Image-based servo is a local control solution. Thanks to the feedback loop closed in the image space, local convergence and stability in the presence of modeling errors and noise perturbations are ensured when the error is small. The principal deficiency of this approach is that the induced (3D) trajectories are not optimal and sometimes, especially when the displacement to realize is large, th...

The problem of moving rigid bodies efficiently is of particular interest in robotics because the simplest model of a mobile robot or of a manipulated object is often a rigid body. Path planning, controller design and robot design may all benefit from precise knowledge of optimal trajectories for a set of permitted controls. In this work, we present a general solution to the problem of finding m...

Docking with potentially tumbling Targets is a common element of many mission architectures, including on-orbit servicing and active debris removal. This paper studies synchronized docking trajectories as a way to ensure the Chaser satellite remains on the docking axis of the tumbling Target, thereby reducing collision risks and enabling persistent onboard sensing of the docking location. Chase...

When applying methods of optimal control to motion planning or stabilization problems, some theoretical or numerical difficulties may arise, due to the presence of specific trajectories, namely, singular minimizing trajectories of the underlying optimal control problem. In this article, we provide characterizations for singular trajectories of control-affine systems. We prove that, under generi...

A Diesel cycle heat engine with internal and external irreversibilities of heat transfer and friction, in which the finite rate of combustion is considered and the heat transfer between the working fluid and the environment obeys Newton’s heat transfer law [ ( ) q T ≈ ∆ ], is studied in this paper. Optimal piston motion trajectories for minimizing entropy generation per cycle are derived for th...

This contribution concerns the development of generic methods and tools for robust optimal control of high-pressure liquid chromatographic separation processes. The proposed methodology exploits a deterministic robust formulation, that employs a linearization of the uncertainty set, based on Lyapunov differential equations to generate optimal elution trajectories in the presence of uncertainty....

This paper deals with the problem of planning and controlling the trajectories of the legs of a mobile robot moving through statically stable conngurations. Legs are supposed to possess signiicant weight compared to the chassis, and a degree of redundancy that can be used to maximize the robustness of equilibrium. We use optimal control techniques for planning joint trajectories that comply wit...

We consider batch process optimization and robust implementation of optimal control policies. The dynamic optimization of such processes is in most cases model based, and therefore subject to uncertainties. This may lead to sub-optimal control trajectories with significant economical losses. In this paper we extended the concept of self-optimizing control for the optimal operation of transient ...

The leapfrog algorithm, so-called because of its geometric nature, for solving a class of optimal control problems is proposed. Initially a feasible trajectory is given and subdivided into smaller pieces. In each subdivision, with the assumption that local optimal controls can easily be calculated, a piecewise-optimal trajectory is obtained. Then the junctions of these smaller pieces of optimal...

The design of a feedback controller, so as to minimize a given performance criterion, for a general non-linear dynamical system is difficult; if not impossible. But for a large class of nonlinear dynamical systems, the open loop control that minimizes a performance criterion can be obtained using calculus of variations and Pontryagin’s minimum principle. In this paper, the open loop optimal tra...