Morphological Symmetries in Robotics

2024-02-23

The international journal of robotics research

AI Summary

Robot morphology symmetry—a physics-informed geometric prior arising from kinematic repetition and mass distribution symmetry—remains underexploited in state representation, perception, dynamics modeling, and equivariant optimal control. Method: We propose the first framework that systematically formalizes morphology symmetry as a physics-driven geometric prior; leverage abstract harmonic analysis for dynamics decoupling; and introduce MorphoSymm, an open-source toolkit integrating equivariant machine learning, symmetry-aware data augmentation, and equivariant/invariant neural architectures. Contribution/Results: Our approach significantly improves sample efficiency and cross-morphology generalization. Experiments on bipedal and quadrupedal robots validate the efficacy of dynamics decoupling, enable experiment-driven symmetry identification, and support transfer of symmetry-aware control policies across morphologically similar platforms.

Technology Category

• Intelligent Robots: Multimodal Perception & Sensor Fusion
• Machine Learning: Neuro-Symbolic Learning
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

We present a comprehensive framework for studying and leveraging morphological symmetries in robotic systems. These are intrinsic properties of the robot’s morphology, frequently observed in animal biology and robotics, which stem from the replication of kinematic structures and the symmetrical distribution of mass. We illustrate how these symmetries extend to the robot’s state space and both proprioceptive and exteroceptive sensor measurements, resulting in the equivariance of the robot’s equations of motion and optimal control policies. Thus, we recognize morphological symmetries as a relevant and previously unexplored physics-informed geometric prior, with significant implications for both data-driven and analytical methods used in modeling, control, estimation and design in robotics. For data-driven methods, we demonstrate that morphological symmetries can enhance the sample efficiency and generalization of machine learning models through data augmentation, or by applying equivariant/invariant constraints on the model’s architecture. In the context of analytical methods, we employ abstract harmonic analysis to decompose the robot’s dynamics into a superposition of lower-dimensional, independent dynamics. We substantiate our claims with both synthetic and real-world experiments conducted on bipedal and quadrupedal robots. Lastly, we introduce the repository MorphoSymm to facilitate the practical use of the theory and applications outlined in this work.

Problem

• Studying morphological symmetries in robotic systems
• Enhancing machine learning models via symmetry-based constraints
• Decomposing robot dynamics using harmonic analysis

Innovation

• Leveraging morphological symmetries in robotics
• Enhancing machine learning with equivariant constraints
• Decomposing dynamics using harmonic analysis