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Whole-Body Trajectory Optimization for Robot Multimodal Locomotion

Giuseppe L'Erario, Gabriele Nava, Giulio Romualdi, Fabio Bergonti, Valentino Razza, Stefano Dafarra, Daniele Pucci

TL;DR

The paper addresses multimodal robot trajectory planning by formulating a whole-body trajectory optimization that unifies aerial and terrestrial locomotion through centroidal momentum dynamics. It integrates thrust, contact forces, and full kinematics within a kino-dynamic framework, including a relaxed complementarity treatment for contacts and a second-order jet dynamics model. The approach is implemented via the ADAM CasADi-based dynamics library and solved with IPOPT on the iRonCub platform, demonstrating take-off, landing, gait transitions, and jumping. While capable of generating rich multimodal motions, the method incurs substantial computation time, indicating suitability for planning rather than real-time control, with future work aimed at developing a stabilizing whole-body controller. The results highlight the potential of unified trajectory optimization to seamlessly switch between locomotion modalities in complex environments.

Abstract

The general problem of planning feasible trajectories for multimodal robots is still an open challenge. This paper presents a whole-body trajectory optimisation approach that addresses this challenge by combining methods and tools developed for aerial and legged robots. First, robot models that enable the presented whole-body trajectory optimisation framework are presented. The key model is the so-called robot centroidal momentum, the dynamics of which is directly related to the models of the robot actuation for aerial and terrestrial locomotion. Then, the paper presents how these models can be employed in an optimal control problem to generate either terrestrial or aerial locomotion trajectories with a unified approach. The optimisation problem considers robot kinematics, momentum, thrust forces and their bounds. The overall approach is validated using the multimodal robot iRonCub, a flying humanoid robot that expresses a degree of terrestrial and aerial locomotion. To solve the associated optimal trajectory generation problem, we employ ADAM, a custom-made open-source library that implements a collection of algorithms for calculating rigid-body dynamics using CasADi.

Whole-Body Trajectory Optimization for Robot Multimodal Locomotion

TL;DR

The paper addresses multimodal robot trajectory planning by formulating a whole-body trajectory optimization that unifies aerial and terrestrial locomotion through centroidal momentum dynamics. It integrates thrust, contact forces, and full kinematics within a kino-dynamic framework, including a relaxed complementarity treatment for contacts and a second-order jet dynamics model. The approach is implemented via the ADAM CasADi-based dynamics library and solved with IPOPT on the iRonCub platform, demonstrating take-off, landing, gait transitions, and jumping. While capable of generating rich multimodal motions, the method incurs substantial computation time, indicating suitability for planning rather than real-time control, with future work aimed at developing a stabilizing whole-body controller. The results highlight the potential of unified trajectory optimization to seamlessly switch between locomotion modalities in complex environments.

Abstract

The general problem of planning feasible trajectories for multimodal robots is still an open challenge. This paper presents a whole-body trajectory optimisation approach that addresses this challenge by combining methods and tools developed for aerial and legged robots. First, robot models that enable the presented whole-body trajectory optimisation framework are presented. The key model is the so-called robot centroidal momentum, the dynamics of which is directly related to the models of the robot actuation for aerial and terrestrial locomotion. Then, the paper presents how these models can be employed in an optimal control problem to generate either terrestrial or aerial locomotion trajectories with a unified approach. The optimisation problem considers robot kinematics, momentum, thrust forces and their bounds. The overall approach is validated using the multimodal robot iRonCub, a flying humanoid robot that expresses a degree of terrestrial and aerial locomotion. To solve the associated optimal trajectory generation problem, we employ ADAM, a custom-made open-source library that implements a collection of algorithms for calculating rigid-body dynamics using CasADi.
Paper Structure (25 sections, 33 equations, 5 figures)

This paper contains 25 sections, 33 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Background
  3. Notation
  4. Floating-base modeling
  5. Models for Trajectory Optimisation
  6. Centroidal Momentum Dynamics
  7. Models for the actuation of aerial locomotion
  8. Models for the actuation of terrestrial locomotion
  9. Trajectory optimisation
  10. Constraints
  11. Centroidal dynamics
  12. Centroidal Momentum and Kinematics
  13. Contact points and forces
  14. Jet location and dynamics
  15. Variables integration
  16. ...and 10 more sections

Figures (5)

  • Figure 1: iRonCub: the jet-powered humanoid robot. The jets are attached to the arms and the chest and exert 160N and 220N respectively.
  • Figure 2: Snapshots and trajectories of the robot during the take-off.
  • Figure 3: Snapshots and trajectories of the robot during the take-off and landing.
  • Figure 4: Snapshots and trajectories of the transition from walking to flight.
  • Figure 5: Snapshots of the robot jumping.