tailieunhanh - Autonomous Underwater Vehicles Part 5

Tham khảo tài liệu 'autonomous underwater vehicles part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Real-Time Optimal Guidance and Obstacle Avoidance for UMVs 69 sonar FLS systems employed for OA research at NPS. Section 6 addresses path-following considerations and practical implementation details for tracking nonlinear trajectories with conventional vehicle autopilots. Section 7 presents results from computer simulations and field experiments for several different scenarios which benefit from faster-than-real-time computation of near-optimal trajectories. 2. Problem formulation Let us consider the most general case and formulate an optimization problem for computing collision-free trajectories in 3D it can always be reduced to a 2D problem by eliminating two states . We will be searching within a set of admissible trajectories described by the state vector z t x t y t z t u t v t w t T e S S z t e Z6 c E6 t e t0 ty 1 where the components of the velocity vector - surge u sway v and heave w defined in the body frame U - are added to the UUV NED coordinates x y and z z 0 at the surface and increases in magnitude with depth . While many UUVs are typically programmed to operate at a constant altitude above the ocean floor it is still preferable to generate vertical trajectories in the NED local tangent plane because the water surface is a more reliable absolute reference datum than a possibly uneven sea floor. In general however it is a trivial matter to convert the resulting depth trajectory z t to an altitude trajectory h t for vehicles equipped with both altitude and depth sensors. Section describes such practical considerations in detail. The admissible trajectories should satisfy the set of ordinary differential equations describing the UUV kinematics j t u t y t ur v t _ z t _ _w t _ 2 In 2 uR is the rotation matrix from the body frame U to the NED frame u defined using two Euler angles pitch 0 t and yaw y t and neglecting a roll angle as UR t cos t cos 0 t sin Ip t cos 0 t - sin 0 t - sin y t cos t sin 0 t cos y t sin t sin 0 t 0 cos 0 t 3 Although we are