Solving Models of Controlled Dynamic Planar Rigid-Body Systems with                 Frictional Contact

Greenfield, Aaron; Saranlı, Uluç

doi:10.1177/0278364905059056

Cited by 11 publications

(6 citation statements)

References 31 publications

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“…The existence of efficient contact mode enumeration algorithms which are polynomial in the number of contacts is not widely appreciated in the literature. For instance, Greenfield et al (2005) used the exponential time algorithm for contact mode enumeration in 2D. The work in Li et al (2015) proposed a 3D contact mode state estimation pipeline that generates the contact modes offline using the naive exponential enumeration method.…”

Section: Enumeration Of Contact Modesmentioning

confidence: 99%

Autogenerated manipulation primitives

Huang

Cheng

Mao

et al. 2023

The International Journal of Robotics Research

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The central theme in robotic manipulation is that of the robot interacting with the world through physical contact. We tend to describe that physical contact using specific words that capture the nature of the contact and the action, such as grasp, roll, pivot, push, pull, tilt, close, open etc. We refer to these situation-specific actions as manipulation primitives. Due to the nonlinear and nonsmooth nature of physical interaction, roboticists have devoted significant efforts towards studying individual manipulation primitives. However, studying individual primitives one by one is an inherently limited process, due engineering costs, overfitting to specific tasks, and lack of robustness to unforeseen variations. These limitations motivate the main contribution of this paper: a complete and general framework to autogenerate manipulation primitives. To do so, we develop the theory and computation of contact modes as a means to classify and enumerate manipulation primitives. The contact modes form a graph, specifically a lattice. Our algorithm to autogenerate manipulation primitives (AMP) performs graph-based optimization on the contact mode lattice and solves a linear program to generate each primitive. We designed several experiments to validate our approach. We benchmarked a wide range of contact scenarios and our pipeline’s runtime was consistently in the 10 s of milliseconds. In simulation, we planned manipulation sequences using AMP. In the real-world, we showcased the robustness of our approach to real-world modeling errors. We hope that our contributions will lead to more general and robust approaches for robotic manipulation.

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Section: Enumeration Of Contact Modesmentioning

confidence: 99%

Autogenerated manipulation primitives

Huang

Cheng

Mao

et al. 2023

The International Journal of Robotics Research

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“…Note that this precludes the possibility of redundant constraints, though there are methods of resolving such redundancies, e.g. in Greenfield et al (2005). In particular, this requirement is met if a K n ∈ C ω ( Q , ℝ | scriptK n | ) and A K ∈ C ω ( T Q , ℝ | scriptK | ) are constant rank 8…”

Section: Modeling Assumptionsmentioning

confidence: 99%

Section: Setup and Notationmentioning

confidence: 99%

A hybrid systems model for simple manipulation and self-manipulation systems

Johnson

Burden

Koditschek

2016

The International Journal of Robotics Research

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Rigid bodies, plastic impact, persistent contact, Coulomb friction, and massless limbs are ubiquitous simplifications introduced to reduce the complexity of mechanics models despite the obvious physical inaccuracies that each incurs individually. In concert, it is well known that the interaction of such idealized approximations can lead to conflicting and even paradoxical results. As robotics modeling moves from the consideration of isolated behaviors to the analysis of tasks requiring their composition, a mathematically tractable framework for building models that combine these simple approximations yet achieve reliable results is overdue. In this paper we present a formal hybrid dynamical system model that introduces suitably restricted compositions of these familiar abstractions with the guarantee of consistency analogous to global existence and uniqueness in classical dynamical systems. The hybrid system developed here provides a discontinuous but self-consistent approximation to the continuous (though possibly very stiff and fast) dynamics of a physical robot undergoing intermittent impacts. The modeling choices sacrifice some quantitative numerical efficiencies while maintaining qualitatively correct and analytically tractable results with consistency guarantees promoting their use in formal reasoning about mechanism, feedback control, and behavior design in robots that make and break contact with their environment. 1 Here, consistent refers to a combination of properties detailed in Section 3.4 analogous to the guarantee of global existence and uniqueness of solutions for a classical dynamical system. 2 Wolfram Mathematica 9, Numerical integration uses the NDSolve command, event detection uses the WhenEvent command. http://www.wolfram.com/mathematica/ 4 An execution of a hybrid dynamical system exhibits the Zeno phenomena if it undergoes an infinite number of discrete or logical switches in finite time (Definition 6). 5 E.g. using the algorithm proposed in Burden, Gonzalez, Vasudevan, Bajcsy and Sastry (2015) for hybrid control systems.3 phenomena (Drumwright 2010) as well as apparent contradictions between frictional forces and impulses discussed in Section 1.2.5) seems to come at the cost of persistence of contact. In contrast, here, persistence is one of the key simplifying modeling assumptions, expressing our intuitive experience of limbs interacting with the world, enabling some of the other assumptions, and affording our strong formal results. Despite being targeted at a different numerical integration scheme, many of the results in this paper, such as the consistent handling of massless limbs, are potentially applicable to time-stepping schemes. Hybrid Dynamical SystemsThis paper models manipulation and self-manipulation systems using a hybrid systems paradigm that assumes instantaneous transitions. Though we develop our (so-called) self-manipulation hybrid dynamical system for a similar class of mechanical systems as that considered in (van der Schaft and Schumacher 1998, Ex. 3.3), we specialize fr...

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“…When contralateral legs on this platform are used in synchrony for behaviors such as the pronk, the sprawled posture of the morphology ensures that locomotion dynamics live on the saggital plane. Consequently, a saggital planar model is often capable of capturing relevant aspects of the dynamics for the purposes of modeling and analyzing such behaviors (Saranli et al 2004;Greenfield et al 2005). In this section, we describe and use such a planar model, Slimpod (Saranli 2000(Saranli , 2002, to design a feedback controller for pronking.…”

Section: Dynamics and Control Of Planar Hexapedal Pronkingmentioning

confidence: 99%

Control of underactuated planar pronking through an embedded spring-mass Hopper template

Ankaralı

Saranlı

2010

Auton Robot

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Autonomous use of legged robots in unstructured, outdoor settings requires dynamically dexterous behaviors to achieve sufficient speed and agility without overly complex and fragile mechanics and actuation. Among such behaviors is the relatively under-studied pronking (aka. stotting), a dynamic gait in which all legs are used in synchrony, usually resulting in relatively slow speeds but long flight phases and large jumping heights. Instantiations of this gait for robotic systems have been mostly limited to open-loop strategies, suffering from severe pitch instability for underactuated designs due to the lack of active feedback. However, both the kinematic simplicity of this gait and its dynamic nature suggest that the Spring-Loaded Inverted Pendulum model (SLIP) would be a good basis for the implementation of a more robust feedback controller for pronking. In this paper, we describe how template-based control, a controller structure based on the embedding of a simple dynamical "template" within a more complex "anchor" system, can be used to achieve very stable pronking for a planar, underactuated hexapod robot. In this context, high-level control of the gait is regulated through speed and height commands to the SLIP template, while the embedding controller ensures the stability of the remaining degrees of freedom. We use simulation studies to show that unlike existing open-loop alternatives, the resulting control struc-M.M. Ankaralı Dept. of Electrical and Electronics Eng., Middle East Technical University, Ankara, Turkey e-mail: e134441@metu.edu.tr U. Saranlı ( ) Dept. of Computer Engineering, Bilkent University, Ankara, Turkey e-mail: saranli@cs.bilkent.edu.tr ture provides explicit gait control authority and significant robustness against sensor and actuator noise.

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Solving Models of Controlled Dynamic Planar Rigid-Body Systems with Frictional Contact

Cited by 11 publications

References 31 publications

Autogenerated manipulation primitives

Autogenerated manipulation primitives

A hybrid systems model for simple manipulation and self-manipulation systems

Control of underactuated planar pronking through an embedded spring-mass Hopper template

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