Consider the following linearized open loop diving motion eq

Consider the following linearized open loop diving motion equation for a glider (pitch theta and stern 5 are in radian) 6 theta + 4 theta + 3 theta = delta Determine the PD gain values that will result in the damping ratio of 0.5, and time constant 2 seconds. Determine the steady state closed loop pitch error subject to a command pitch angle of 0.2 radian.

Solution

In this paper, a path planning system is proposed for optimal motions of underwater glider in three-dimensional (3D) space. Inspired by the Dubins Paths consisting of straight lines and circular arcs, this paper presents the 3D Dubins curve to accommodate the characteristic glider motions, including sawtooth motion and spiral motion. This modified 3D Dubins scheme is combined with genetic algorithm (GA), to find the trajectory with minimal energy consumption of the vehicle. The properties and capabilities of the proposed path planning methodology are illustrated through simulating comparisons with conventional method which has maximal translational velocity. The results demonstrate that the proposed path planner identifies the optimal trajectories for gliders that ensures they reach their destination with optimized energy consumption.