Modes, Motions, and Morphology - Design Optimization for Legged Robots and Other Periodically Operating Mechanisms

Prof. Dr. C. David Remy (Stuttgart)

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We use optimal control for the concurrent computation of motions and ..

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... mechanical design. In the process, we will exploit the use of different ...

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... gaits at different speeds. These gaits are a consequence of ...

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...nonlinear modes (un-actuated periodic motions) of the mechanical dynamics.

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Project goals

  • development of a design assistant for finding optimal designs in mechatronic systems (mechanisms and machines) that perform quasi-periodic motions.
  • design optimization of legged systems
  • systematic methodologies
    • co-design of motion and morphology
    • leveraging passive (un-actuated) periodic motions
    • enhancing optimization with machine learning, continuation methods, and other techniques

First Phase Achievements

  • development of parametric design optimization framework comprising an upper level (design parameter exploration) and lower level (parameterized periodic trajectory optimization)
    • applied to find optimal leg stiffness in one-legged hopper [7]
  • enhancements of framework in finding globally optimal designs:
    • trajectory optimization through learned Koopman surrogates [6]
    • continuation in lower level: relating passive and optimal motions, exploiting indirect trajectory optimization [1-5]

How can we support other projects?

  • Tools
    • Optimal control
    • Transcriptions via single/multiple shooting and direct collocation
    • Numerical continuation of optimal solutions
    • Parametric models
    • Various implementations
  • Domain knowledge
    • Modeling of hybrid / nonsmooth dynamics
    • Simple and / or passive models
    • Practical perspective on robotics
    • Custom build hardware of legged and soft robots
  • Control
    • Locomotion/gaits/biomechanics

How could other projects support our work?

  • Model reduction
  • Learned models
  • Mixed integeroptimization

First Phase Publications

  1. Raff, M.; Rosa, N.; Remy, C. D. (2022). Generating Families of Optimally Actuated Gaits from a Legged System's Energetically Conservative Dynamics. International Conference on Intelligent Robots and Systems (IROS), p. 8866-8872, Kyoto, Japan. URL: https://doi.org/10.1109/IROS47612.2022.9981693
  2. Raff, M; Remy, C. D. (2023). Hard vs. Soft Contacts in Trajectory Optimization of Legged Robots: An Example with a Compliant Rubber Foot. ICRA 2023 Workshop on Embracing Contacts. URL: https://openreview.net/forum?id=k3O1RL0v_x
  3. Rosa, N.; Katamish, B.; Raff, M.; Remy, C. D. (2023). An Approach for Generating Families of Energetically Optimal Gaits from Passive Dynamic Walking Gaits, 2023 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 8551-8557, Detroit, MI, USA. DOI: https://doi.org/10.1109/IROS55552.2023.10342322
  4. Raff, M.; Remy, C. D. (2024). Continuation of Periodic Orbits in Conservative Hybrid Dynamical Systems and its Application to Mechanical Systems with Impulsive Dynamics. URL: https://doi.org/10.48550/arXiv.2402.06502, accepted on 25.10.2024 to Nonlinear Dynamics
  5. Raff, M.; Flaßkamp, K.; Remy, C. D. (2024). The Indirect Method for Generating Libraries of Optimal Periodic Trajectories and Its Application to Economical Bipedal Walking. URL: https://doi.org/10.48550/arXiv.2410.09512. submitted on 12.10.2024 to International Journal of Robotics Research (IJRR)
  6. Abou-Taleb, M.; Raff, M.; Flaßkamp, K.; Remy, C. D. (2024). Koopman Based Trajectory Optimization with Mixed Boundaries. URL: https://doi.org/10.48550/arXiv.2412.03195. submitted on 02.12.2024 to 7th Annual Learning for Dynamics & Control Conference Research (L4DC 2025)
  7. Khemakhem, I., Tschemernjak, D., Raff, M., & Remy, C. D. (2025). Impact of Leg Stiffness on Energy Efficiency in One Legged Hopping. URL: https://doi.org/10.48550/arXiv.2501.03971
  8. Payrebrune, K. de; Flasskamp, K.; Ströhla, T.; Sattel, T.; Bestle, D.; Röder, B.; Eberhard, P.; Peitz, S.; Stoffel, M.; Gulakala, R.; Borse, A.; Wohlleben, M.; Sextro, W.; Raff, M.; Remy, C. D.; Yadav, M.; Stender, M.; Delden, J. van; Lüddecke, T.; Langer, S. C.; Schultz, J.; Blech, C. (2024). The Impact of AI on Engineering Design Procedures for Dynamical Systems.URL: https://arxiv.org/abs/2412.12230. submitted on  20.11.2024 to Technische Mechanik.
  9. Ebel, H.; Delden, J. van; Lüddecke, T.; Borse, A.; Gulakala, R.; Stoffel, M.; Yadav, M.; Stender, M.; Schindler, L.; Payrebrune, K. de; Raff, M.; Remy, C.D.; Röder, B.; Eberhard, P. (2024). Data Publishing in Mechanics and Dynamics: Challenges, Guidelines, and Examples from Engineering Design. URL: https://doi.org/10.48550/arXiv.2410.18358. submitted on 27.11.2024 to Data-Centric Engineering.
  10. Raff, M.; Remy, C. D. (2024). Periodic Trajectories of a Passive One-Legged Hopper. In: DaRUS - Data Repository of the University of Stuttgart. URL: https://darus.uni-stuttgart.de/dataset.xhtml?persistentId=doi:10.18419/darus-4237

Contact

Prof. Dr. C. David Remy
Universität Stuttgart
Pfaffenwaldring 9
70569 Stuttgart
Room 3.133
Tel.: +49 711 685 60914
Email: remy@inm.uni-stuttgart.de

Further Information

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