Robust Jumping with an Articulated Soft Quadruped via Trajectory Optimization and Iterative Learning

Jiatao Ding, Mees A.van Loben Sels, Franco Angelini, Jens Kober, Cosimo Della Santina

Research output: Contribution to journalArticleScientificpeer-review


Quadrupeds deployed in real-world scenarios need to be robust to unmodelled dynamic effects. In this work, we aim to increase the robustness of quadrupedal periodic forward jumping (i.e., pronking) by unifying cutting-edge model-based trajectory optimization and iterative learning control. Using a reduced-order soft anchor model, the optimization-based motion planner generates the periodic reference trajectory. The controller then iteratively learns the feedforward control signal in a repetition process, without requiring an accurate full-body model. When enhanced by a continuous learning mechanism, the proposed controller can learn the control inputs without resetting the system at the end of each iteration. Simulations and experiments on a quadruped with parallel springs demonstrate that continuous jumping can be learned in a matter of minutes, with high robustness against various types of terrain.

Original languageEnglish
Pages (from-to)255-262
Number of pages8
JournalIEEE Robotics and Automation Letters
Issue number1
Publication statusPublished - 2023

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • Dynamics
  • Feedforward systems
  • Legged Robots
  • Morphology
  • Motion Control
  • Optimization and Optimal Control
  • Quadrupedal robots
  • Robots
  • Springs
  • Trajectory optimization


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