[Paper Review] Optimizing Gait Libraries via a Coverage Metric

Brian Bittner, Shai Revzen|arXiv (Cornell University)|Jul 19, 2021

Robotic Locomotion and Control31 references4 citations

TL;DR

This paper proposes a coverage metric to optimize locomotion primitive libraries for robots, enabling them to maintain navigational capability after damage. By using data-driven system identification and Lie group-based state lattices, the method discovers non-intuitive, high-coverage gaits—demonstrated on simulated and physical robots, including one made of tree branches—achieving rapid recovery of mobility post-injury with minimal human bias.

ABSTRACT

Many robots move through the world by composing locomotion primitives like steps and turns. To do so well, robots need not have primitives that make intuitive sense to humans. This becomes of paramount importance when robots are damaged and no longer move as designed. Here we propose a goal function we call "coverage", that represents the usefulness of a library of locomotion primitives in a manner agnostic to the particulars of the primitives themselves. We demonstrate the ability to optimize coverage on both simulated and physical robots, and show that coverage can be rapidly recovered after injury. This suggests that by optimizing for coverage, robots can sustain their ability to navigate through the world even in the face of significant mechanical failures. The benefits of this approach are enhanced by sample-efficient, data-driven approaches to system identification that can rapidly inform the optimization of primitives. We found that the number of degrees of freedom improved the rate of recovery of our simulated robots, a rare result in the fields of gait optimization and reinforcement learning. We showed that a robot with limbs made of tree branches (for which no CAD model or first principles model was available) is able to quickly find an effective high-coverage library of motion primitives. The optimized primitives are entirely non-obvious to a human observer, and thus are unlikely to be attainable through manual tuning.

Motivation & Objective

• To develop a metric that evaluates the utility of a library of locomotion primitives in a way independent of human intuition or predefined motion types.
• To enable robots to recover navigational capability after mechanical damage by re-optimizing their gait libraries using a coverage-based objective.
• To reduce reliance on manually designed primitives by allowing the robot to discover effective gaits through optimization.
• To demonstrate that coverage optimization can yield high-performing, non-obvious gaits even in robots with unconventional or unmodeled morphologies.
• To investigate the role of degrees of freedom in recovery performance and the robustness of the coverage metric across varying robot designs.

Proposed method

• The coverage metric is defined as the extent to which a library of motion primitives can densely populate a region of the robot’s configuration space, modeled as a Lie group (SE(2) or SE(3)).
• The method uses sample-efficient, data-driven system identification to model robot dynamics from experimental motion data, bypassing the need for CAD or first-principles models.
• Primitives are optimized via a goal function that minimizes the average distance from a set of target points in SE(2) to the reachable states via primitive compositions.
• The optimization is performed iteratively: initial gaits are explored, and the best-performing subset is refined through repeated trials and performance evaluation.
• The approach leverages Lie group composition to model sequential motion, enabling accurate computation of reachable configurations from primitive sequences.
• The method is applied to both simulated robots and a physical robot made of tree branches, with no prior CAD or mechanical model available.

Experimental results

Research questions

• RQ1 Can a coverage metric be used to discover high-performing, non-intuitive locomotion primitives without human bias or predefined motion types?
• RQ2 How effectively can a robot recover navigational capability after mechanical damage by re-optimizing its gait library using the coverage metric?
• RQ3 What is the impact of degrees of freedom on the rate and quality of coverage recovery in damaged robots?
• RQ4 Can the coverage optimization method be applied to robots with unmodeled or unconventional morphologies, such as a tree branch robot?
• RQ5 Does the coverage metric lead to more robust and complementary primitive libraries compared to traditional hand-designed or direction-constrained gaits?

Key findings

• The robot achieved 40% of its body length per cycle in forward motion with a turning rate of 0.10 radians per cycle after 8 iterations of gait optimization.
• The coverage score decreased from 0.97 to 0.76 after 5 iterations of gait library optimization on hardware, indicating improved spatial coverage.
• A robot made of tree branches successfully discovered a non-intuitive, high-coverage gait library despite lacking a CAD model or first-principles dynamics.
• The optimization process recovered high-coverage gaits in a timescale competitive with reinforcement learning methods, such as those used by Google.
• The addition of degrees of freedom beyond four provided diminishing returns in recovery performance, suggesting a threshold for effective redundancy in damage recovery.
• The coverage metric enabled the discovery of gaits that rotate significantly during translation—non-obvious to humans but highly effective for navigation.