Optimal Manoeuver Trajectory Synthesis for Autonomous Space and Aerial Vehicles and Robots

Abstract

In this paper the problem of the synthesis of optimal manoeuver trajectories for autonomous space vehicles and robots is revisited. It is shown that it is entirely feasible to construct optimal manoeuver trajectories from considerations of only the rigid body kinematics rather than the complete dynamics of the space vehicle or robot under consideration. Such an approach lends itself to several simplifications which allow the optimal angular velocity and translational velocity profiles to be constructed, purely from considerations of the body kinematic relations. In this paper the body kinematics is formulated, in general, in terms of the quaternion representation attitude and the angular velocities are considered to be the steering inputs. The optimal inputs for a typical attitude manoeuver is synthesized by solving for the states and co-states defined by a two point boundary value problem. A typical example of a space vehicle pointing problem is considered and the optimal torque inputs for the synthesis of a reference attitude trajectory and the reference trajectories are obtained.