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Quadruped-Frog: Rapid Online Optimization of Continuous Quadruped Jumping

Guillaume Bellegarda, Milad Shafiee, Merih Ekin Özberk, Auke Ijspeert

TL;DR

This paper designs foot force profiles parameterized by only a few parameters which they optimize for directly on hardware with Bayesian Optimization, and shows that this control architecture is capable of diverse and omnidirectional jumps including forward, lateral, and twist (turning) jumps, even on uneven terrain.

Abstract

Legged robots are becoming increasingly agile in exhibiting dynamic behaviors such as running and jumping. Usually, such behaviors are either optimized and engineered offline (i.e. the behavior is designed for before it is needed), either through model-based trajectory optimization, or through deep learning-based methods involving millions of timesteps of simulation interactions. Notably, such offline-designed locomotion controllers cannot perfectly model the true dynamics of the system, such as the motor dynamics. In contrast, in this paper, we consider a quadruped jumping task that we rapidly optimize online. We design foot force profiles parameterized by only a few parameters which we optimize for directly on hardware with Bayesian Optimization. The force profiles are tracked at the joint level, and added to Cartesian PD impedance control and Virtual Model Control to stabilize the jumping motions. After optimization, which takes only a handful of jumps, we show that this control architecture is capable of diverse and omnidirectional jumps including forward, lateral, and twist (turning) jumps, even on uneven terrain, enabling the Unitree Go1 quadruped to jump 0.5 m high, 0.5 m forward, and jump-turn over 2 rad. Video results can be found at https://youtu.be/SvfVNQ90k_w.

Quadruped-Frog: Rapid Online Optimization of Continuous Quadruped Jumping

TL;DR

This paper designs foot force profiles parameterized by only a few parameters which they optimize for directly on hardware with Bayesian Optimization, and shows that this control architecture is capable of diverse and omnidirectional jumps including forward, lateral, and twist (turning) jumps, even on uneven terrain.

Abstract

Legged robots are becoming increasingly agile in exhibiting dynamic behaviors such as running and jumping. Usually, such behaviors are either optimized and engineered offline (i.e. the behavior is designed for before it is needed), either through model-based trajectory optimization, or through deep learning-based methods involving millions of timesteps of simulation interactions. Notably, such offline-designed locomotion controllers cannot perfectly model the true dynamics of the system, such as the motor dynamics. In contrast, in this paper, we consider a quadruped jumping task that we rapidly optimize online. We design foot force profiles parameterized by only a few parameters which we optimize for directly on hardware with Bayesian Optimization. The force profiles are tracked at the joint level, and added to Cartesian PD impedance control and Virtual Model Control to stabilize the jumping motions. After optimization, which takes only a handful of jumps, we show that this control architecture is capable of diverse and omnidirectional jumps including forward, lateral, and twist (turning) jumps, even on uneven terrain, enabling the Unitree Go1 quadruped to jump 0.5 m high, 0.5 m forward, and jump-turn over 2 rad. Video results can be found at https://youtu.be/SvfVNQ90k_w.
Paper Structure (16 sections, 10 equations, 9 figures, 1 table)

This paper contains 16 sections, 10 equations, 9 figures, 1 table.

Table of Contents

  1. Introduction
  2. Contribution
  3. Method
  4. Generating Jumping Motion Behaviors
  5. Leg Controller
  6. Virtual Model Control
  7. Bayesian Optimization
  8. Forward Jumping
  9. Lateral Jumping
  10. Twist Jumping
  11. Experimental Results and Discussion
  12. Implementation Details
  13. Optimization Convergence
  14. Continuous Jumping Optimization
  15. Rough Terrain Adaptation
  16. ...and 1 more sections

Figures (9)

  • Figure 1: Online optimized jumping. Top: forward jumping on rough terrain (0.5 $m$ height, 0.5 $m$ distance). Middle: twist jump, over 2 $rad$. Bottom: lateral jumping 0.3 $m$.
  • Figure 2: Control architecture for online jumping optimization. The right (blue) box represents the environment, where the solid arrows operate at 1 kHz. Desired foot force profiles are mapped to torques with the Jacobian. Cartesian PD impedance control helps to regulate the foot at a nominal position below the hips, and Virtual Model Control is added to help stabilize the robot and allow jumping in uneven terrain. The left (yellow) box represents the Bayesian Optimization, which selects new force profile parameters after each jump based on the accumulated cost function specifying the task.
  • Figure 3: Force trajectories for hopping forwards and right in the body frame. When the impulse is not active, the system is in the air, or landing. Parameter $f_0$ determines the frequency of the impulse, and parameter $f_1$ is the frequency between impulses (and is not optimized).
  • Figure 4: Jumping force directions visualized at the feet of the Unitree Go1 quadruped. Left: planar $XZ$ forces applied at the feet for jumping forward. Right: top view of lateral forces for performing a counterclockwise twist jump.
  • Figure 5: Training curves averaged across 5 runs with different random seeds for optimizing forward (top), lateral left (middle), and twist-turn (bottom) jumps in Gazebo. All runs result in successful jumping.
  • ...and 4 more figures