This paper addresses the problem of time-optimal motions for a mobile platform in a planar environment. The platform has two non-steerable independently driven wheels. The overall mission of the robot is expressed in terms of a sequence of via points at which the platform must be at rest in a given configuration (position and orientation). The objective is to plan time-optimal trajectories betw...

Algorithms which guarantee to find globally optimal trajectories by covering a hypervolume of state space become infeasible in high dimensions. We have developed an algorithm which generates locally optimal trajectories without covering a hypervolume which only requires polynomial memory and time. Even though the algorithm does not guarantee a globally optimal trajectory in a deterministic mann...

economists were interested in economic stabilization policies as early as the 1930’s but the formal applications of stability theory from the classical control theory to economic analysis appeared in the early 1950’s when a number of control engineers actively collaborated with economists on economic stability and feedback mechanisms. the theory of optimal control resulting from the contributio...

This paper presents an approach to finding the time-optimal trajectories for a simple rigid-body model of a mobile robot in an obstacle-free plane. Previous work has used Pontryagin’s Principle to find strong necessary conditions on time-optimal trajectories of the rigid body; trajectories satisfying these conditions are called extremal trajectories. The main contribution of this paper is a met...

Abstract In collaborative robotics the manipulator trajectory has to be planned avoid collisions, yet in real-time. this paper we pose problem as minimization of a quadratic functional among piecewise linear trajectories angular (joint) space. The is subjected novel nonlinear inequality constraints that simplify original non-penetration become cheap evaluate real time while still preserving col...

In suitable robotic applications, throwing an object instead of placing it has the potential improving cycle time. this context, a challenge is to generate time-optimal pick-and-throw (P&T) trajectories in order further increase productivity. This article introduces methodology determine minimum-time motion. consists essentially determining optimal release configuration (i.e., position and velo...

We discuss some challenging open problems in the geometric control theory and sub-Riemannian geometry. It is getting harder to prove theorems and easier to force other people to prove them when you are sixty. Some colleagues asked me to describe interesting open problems in geometric control and sub-Riemannian geometry. Here I list few really challenging problems; some of them are open for a lo...

In this study a new approach is proposed for the generation of aircraft trajectories. The relative guidance of an aircraft, which is aimed to join in minimum time the track of a leader aircraft, is particularly considered. In a first place, a minimum time relative convergence problem is considered and optimal trajectories are characterized. Then the synthesis of a neural approximator for optima...