This paper investigates and compares some approaches to trajectory generation for an articulated robot with six degrees of freedom. The trajectory to be planned consists of geometrically predetermined segments and phases where the geometry is free. The overall goal is to minimize the time needed for traversing the whole trajectory from a specified start to a terminal configuration. Constraints ...

This report considers trajectory planning with given design constraints and design of an appropriate feedforward controller for single axis motion control. A motivation is given for using fourth order feedfonvard with fourth order trajectories. An algorithm is given for calculating hqjher order trajectories with bounds on all considered derivatives for point to point moves. It is shown that the...

Time-optimal trajectories with bounded velocities and accelerations are known to be parabolic, i.e., piecewise constant in acceleration. An important characteristic of this class of trajectories is the distribution of the switch points, i.e., the time instants when the acceleration of any robot joint changes. When integrating parabolic trajectory generation into a motion planning pipeline, espe...

A computational approach to generate real-time, optimal trajectories for a flight control experiment is presented. Minimum time trajectories are computed for hover-to-hover and forward flight maneuvers. Instantaneous changes in the trajectory constraints that model obstacles and threats are also investigated. Experimental results using the Nonlinear Trajectory Generation software package show g...

In this paper, we study time-optimal trajectories for fully actuated planar underwater vehicles, with constraints on input forces. Using the Maximum Principle, we focus on the structure of singular extremals and their possible optimality.

The fundamental problem of the calculus of variations on time scales concerns the minimization of a deltaintegral over all trajectories satisfying given boundary conditions. In this paper we prove the second Euler-Lagrange necessary optimality condition for optimal trajectories of variational problems on time scales. As an example of application of the main result, we give an alternative and si...

Based on a nonlinear hybrid dynamical systems model a new planning method for optimal coordination and control of multiple unmanned vehicles is investigated. The time dependent hybrid state of the overall system consists of discrete (roles, actions) and continuous (e.g. position, orientation, velocity) state variables of the vehicles involved. The evolution in time of the system’s hybrid state ...

This paper discusses control strategies adapted for practical implementation and efficient motion of autonomous underwater vehicles (AUV’s). For AUV’s we would like efficiency in both the measured time and the energy consumption, the mission dictating the weight to put on each of these cost. As a first approach to this problem, we focus in this paper on time minimization. Based on the structure...