On Trajectory Generation And Disturbance Rejection Control Of The Quadrotors

Among all of the unmanned aerial vehicles, the micro quadrotor receives more and more attentions in recent years. As the quadrotor can be extensively applied for reconnaissance, photography, rescuing, etc., the development of fully autonomous autopilot for the quadrotor is significantly important. An ideal autopilot should possess numbers of characteristics that are comparable to its biological counterparts, e.g. the birds. To achieve this objective, one of the fundamental but key issue is to guarantee the quadrotor be fully controlled in dynamic environment. To address this issue, there are at least two challenges. On one hand, as the quadrotor is a highly under-actuated system, it is insufficient to adopt merely static smooth feedback technology in the flight control. Instead, dynamically consistent trajectory generation and tracking methods are simultaneously required to establish desired states in given time horizons. On the other hand, different from the traditional airplanes, there are no hardware redundancy for the quadrotor, therefore it might be easy to suffer from creep deformation and rotor failure. In this case, the performance of the control system can be easily deteriorated by the lumped disturbances.To tackle the above problems, this work is devoted to develop high performance trajectory generation and disturbance rejection tracking control strategies, which are carried out as follows. Firstly, the dynamic model of the quadrotor is formulated and identified, and a cascaded control system is developed accordingly. Based on the dynamic model, a disturbance observer based controller is developed to eliminate the lumped disturbances. Then a tracking differentiator is introduced to fast tracking the reference signal while eliminating the noises in the reference as well as overshooting in the response. Subsequently, an optimal trajectory generation approach is adopted to generate dynamically consistent trajectory from state to state in under-actuated cases,and a subspace stabilization approach is proposed to track the generated trajectory. Finally, based on the non-uniform rational B-spline, a fast trajectory generation method,with minimum flight time objective, is proposed based on a linear programming with respect to the navigation way-points. The distinctive features of this work are as follows:1. Disturbance observer-based trajectory tracking controller: a high-performance trajectory tracking controller is developed based on the disturbance observer, which can effectively estimate and reject the lumped disturbances. The disturbance observer is constructed based on the dynamic model and state measurement, thus requires no additional hardware implementation. The developed controller possesses a concise form and is computationally efficient, therefore it can be easily implemented in the embedded control system. Real-time experiments demonstrate that the developed controller guarantees steady performance even with varying payloads, rotor failure and wind gust.The steady-state errors in all of the experiments are less than 0.02 m.2. Model-based active disturbance rejection control: based on the optimal control theory and adopting the tracking differentiator, the reference signals can be effectively smoothed, thus enable steady performance with different types of control inputs. A modeled based extended state observer/predictor is also proposed to further improve the performance of the state estimation and disturbance observation. With the model-based active disturbance rejection controller, the quadrotor shows more steady performance in the real-time flight when under varying control inputs. The steady-state errors in all of the real-time experiments are less than 0.02 m.3. Trajectory tracking in under-actuated cases based on subspace stabilization approach: a subspace stabilization based strategy is proposed for the under-actuated trajectory tracking. The control strategy is consisted of two parts: a base controller regarding the differential flatness of the quadrotor and a compensation controller designed with linear quadratic regulator. Besides, the concept of the confidential error is introduced to eliminate the effects of the fluctuation in the trajectory tracking. To generate dynamically consistent reference trajectory, a computationally efficient method is adopted for minimum jerk trajectory generation. The developed control strategy is applied to ball juggling. Equipped with a racket with diameter of 0.13 m, whose sweet spot is within a circle with radius of 0.03 m, the quadrotor can fulfill averagely 3-4 hits and maximumly 14 hits of ball juggling in each rally.4. Fast trajectory generation for multi-way-point navigation: A fast trajectory generation algorithm is proposed for multi-way-points navigation based on a linear programming. With given navigation points, the geometric profile of the trajectory can be solved analytically. Then a time optimal problem, considering the constraints in velocity, acceleration and jerk, is imposed to interpolate the trajectory in the time domain. The optimal problem is then reduced to a linear program, which significantly enhances the computational efficiency. With the proposed trajectory generation strategy, the quadrotor can smoothly pass through a clustered indoor environment with obstacle rings, and the cross-trajectory tracking error is less than 0.05 m when the flight speed is approximately 1 m/s.