In this work we present a real-time approach for local trajectory replanning for MAVs. Current trajectory generation methods for multicopters achieve high success rates in cluttered environments, but assume the environment is static and require prior knowledge of the map. In our work we utilize the results of such planners and extend them with local replanning algorithm that can handle unmodeled (possibly dynamic) obstacles while keeping MAV close to the global trajectory. To make our approach real-time capable we maintain information about the environment around MAV in an occupancy grid stored in 3D circular buffer that moves together with a drone, and represent the trajectories using uniform B-splines. This representation ensures that trajectory is sufficiently smooth and at the same time allows efficient optimization.
Optimization-based approaches rely on minimizing a cost function that consists of smoothness and collision terms. The trajectory itself can be represented as a set of discrete points @cite_20 or polynomial segments @cite_11 . The approach presented in the present work falls into this category, but represents a trajectory using uniform B-splines.
@cite_20 @cite_11
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In this paper, we present CHOMP (covariant Hamiltonian optimization for motion planning), a method for trajectory optimization invariant to reparametrization. CHOMP uses functional gradient techniques to iteratively improve the quality of an initial trajectory, optimizing a functional that trades off between a smoothness and an obstacle avoidance component. CHOMP can be used to locally optimize feasible trajectories, as well as to solve motion planning queries, converging to low-cost trajectories even when initialized with infeasible ones. It uses Hamiltonian Monte Carlo to alleviate the problem of convergence to high-cost local minima (and for probabilistic completeness), and is capable of respecting hard constraints along the trajectory. We present extensive experiments with CHOMP on manipulation and locomotion tasks, using seven-degree-of-freedom manipulators and a rough-terrain quadruped robot. This paper provides new results for the tracking control of a quadrotor unmanned aerial vehicle (UAV). The UAV has four input degrees of freedom, namely the magnitudes of the four rotor thrusts, that are used to control the six translational and rotational degrees of freedom, and to achieve asymptotic tracking of four outputs, namely, three position variables for the vehicle center of mass and the direction of one vehicle body-fixed axis. A globally defined model of the quadrotor UAV rigid body dynamics is introduced as a basis for the analysis. A nonlinear tracking controller is developed on the special Euclidean group SE(3) and it is shown to have desirable closed loop properties that are almost global. Several numerical examples, including an example in which the quadrotor recovers from being initially upside down, illustrate the versatility of the controller.