The Hamiltonian Structure of Nonlinear Elasticity: The Material and Convective Representations of Solids, Rods, and Plates

No Abstrac

Asymptotic Stability, Instability and Stabilization of Relative Equilibria

In this paper we analyze asymptotic stability, instability and stabilization for the relative equilibria, i.e. equilibria modulo a group action, of natural mechanical systems. The practical applications of these results are to rotating mechanical systems where the group is the rotation group. We use a modification of the Energy-Casimir and Energy-Momentum methods for Hamiltonian systems to analyze systems with dissipation. Our work couples the modern theory of block diagonalization to the classical work of Chetaev

Formalizing behavior-based planning for nonholonomic robots

In this paper we present a formalization of behavior-based planning for nonholonomic robotic systems. This work provides a framework that integrates features of reactive planning models with modern control-theory-based robotic approaches in the area of path-planning for nonholonomic robots. In particular, we introduce a motion description language, MDLe, that provides a formal basis for robot programming using behaviors, and at the same time permits incorporation of kinematic models of robots given in the form of differential equations. The structure of the language MDLe is such as to allow descriptions of triggers (generated by sensors) in the language. Feedback and feedforward control laws are selected and executed by the triggering events. We demonstrate the use of MDLe in the area of motion planning for nonholonomic robots. Such models impose limitations on stabilizability via smooth feedback, i.e. piecing together open loop and closed loop trajectories becomes essential in these circumstances, and MDLe enables one to describe such piecing together in a systematic manner. A reactive planner using the formalism of the paper is described. We demonstrate obstacle avoidance with limited range sensors as a test of this planner.

The Dynamics of Two Coupled Rigid Bodies

In this paper we derive a Poisson bracket on the phase space so(3)^*x so(3)^*x SO(3) such that the dynamics of two three- dimensional rigid bodies coupled by a ball and socket joint can be written as a Hamiltonian system

Echolocating Bats Use a Nearly Time-Optimal Strategy to Intercept Prey

Acquisition of food in many animal species depends on the pursuit and capture of moving prey. Among modern humans, the pursuit and interception of moving targets plays a central role in a variety of sports, such as tennis, football, Frisbee, and baseball. Studies of target pursuit in animals, ranging from dragonflies to fish and dogs to humans, have suggested that they all use a constant bearing (CB) strategy to pursue prey or other moving targets. CB is best known as the interception strategy employed by baseball outfielders to catch ballistic fly balls. CB is a time-optimal solution to catch targets moving along a straight line, or in a predictable fashion—such as a ballistic baseball, or a piece of food sinking in water. Many animals, however, have to capture prey that may make evasive and unpredictable maneuvers. Is CB an optimum solution to pursuing erratically moving targets? Do animals faced with such erratic prey also use CB? In this paper, we address these questions by studying prey capture in an insectivorous echolocating bat. Echolocating bats rely on sonar to pursue and capture flying insects. The bat's prey may emerge from foliage for a brief time, fly in erratic three-dimensional paths before returning to cover. Bats typically take less than one second to detect, localize and capture such insects. We used high speed stereo infra-red videography to study the three dimensional flight paths of the big brown bat, Eptesicus fuscus, as it chased erratically moving insects in a dark laboratory flight room. We quantified the bat's complex pursuit trajectories using a simple delay differential equation. Our analysis of the pursuit trajectories suggests that bats use a constant absolute target direction strategy during pursuit. We show mathematically that, unlike CB, this approach minimizes the time it takes for a pursuer to intercept an unpredictably moving target. Interestingly, the bat's behavior is similar to the interception strategy implemented in some guided missiles. We suggest that the time-optimal strategy adopted by the bat is in response to the evolutionary pressures of having to capture erratic and fast moving insects