Geometric Fabrics for the Acceleration-based Design of Robotic Motion

Xie, Mandy; Wyk, Karl Van; Li, Anqi; Rana, Muhammad Asif; Fox, Dieter; Boots, Byron; Ratliff, Nathan

doi:10.48550/arxiv.2010.14750

Cited by 8 publications

(21 citation statements)

References 16 publications

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“…Section XI of [23] describes such an experimental setup in detail. In those experiments, geometric fabrics are used to navigate between a wall of cubbies and a set of floor boxes in a standard pick and place industrial setting.…”

Section: Heuristicsmentioning

confidence: 99%

Geometric Fabrics: Generalizing Classical Mechanics to Capture the Physics of Behavior

Wyk¹,

Xie²,

Li³

et al. 2021

Preprint

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Classical mechanical systems are central to controller design in energy shaping methods of geometric control. However, their expressivity is limited by position-only metrics and the intimate link between metric and geometry. Recent work on Riemannian Motion Policies (RMPs) has shown that shedding these restrictions results in powerful design tools, but at the expense of theoretical guarantees. In this work, we generalize classical mechanics to what we call geometric fabrics, whose expressivity and theory enable the design of systems that outperform RMPs in practice. Geometric fabrics strictly generalize classical mechanics forming a new physics of behavior by first generalizing them to Finsler geometries and then explicitly bending them to shape their behavior. We develop the theory of fabrics and present both a collection of controlled experiments examining their theoretical properties and a set of robot system experiments showing improved performance over a well-engineered and hardened implementation of RMPs, our current state-of-the-art in controller design.

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Section: Heuristicsmentioning

confidence: 99%

Geometric Fabrics: Generalizing Classical Mechanics to Capture the Physics of Behavior

Wyk¹,

Xie²,

Li³

et al. 2021

Preprint

Self Cite

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“…We use a generalized notion of a Riemannian Motion Policy (RMP) [1,2] as a building block for this theory, a mathematical object we call a spectral semi-spray (spec). 4 Second-order differential equations of the form M(x, ẋ)ẍ + f (x, ẋ) = 0 generally follow an algebra of summation and pullback across maps x = φ(q) (composition with ẋ = J q and ẍ = Jq + J q) that parallels RMPs. Specs have a natural (M, f ) X and canonical (M, M −1 f ) C X form as in [2].…”

Section: Treesmentioning

confidence: 99%

“…When π is a geometry, quickly reaching a high speed means that the influence of the non-geometric potential is diminished, promoting path consistency. See [4] for a concrete application of speed control.…”

Section: Regulationmentioning

confidence: 99%

“…In a series of three experiments, we demonstrate that Lagrangian systems can easily have behavioral terms that compete with one another, while the matching geometric fabric system generated by simply converting the policies to geometries exhibits the desired unbiased behavior. Even if we restrict the fabric's policies to those expressible as acceleration-based potentials which more intuitively combine as metric-weighted averages (see Section VI.B of [4]), Lagrangian fabrics still exhibit these issues.…”

Section: Planar Manipulator Experimentsmentioning

confidence: 99%

“…The expanded version of this paper [3] includes as well a sizable suite of controlled experiments on simple 2D point and planar arm systems validating the theoretical properties, exposing the utility of fabrics over standard Lagrangian systems (see Subsection I-A), and demonstrating the expected behavioral consistency of geometric fabrics (see Section V). Additionally, we present the design of a complete robotic system built on geometric fabrics in [4] and include a detailed discussions of the specific modeling tools and techniques used. 1…”

Section: Introductionmentioning

confidence: 99%

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Optimization Fabrics for Behavioral Design

Ratliff¹,

Wyk²,

Xie³

et al. 2020

Preprint

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Second-order differential equations define smooth system behavior. In general, there is no guarantee that a system will behave well when forced by a potential function, but in some cases they do and may exhibit smooth optimization properties such as convergence to a local minimum of the potential. Such a property is desirable and inherently linked to asymptotic stability. This paper presents a comprehensive theory of optimization fabrics which are second-order differential equations that encode nominal behaviors on a space and are guaranteed to optimize when forced by a potential function. Optimization fabrics, or fabrics for short, can encode commonalities among optimization problems that reflect the structure of the space itself, enabling smooth optimization processes to intelligently navigate each problem even when the potential function is simple and relatively naïve. Importantly, optimization over a fabric is asymptotically stable, so optimization fabrics constitute a building block for stable system design.

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An Optimization-based Motion Planning Method for Autonomous Driving Vehicle

Luo

Sun

2020

2020 3rd International Conference on Unmanned Systems (ICUS)

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Effective motion planning in high dimensional spaces is a long-standing open problem in robotics. One class of traditional motion planning algorithms corresponds to potential-based motion planning. An advantage of potential based motion planning is composability -different motion constraints can be easily combined by adding corresponding potentials. However, constructing motion paths from potentials requires solving a global optimization across configuration space potential landscape, which is often prone to local minima. We propose a new approach towards learning potential based motion planning, where we train a neural network to capture and learn an easily optimizable potentials over motion planning trajectories. We illustrate the effectiveness of such approach, significantly outperforming both classical and recent learned motion planning approaches and avoiding issues with local minima. We further illustrate its inherent composability, enabling us to generalize to a multitude of different motion constraints. Project website at https://energy-based-model.github.io/potentialmotion-plan.

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Geometric Fabrics for the Acceleration-based Design of Robotic Motion

Cited by 8 publications

References 16 publications

Geometric Fabrics: Generalizing Classical Mechanics to Capture the Physics of Behavior

Geometric Fabrics: Generalizing Classical Mechanics to Capture the Physics of Behavior

Optimization Fabrics for Behavioral Design

An Optimization-based Motion Planning Method for Autonomous Driving Vehicle

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