A mission design technique that uses invariant manifold techniques together with the optimal control algorithm DMOC produces locally optimal, low ∆V trajectories. Previously, invariant manifolds of the planar circular restricted three body problem (PCR3BP) have been used to design trajectories with relatively small ∆V . Using local optimal control methods, specifically DMOC, it is possible to r...

The optimal trajectory with respect to some metric for a system with a discrete set of controls may require very many switches between controls, or even infinitely many, a phenomenon called chattering; this can be problematic for existing motion planning algorithms that plan using a finite set of motion primitives. One remedy is to add some penalty for switching between controls. This paper exp...

An optimal control problem with time delay is considered in this paper. The asymptotic stability of optimal trajectories in terms of a terminal type functional is investigated. Under some conditions it is proved that there is a unique stationary point attracting all optimal trajectories not depending on initial functions.

We consider the continuous trajectories of the vector field induced by the primal affine scaling algorithm as applied to linear programming problems in standard form. By characterizing these trajectories as solutions of certain parametrized logarithmic barrier families of problems, we show that these trajectories tend to an optimal solution which in general depends on the starting point. By con...

In recent papers it has been suggested that human locomotion may be modeled as an inverse optimal control problem. In this paradigm, the trajectories are assumed to be solutions of an optimal control problem that has to be determined. We discuss the modeling of both the dynamical system and the cost to be minimized, and we analyze the corresponding optimal synthesis. The main results describe t...

We deal with the problem of planning collisionfree trajectories for robots operating in a shared space. Given the start and destination position for each of the robots, the task is to find trajectories for all robots that reach their destinations with minimum total cost such that the robots will not collide when following the found trajectories. Our approach starts from individually optimal tra...

Robot motion planning has applications in a wide range of areas such as robot navigation and medical surgery. Among the topics that are related to motion planning, computing time-optimal trajectories is challenging and of great importance. We want to move a robot from the start to the goal in the shortest time. There are four different vehicle designs that are considered in our work: Dubins car...

We deal with the problem of planning collisionfree trajectories for robots operating in a shared space. Given the start and destination position for each of the robots, the task is to find trajectories for all robots that reach their destinations with minimum total cost such that the robots will not collide when following the found trajectories. Our approach starts from individually optimal tra...

Singular systems have been studied extensively during the last two decades due Abstract to their many practical applications. Such systems possess numerous properties not shared by the well-known state variable systems. This paper considers the linear tracking problem for the continuous-time singular systems. The Hamilton-Jacobi theory is used in order to compute the optimal control and associa...

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...