Optimization Fabrics for Behavioral Design

Ratliff, Nathan; Wyk, Karl Van; Xie, Mandy; Li, Anqi; Rana, Muhammad Asif

doi:10.48550/arxiv.2010.15676

Cited by 4 publications

(21 citation statements)

References 15 publications

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“…The algebra defined in Subsection V-A is equivalent to the reduction of sums and pullback to the sums and pullback of these individual pairs. For concreteness, and in alignment with the terminology of [17], we call these pairs specs, short for spectral semisprays, which is descriptive of the differential equation they represent emphasizing the spectral role of the metric M.…”

Section: Appendix V Details On Designing With Fabrics a Derivations O...mentioning

confidence: 99%

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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: Appendix V Details On Designing With Fabrics a Derivations O...mentioning

confidence: 99%

“…There is a broader theory of optimization fabrics[17] that drops the geometric requirement but retains the optimization properties outlined in Theorem IV.4. Geometric fabrics are the most concrete type of fabric and the most natural generalization of classical mechanics.…”

mentioning

confidence: 99%

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

Wyk¹,

Xie²,

Li³

et al. 2021

Preprint

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“…Optimization fabrics [1] are the culmination of that line of work into a comprehensive mathematical theory of behavioral design with rigorous stability guarantees, and geometric fabrics are their concrete incarnation. Earlier systems orchestrated RMPs in system applications using complex state machines to skirt the difficulty of designing nonlinear policies directly.…”

Section: A Related Workmentioning

confidence: 99%

“…Fast, reactive motion is essential for most modern tasks, especially in highly-dynamic and uncertain collaborative environments. We describe here a set of tools built from geometric fabrics, derived from our recent theory of optimization fabrics [1], for the direct construction of stable robotic behavior in modular parts. 1 Fabrics define a nominal behavior independent of a specific task, capturing cross-task commonalities like joint-limit avoidance, obstacle avoidance, and redundancy resolution, and implement a task as an optimization problem across the fabric.…”

Section: Introductionmentioning

confidence: 99%

“…We derive tools for designing these fabrics and demonstrate their utility on a Franka Panda robot in a standard setting commonplace in industry. *Equal contribution, 1 All authors are with (or interned at) NVIDIA, 2 Georgia Tech, 3 University of Washington 1 The term fabric is used analogously to the term fabric of spacetime from theoretical physics, but formalizes the idea as a second-order nonlinear differential equation characterizing an unbiased nominal behavior.…”

Section: Introductionmentioning

confidence: 99%

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Geometric Fabrics for the Acceleration-based Design of Robotic Motion

Xie¹,

Wyk²,

Li³

et al. 2020

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Generalized Nonlinear and Finsler Geometry for Robotics

Ratliff¹,

Wyk²,

Xie

et al. 2021

2021 IEEE International Conference on Robotics and Automation (ICRA)

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Most physical systems have dynamics functions that are just a nuisance to policies. Torque policies, for instance, usually have to effectively invert the natural classical mechanical dynamics to get their job done. Because of this, we often use controllers to make things easier on policies. For instance, inverse dynamics controllers wipe out the physical dynamics so the policy starts from a clean slate. That makes learning easier, but still the policy needs to learn everything about the problem, including aspects of a solution which are common to many other problems, such as how to make the end-effector move in a straight line, how to avoid joints and self collisions, how to avoid obstacles, etc. Over the past few years it's become standard to formulate learning not in C-space, but in end-effector space and use controllers such as Operational Space Control (OSC) to capture some of these commonalities. These controllers, whether inverse dynamics or OSC, reshape the natural dynamics of the system into a different second-order dynamical system whose behavior is more useful. And the trend is, the more useful behavior we can pack into these reshaped systems, the easier it is to learn policies.However, OSC is from the 80's, and captures only straight line end-effector motion. There's a lot more behavior we could and should be packing into these systems. Earlier work [15,16,19] developed a theory that generalized these ideas and constructed a broad and flexible class of second-order dynamical systems which was simultaneously expressive enough to capture substantial behavior (such as that listed above), and maintained the types of stability properties that make OSC and controllers like it a good foundation for policy design and learning. This paper, motivated by the empirical success of the types of fabrics used in [20], reformulates the theory of fabrics into a form that's more general and easier to apply to policy learning problems. We focus on the stability properties that make fabrics a good foundation for policy synthesis. Fabrics create a fundamentally stable medium within which a policy can operate; they influence the system's behavior without preventing it from achieving tasks within its constraints. When a fabrics is geometric (path consistent) we can interpret the fabric as forming a road network of paths that the system wants to follow at constant speed absent a forcing policy, giving geometric intuition to its role as a prior. The policy operating over the geometric fabric acts to modulate speed and steers the system from one road to the next as it accomplishes its task.We reformulate the theory of fabrics here rigorously and develop theoretical results characterizing system behavior and illuminating how to design these systems, while also emphasizing intuition throughout.

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Optimization Fabrics for Behavioral Design

Cited by 4 publications

References 15 publications

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

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

Geometric Fabrics for the Acceleration-based Design of Robotic Motion

Generalized Nonlinear and Finsler Geometry for Robotics

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