimation on Matrix Lie Groups , author=

  20. [20]

    2008 , publisher=

    Optimization algorithms on matrix manifolds , author=. 2008 , publisher=

    2008

  21. [21]

    Journal of Global Optimization , volume=

    The geometry of the Newton method on non-compact Lie groups , author=. Journal of Global Optimization , volume=. 2002 , publisher=

    2002

  22. [22]

    2020 IEEE International Conference on Robotics and Automation (ICRA) , pages=

    Crocoddyl: An efficient and versatile framework for multi-contact optimal control , author=. 2020 IEEE International Conference on Robotics and Automation (ICRA) , pages=. 2020 , organization=

    2020

  23. [23]

    IEEE Transactions on Robotics , volume=

    A comparative study of nonlinear mpc and differential-flatness-based control for quadrotor agile flight , author=. IEEE Transactions on Robotics , volume=. 2022 , publisher=

    2022

  24. [24]

    arXiv preprint arXiv:1905.07654 , year=

    Trajectory optimization on manifolds: A theoretically-guaranteed embedded sequential convex programming approach , author=. arXiv preprint arXiv:1905.07654 , year=

    Pith/arXiv arXiv 1905

  25. [25]

    ACM Transactions on Mathematical Software (TOMS) , volume=

    Performance and scalability of the block low-rank multifrontal factorization on multicore architectures , author=. ACM Transactions on Mathematical Software (TOMS) , volume=. 2019 , publisher=

    2019

  26. [26]

    Clark AND Ram Vasudevan AND Maani Ghaffari , TITLE =

    Sangli Teng AND Tzu-Yuan Lin AND William A. Clark AND Ram Vasudevan AND Maani Ghaffari , TITLE =. Proceedings of Robotics: Science and Systems , YEAR =

  27. [27]

    arXiv preprint arXiv:2403.16252 , year=

    Legged robot state estimation within non-inertial environments , author=. arXiv preprint arXiv:2403.16252 , year=

    arXiv

  28. [28]

    2022 American Control Conference (ACC) , pages=

    Input Influence Matrix Design for MIMO Discrete-Time Ultra-Local Model , author=. 2022 American Control Conference (ACC) , pages=. 2022 , organization=

    2022

  29. [29]

    arXiv preprint arXiv:2103.14252 , year=

    Toward safety-aware informative motion planning for legged robots , author=. arXiv preprint arXiv:2103.14252 , year=

    arXiv

  30. [30]

    arXiv preprint arXiv:2503.01842 , year=

    Discrete-Time Hybrid Automata Learning: Legged Locomotion Meets Skateboarding , author=. arXiv preprint arXiv:2503.01842 , year=

    arXiv

  31. [31]

    IEEE Robotics and Automation Letters , year=

    Towards Optimizing a Convex Cover of Collision-Free Space for Trajectory Generation , author=. IEEE Robotics and Automation Letters , year=

  32. [32]

    A Generalized Metriplectic System via Free Energy and System\

    Teng, Sangli and Iwasaki, Kaito and Clark, William and Yu, Xihang and Bloch, Anthony and Vasudevan, Ram and Ghaffari, Maani , journal=. A Generalized Metriplectic System via Free Energy and System\

  33. [33]

    Smooth Manifolds

    Lee, John M. Smooth Manifolds. Introduction to Smooth Manifolds. 2003. doi:10.1007/978-0-387-21752-9_1

    work page doi:10.1007/978-0-387-21752-9_1 2003

  34. [34]

    IFAC Proceedings Volumes , volume=

    Discrete mechanics and optimal control , author=. IFAC Proceedings Volumes , volume=. 2005 , publisher=

    2005

  35. [35]

    arXiv preprint arXiv:2502.04640 , year=

    Building Rome with Convex Optimization , author=. arXiv preprint arXiv:2502.04640 , year=

    arXiv

  36. [36]

    Science Robotics , volume=

    Unlocking aerobatic potential of quadcopters: Autonomous freestyle flight generation and execution , author=. Science Robotics , volume=. 2025 , publisher=

    2025

  37. [37]

    On the imbeddability of the real projective spaces in

    Massey, WS , year=. On the imbeddability of the real projective spaces in

  38. [38]

    2022 , organization=

    Howell, Taylor A and Tracy, Kevin and Le Cleac’h, Simon and Manchester, Zachary , booktitle=. 2022 , organization=

    2022

  39. [39]

    arXiv preprint arXiv:2406.05846 , year=

    Fast and Certifiable Trajectory Optimization , author=. arXiv preprint arXiv:2406.05846 , year=

    arXiv

  40. [40]

    Journal of guidance, control, and dynamics , volume=

    Direct trajectory optimization using nonlinear programming and collocation , author=. Journal of guidance, control, and dynamics , volume=

  41. [41]

    Optimality conditions for the nonlinear programming problems on

    Yang, Wei Hong and Zhang, Lei-Hong and Song, Ruyi , journal=. Optimality conditions for the nonlinear programming problems on

  42. [42]

    2014 , publisher=

    Boumal, Nicolas and Mishra, Bamdev and Absil, P-A and Sepulchre, Rodolphe , journal=. 2014 , publisher=

    2014

  43. [43]

    Numerical optimization , author=

  44. [44]

    Part II: Multibody dynamics , author=

    The discrete null space method for the energy consistent integration of constrained mechanical systems. Part II: Multibody dynamics , author=. International journal for numerical methods in engineering , volume=. 2006 , publisher=

    2006

  45. [45]

    Optimal Control Applications and Methods , volume=

    Discrete mechanics and optimal control for constrained systems , author=. Optimal Control Applications and Methods , volume=. 2010 , publisher=

    2010

  46. [46]

    Computer Methods in Applied Mechanics and Engineering , volume=

    The discrete null space method for the energy consistent integration of constrained mechanical systems: Part I: Holonomic constraints , author=. Computer Methods in Applied Mechanics and Engineering , volume=. 2005 , publisher=

    2005

  47. [47]

    Mathematical programming , volume=

    A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization , author=. Mathematical programming , volume=. 2003 , publisher=

    2003

  48. [48]

    Convex geometric motion planning of multi-body systems on

    Teng, Sangli and Jasour, Ashkan and Vasudevan, Ram and Ghaffari, Maani , journal=J-IJRR, pages=. Convex geometric motion planning of multi-body systems on. 2024 , publisher=

    2024

  49. [49]

    arXiv preprint arXiv:2303.01722 , year=

    Solving low-rank semidefinite programs via manifold optimization , author=. arXiv preprint arXiv:2303.01722 , year=

    arXiv

  50. [50]

    2015 , organization=

    Differential dynamic programming for optimal estimation , author=. 2015 , organization=

    2015

  51. [51]

    Discrete geometric optimal control on

    Kobilarov, Marin B and Marsden, Jerrold E , journal=. Discrete geometric optimal control on. 2011 , publisher=

    2011

  52. [52]

    arXiv preprint arXiv:1909.06586 , year=

    Highly dynamic quadruped locomotion via whole-body impulse control and model predictive control , author=. arXiv preprint arXiv:1909.06586 , year=

    arXiv 1909

  53. [53]

    2014 , publisher=

    Patterson, Michael A and Rao, Anil V , journal=. 2014 , publisher=

    2014

  54. [54]

    Discrete-time differential dynamic programming on

    Boutselis, George I and Theodorou, Evangelos , journal=. Discrete-time differential dynamic programming on. 2020 , publisher=

    2020

  55. [55]

    2011 , publisher=

    Houska, Boris and Ferreau, Hans Joachim and Diehl, Moritz , journal=. 2011 , publisher=

    2011

  56. [56]

    2013 , organization=

    A computationally efficient algorithm for state-to-state quadrocopter trajectory generation and feasibility verification , author=. 2013 , organization=

    2013

  57. [57]

    IEEE Transactions on Robotics , volume=

    Geometrically constrained trajectory optimization for multicopters , author=. IEEE Transactions on Robotics , volume=. 2022 , publisher=

    2022

  58. [58]

    IEEE Transactions on Robotics , volume=

    Perceptive locomotion through nonlinear model-predictive control , author=. IEEE Transactions on Robotics , volume=. 2023 , publisher=

    2023

  59. [59]

    2022 , organization=

    Vision-aided dynamic quadrupedal locomotion on discrete terrain using motion libraries , author=. 2022 , organization=

    2022

  60. [60]

    IEEE Transactions on Robotics , volume=

    Representation-free model predictive control for dynamic motions in quadrupeds , author=. IEEE Transactions on Robotics , volume=. 2021 , publisher=

    2021

  61. [61]

    2019 , organization=

    Howell, Taylor A and Jackson, Brian E and Manchester, Zachary , booktitle=C-IROS, pages=. 2019 , organization=

    2019

  62. [62]

    Consensus complementarity control for multi-contact

    Aydinoglu, Alp and Wei, Adam and Huang, Wei-Cheng and Posa, Michael , journal=. Consensus complementarity control for multi-contact. 2024 , publisher=

    2024

  63. [63]

    IEEE Transactions on Robotics , year=

    Fast contact-implicit model predictive control , author=. IEEE Transactions on Robotics , year=

  64. [64]

    Automatica , volume=

    Kalabi. Automatica , volume=. 2017 , publisher=

    2017

  65. [65]

    2024 , organization=

    Tinympc: Model-predictive control on resource-constrained microcontrollers , author=. 2024 , organization=

    2024

  66. [66]

    2005 , publisher=

    Gill, Philip E and Murray, Walter and Saunders, Michael A , journal=. 2005 , publisher=

    2005

  67. [67]

    Chomp: Covariant

    Zucker, Matt and Ratliff, Nathan and Dragan, Anca D and Pivtoraiko, Mihail and Klingensmith, Matthew and Dellin, Christopher M and Bagnell, J Andrew and Srinivasa, Siddhartha S , journal=J-IJRR, volume=. Chomp: Covariant. 2013 , publisher=

    2013

  68. [68]

    2019 , publisher=

    Contact-implicit trajectory optimization using variational integrators , author=. 2019 , publisher=

    2019

  69. [69]

    2023 , publisher=

    Autonomous navigation of underactuated bipedal robots in height-constrained environments , author=. 2023 , publisher=

    2023

  70. [70]

    Teng, Sangli and Zhang, Harry and Jin, David and Jasour, Ashkan and Ghaffari, Maani and Carlone, Luca , journal=

  71. [71]

    Proceedings of Robotics: Science and Systems , YEAR =

    Dayi E Dong AND Henry P Berger AND Ian Abraham , TITLE =. Proceedings of Robotics: Science and Systems , YEAR =

  72. [72]

    2014 , publisher=

    Motion planning with sequential convex optimization and convex collision checking , author=. 2014 , publisher=

    2014

  73. [73]

    2024 , publisher=

    Lai, Zhijian and Yoshise, Akiko , journal=. 2024 , publisher=

    2024

  74. [74]

    Simple algorithms for optimization on

    Liu, Changshuo and Boumal, Nicolas , journal=. Simple algorithms for optimization on. 2020 , publisher=

    2020

  75. [75]

    Sequential optimality conditions for nonlinear optimization on

    Yamakawa, Yuya and Sato, Hiroyuki , journal=. Sequential optimality conditions for nonlinear optimization on. 2022 , publisher=

    2022

  76. [76]

    Sequential quadratic optimization for nonlinear optimization problems on

    Obara, Mitsuaki and Okuno, Takayuki and Takeda, Akiko , journal=. Sequential quadratic optimization for nonlinear optimization problems on. 2022 , publisher=

    2022

  77. [77]

    Schiela, Anton and Ortiz, Julian , journal=. An

  78. [78]

    Ratliff, Nathan D and Issac, Jan and Kappler, Daniel and Birchfield, Stan and Fox, Dieter , journal=

  79. [79]

    Park, Frank C and Bobrow, James E and Ploen, Scott R , journal=J-IJRR, volume=. A. 1995 , publisher=

    1995

  80. [80]

    2023 , publisher=

    An introduction to optimization on smooth manifolds , author=. 2023 , publisher=

    2023

Showing first 80 references.