This paper presents a method for generating neartime optimal trajectories in cluttered environments for manipulators wath invariant inertia matrices. For one obsdacle, the .methop generates the time-optimal trajectory b y manamatang the fame-deravatave of the return (cost) function for this problem, satisfying the HamiltonJacobi-Bellman (HJB) equation. For multiple obstacles, the trajectory i s...

The theory of optimal control is applied to obtain minimum-time trajectories for solar sail spacecraft for interplanetary missions. We consider the gravitational and solar radiation forces due to the Sun. The spacecraft is modelled as a flat sail of mass m and surface area A and is treated dynamically as a point mass. Coplanar circular orbits are assumed for the planets. We obtain optimal traje...

we design a two-stage scheme to consider trajectory planning problem of two mobile manipulators for cooperative transportation of a rigid body in presence of static obstacles. within the first stage, regarding the static obstacles we develop a method that searches the workspace for the shortest possible path between start and goal configurations by constructing a graph on a portion of the confi...

We show how optimal Hankel-norm approximations of dynamical systems allow for a straightforward interpretation in terms of system trajectories. It is shown that for discrete time single-input systems optimal reductions are obtained by cutting ’balanced trajectories’, i.e., by disconnecting the past and future in the input-output pairs relating to leftand right singular vectors of the system. A ...

The main contribution of this paper is a novel method for planning globally optimal trajectories dynamical systems subject to polygonal constraints. proposed hybrid trajectory approach, which combines graph search, i.e. discrete roadmap method, with convex optimization, complete path method. Contrary past approaches, have focused on using simple obstacle approximations, or sub-optimal spatial d...

The main objective of this article is to optimize the walking pattern of a 2D humanoid robot with heel-off and toe-off motions in order to minimize the energy consumption and maximize the stability margin. To this end, at first, a gait planning method is introduced based on the ankle and hip joint position trajectories. Then, using these trajectories and the inverse kinematics, the position tra...

We solve an optimal growth model in continuous space, continuous and bounded time. The optimizer chooses the optimal trajectories of capital and consumption across space and time by maximizing an objective function with both space and time discounting. We extract the corresponding Pontryagin conditions and prove their sufficiency. We end up with a system of two parabolic differential equations ...

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...

A dynamic model of investment process for a technology innovator in a market environment is designed. The ”light” dynamics of the active innovator is described by the system of exponential trajectories in which one can quickly change growth parameters. It is assumed that the innovator operates in the inert market environment which can be presented by ”heavy” exponential trajectories. The growth...

Two major projects have been initiated to improve air traffic management by enabling 4D trajectory planning, whereby the aircraft plan their trajectory both in position and in time. In this paper, we are interested in a Free Flight variant of the concept, whereby airspace users are allowed maximum freedom when selecting routes: aircraft are no longer restricted to fly along airways; rather, the...