I INTRODUCTION Minimum time point to point motion planning has been solved considering kinematical constraints on speed and acceleration [3]. These bounds are approximations and imply the full capability of the robot cannot be utilized. Efficiency can be increased by considering the characteristics of the robot dynamics. [l] has presented a trajectory generation based on optimal control formula...

The problem of computing a single continuous trajectory which connects an arbitrary initial posture (position, heading, curvature) with a final posture remains unsolved. Previous approaches have either failed to achieve curvature continuity for the general case or generated sampled solutions which have not been efficient enough for real time use. The polynomial spiral is a generalization of the...

In this paper, we present an approach for designing feedback controllers for polynomial systems that maximize the size of the time-limited backwards reachable set (BRS). We rely on the notion of occupation measures to pose the synthesis problem as an infinite dimensional linear program (LP) and provide finite dimensional approximations of this LP in terms of semidefinite programs (SDPs). The so...

This article provides an introduction to some recent results in billiard dynamics. We present results that follow from a study of compact Riemann surfaces (equipped with a holomorphic 1-form) and an SL2R action on the moduli spaces of these surfaces. We concentrate on the progress toward classification of “optimal” billiard tables, those with the simplest trajectory structure.

this paper aims to discuss the requirements of safe and smooth trajectory planning of transporter mobile robots to perform non-prehensile object manipulation task. in non-prehensile approach, the robot and the object must keep their grasp-less contact during manipulation task. to this end, dynamic grasp concept is employed for a box manipulation task and corresponding conditions are obtained an...

In this paper, we present an approach for designing feedback controllers for polynomial systems that maximize the size of the time-limited backwards reachable set (BRS). We rely on the notion of occupation measures to pose the synthesis problem as an infinite dimensional linear program (LP) and provide finite dimensional approximations of this LP in terms of semidefinite programs (SDPs). The so...

A new method is investigated to reconfigure smart structures by the technique of polynomial series, used to approximate a true heteroclinic connection between unstable equilibria in a smart structure model. We explore the use of polynomials of varying order to firstly approximate the heteroclinic connection between two equalenergy unstable equilibrium points, and then develop an inverse method ...

This paper presents a novel algorithm for industrial robot trajectory planning based on the NURBS(Non-Uniform Rational B-Spline) curve and Slerp interpolation aiming at problems that of six-axis is not smooth enough in operation process, posture process non-uniform, starts stops frequently. Firstly, first problem, NURBS presented to improve smoothness curve. Combined with quaternion description...

for every $1leq s< n$, the $s^{th}$ derivative of a polynomial $p(z)$ of degree $n$ is a polynomial $p^{(s)}(z)$ whose degree is $(n-s)$. this paper presents a result which gives generalizations of some inequalities regarding the $s^{th}$ derivative of a polynomial having zeros outside a circle. besides, our result gives interesting refinements of some well-known results.