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Minimum snap trajectory generation and control for quadrotors

Minimum snap trajectory generation and control for quadrotors,10.1109/ICRA.2011.5980409,Daniel Mellinger,Vijay Kumar

Minimum snap trajectory generation and control for quadrotors   (Citations: 2)
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We address the controller design and the tra- jectory generation for a quadrotor maneuvering in three dimensions in a tightly constrained setting typical of indoor environments. In such settings, it is necessary to allow for significant excursions of the attitude from the hover state and small angle approximations cannot be justified for the roll and pitch. We develop an algorithm that enables the real-time generation of optimal trajectories through a sequence of 3-D positions and yaw angles, while ensuring safe passage through specified corridors and satisfying constraints on velocities, accelerations and inputs. A nonlinear controller ensures the faithful tracking of these trajectories. Experimental results illustrate the application of the method to fast motion (5-10 body lengths/second) in three-dimensional slalom courses. I. INTRODUCTION The last decade has seen many exciting developments in the area of micro Unmanned Aerial Vehicles that are between 0.1-0.5 meters in length and 0.1-0.5 kilograms in mass (1). In particular, there has been extensive work on multi- rotor aircrafts, with many recent advances in the design (2), control (3) and planning (4) for quadrotors, rotorcrafts with four rotors. Our focus in this paper is on the modeling, controller design, and trajectory generation for quadrotors. Most of the work in this area uses controllers that are derived from linearization of the model around hover con- ditions and are stable only under reasonably small roll and pitch angles (5). Exploring the full state space using reachability algorithms (6), incremental search techniques (7) or LQR-tree-based searches (8) is impractical for a dynamic system with six degrees of freedom. Some work in this area has addressed aerobatic maneuvers (3, 6, 9, 10). However, there are no stability and convergence guarantees when the attitude of the rotor craft deviates substantially from level hover conditions. While machine learning techniques have been successful in learning models using data from human pilots (9) and in improving performance using reinforce- ment learning (3), these approaches do not appear to lend themselves to motion planning or trajectory generation in environments with obstacles. Similar problems have been addressed using model predictive control (MPC) (11, 12). With these approaches, guarantees of convergence are only available when the linearized model is fully controllable (12) or if a control Lyapunov function can be synthesized (13). As such it appears to be difficult to directly apply such techniques to the trajectory generation of a quadrotor. In this paper, we address the controller design and the trajectory generation for a quadrotor maneuvering in three- dimensions in a tightly constrained setting typical of indoor environments. In such settings, it is necessary to develop flight plans that leverage the dynamics of the system instead of simply viewing the dynamics as a constraint on the system. It is necessary to relax small angle assumptions and allow for significant excursions from the hover state. We develop an algorithm that enables the generation of optimal trajectories through a series of keyframes or waypoints in the set of positions and orientations, while ensuring safe passage through specified corridors and satisfying constraints on achievable velocities, accelerations and inputs.
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