This paper considers the optimal control problem of connecting two periodic trajectories with maximal persistence. A maximally persistent trajectory is close to the periodic type in the sense that the norm of the image of this trajectory under the operator defining the periodic type is minimal among all trajectories. A solution is obtained in this paper for the case when the two trajectories ha...

Many mechatronic systems are controlled with predefined input trajectories, either in open loop or using feedback. This research considers the optimization of these trajectories, for mechatronic applications whose dynamics are difficult to model, and vary in a significant and unpredictable manner over time. For these applications, solving the trajectories with an optimal control problem require...

We describe a numerical method for computing optimal trajectories for fully actuated mechanical systems. This method uses the fact that fully actuated mechanical systems are diierentially at with conngura-tion variables as at outputs to parametrize the system trajectories by connguration space trajectories. Our approach has the advantage that the system ODEs are implicitly satissed and hence we...

In this paper a control law for tracking of underactu-ated surface vessels is presented. Optimal trajectories for surface vessels are given as combinations of arcs of circles and line segments. It is shown how optimal trajectories can be made smooth by a technique called splines, and how these trajectories can be stabilized by backstepping. The control law depends on that the forward velocity o...

A common mobile robot design consists of three ‘omniwheels’ arranged at the vertices of an equilateral triangle, with wheel axles aligned with the rays from the center of the triangle to each wheel. Omniwheels, like standard wheels, are driven by the motors in a direction perpendicular to the wheel axle, but unlike standard wheels, can slip in a direction parallel to the axle. Unlike a steered ...

This paper deiielops a method for generating smooth trajectories f o r mobile robots in formation. The problem of trajectory generation is cast in terms of designing optimal curves on the Euclidean group, SE(3 ) . Specifically, the method generates the trajectory that minimizes the total energy associated with the translations and rotations of the robots, while maintaining a rigid formation. W ...

This paper investigates the value function, V , of a Mayer optimal control problem with the state equation given by a differential inclusion. First, we obtain an invariance property for the proximal and Fréchet subdifferentials of V along optimal trajectories. Then, we extend the analysis to the sub/superjets of V , obtaining new sensitivity relations of second order. By applying sensitivity an...

this paper presents optimal control method to path planning of mobile robots with flexible joints. dynamic equations are derived and additional kinematic constraints are used to solve the extra dofs arose from base mobility. then with modeling the elasticity at each joint as a linear torsinal spring, the set of equations are formed. the hamiltonian function is formed and the necessary condition...

The optimal trajectories are known analytically for only a few ground vehicles: steered cars (Dubins 1957; Reeds & Shepp 1990), and wheel-chair-like differential-drive vehicles (Balkcom & Mason 2002). This paper presents the analytical time-optimal trajectories for a kinematic model of a vehicle of a new class, shown in figure 1(a). The wheels are omniwheels; unlike regular wheels, omniwheels s...

This article deals with the optimal transfer of a satellite between Keplerian orbits using low propulsion. It is based on preliminary results of Geffroy [Généralisation des techniques de moyennation en contrôle optimal, application aux problèmes de rendez-vous orbitaux à poussée faible, Ph.D. Thesis, Institut National Polytechnique de Toulouse, France, Octobre 1997] where the optimal trajectori...