Two-Dimensional Rigid-Body Collisions With Friction

Summary. In this paper, we report on the design of a model-based controller that can achieve dynamical self-righting of a hexapod robot. Extending on our earlier work in this domain, we introduce a tractable multi-point contact model with Coulomb friction. We contrast the singularities inherent to the new model with other available methods and show that for our specific application, it yields dynamics which are well-defined. We then present a feedback controller that achieves "maximal" performance under morphological and actuation constraints, while ensuring the validity of the model by staying away from singularities. Finally, through systematic experiments, we demonstrate that our controller is capable of robust flipping behavior.

Section: Existence Of Solutions and Leg Jammingmentioning

confidence: 99%

Multi-Point Contact Models for Dynamic Self-Righting of a Hexapod

Saranlı¹,

Koditschek²

2005

“…At each iteration step, update v cb , v bt according to (18), and E 1 , E 2 according to (19)-(20). In case one impact is starting restitution, set maximum elastic energy E 1max or E 2max accordingly.…”

Section: Dynamics and Impact State Analysismentioning

confidence: 99%

“…Routh [15] developed a graphical method that constructs the trajectory of impulse accumulation based on Poisson's hypothesis. It was applied in the subsequent studies of two-dimensional rigid-body collisions with friction by Han and Gilmore [6] and by Wang and Mason [18] who classified impact and contact modes and offered a solution for each case. Later, Ahmed et al [1] extended Routh's method to impact analysis for multibody mechanical systems with a similar classification.…”

Section: Introductionmentioning

confidence: 99%

A State Transition Diagram for Simultaneous Collisions with Application in Billiard Shooting

Jia

Mason

Erdmann

2009

Abstract. This paper models a multibody collision in the impulse space as a state transition diagram, where each state represents a phase during which impacts are "active" at only a subset of the contact points. A state transition happens whenever an active impact finishes restitution, or an inactive impact gets reactivated, depending on whether the two involved bodies are instantaneously penetrating into each other or not. The elastic energy due to an impact is not only affected by the impulse at the corresponding contact point, but also by other impulses exerted on the two involved bodies during the impact. Consequently, Poisson's impulse-based law of restitution could result in negative energy. A new law governing the loss of elastic energy during restitution is introduced. Convergence of the impulse sequence generated by the state transition diagram is established. The collision outcome depends on the ratios of the contact stiffnesses rather than on their individual values. The collision model is then applied in an analysis of billiard shooting in which the cue stick impacts the cue ball, which in turn impacts the pool table.

“…Routh's graphical method [10] to construct the impulse trajectory has proven successful for analyzing 2-dimensional impacts, and has been later extended by various researchers [4,15,1]. For 3-dimensional impact, Darboux [3] was the first to describe impact dynamics in terms of normal impulse in the form of a differential equation.…”

Section: Introductionmentioning

confidence: 99%

Energy-Based Modeling of Tangential Compliance in 3-Dimensional Impact

Jia

2010

Abstract. This paper studies modeling of tangential compliance as two rigid bodies collide in the space. Stronge's spring-based contact structure [13, pp. 95-96] is extended to three dimensions. Slip or stick is indicated by the tangential motion of a massless particle connected to the contact point (viewed as an infinitesimal region) on one body via three orthogonal springs. We show that the effect of tangential compliance can be analyzed using normal impulse rather than time, contrary to a previous claim by Stronge. This is primarily due to the ability of updating the elastic energies of the three springs without knowledge of their stiffnesses or length changes. The change rates, nevertheless, are computable. So are sliding velocity and tangential impulse. The latter is then integrated into impact equations and contact kinematics, making the whole system driven by normal impulse alone. Examples include a ball and a pencil bouncing on a table, and a massé billiard shot. The theory has potential impact on impulsive robotic manipulation in which the ability to deal with friction and compliance is vital for skillful maneuvers.