A Robust Inner and Outer Loop Control Method for Trajectory Tracking of a Quadrotor

Abstract

In order to achieve the complicated trajectory tracking of quadrotor, a geometric inner and outer loop control scheme is presented. The outer loop generates the desired rotation matrix for the inner loop. To improve the response speed and robustness, a geometric SMC controller is designed for the inner loop. The outer loop is also designed via sliding mode control (SMC). By Lyapunov theory and cascade theory, the closed-loop system stability is guaranteed. Next, the tracking performance is validated by tracking three representative trajectories. Then, the robustness of the proposed control method is illustrated by trajectory tracking in presence of model uncertainty and disturbances. Subsequently, experiments are carried out to verify the method. In the experiment, ultra wideband (UWB) is used for indoor positioning. Extended Kalman Filter (EKF) is used for fusing inertial measurement unit (IMU) and UWB measurements. The experimental results show the feasibility of the designed controller in practice. The comparative experiments with PD and PD loop demonstrate the robustness of the proposed control method.

Keywords: SMC; UWB; inner and outer loop; quadrotor UAV; trajectory tracking.

Figure 1

The structure of quadrotor and its coordinate system.

Figure 2

Control structure diagram.

Figure 3

Tracking rotation matrix simulation (a) $e_{R_{e1}}$; (b) $e_{R_{e2}}$; (c) $e_{R_{e3}}$; (d) The control input $u_2$; (e) The control input $u_3$; (f) The control input $u_4$.

Figure 4

Tracking helical trajectory simulation (a) Position; (b) Error of position; (c) Error of angular velocity; (d)Vector form of attitude error; (e) The sliding variables in outer loop; (f) The sliding variables in inner loop; (g) The control variables; (h) The desired trajectory and the actual trajectory in the simulation.

Figure 4

Tracking helical trajectory simulation (a) Position; (b) Error of position; (c) Error of angular velocity; (d)Vector form of attitude error; (e) The sliding variables in outer loop; (f) The sliding variables in inner loop; (g) The control variables; (h) The desired trajectory and the actual trajectory in the simulation.

Figure 5

Tracking circular trajectory simulation (a) Position; (b) Error of position; (c) Error of angular velocity; (d) Vector form attitude error; (e) The sliding variables in outer loop; (f) The sliding variables in inner loop; (g) The control variables; (h) The desired trajectory and the actual trajectory in the simulation.

Figure 6

Tracking rectangular trajectory simulation (a) Position; (b) Error of position; (c) Error of angular velocity; (d)Vector form of attitude error; (e) The sliding variables in outer loop; (f) The sliding variables in inner loop; (g) The control variables; (h) The desired trajectory and the actual trajectory in the simulation.

Figure 6

Tracking rectangular trajectory simulation (a) Position; (b) Error of position; (c) Error of angular velocity; (d)Vector form of attitude error; (e) The sliding variables in outer loop; (f) The sliding variables in inner loop; (g) The control variables; (h) The desired trajectory and the actual trajectory in the simulation.

Figure 7

Comparisons under both controllers for trajectory tracking simulation in two cases (a) The trajectory in Case 1; (b) The trajectory in Case 2; (c) The control inputs in Case 1; (d) The control inputs in Case 2.

Figure 8

The experimental system.

Figure 9

The flow diagram of the algorithm of the system.

Figure 10

The placement of base stations and the tag.

Figure 11

The measured position by UWB system and the corresponding errors (a) The measured position by UWB system; (b) The corresponding position errors.

Figure 12

Actual position of quadrotor in the experiment.

Figure 13

Position errors and histograms of position errors in Case 1 (a) $x$ position error; (b) Percentage of $x$ position error; (c) $y$ position error; (d) Percentage of $y$ position error; (e) $z$ position error; (f) Percentage of $z$ position error.

Figure 13

Position errors and histograms of position errors in Case 1 (a) $x$ position error; (b) Percentage of $x$ position error; (c) $y$ position error; (d) Percentage of $y$ position error; (e) $z$ position error; (f) Percentage of $z$ position error.

Figure 14

Position errors and histograms of position errors in Case 2 (a) $x$ position error; (b) Percentage of $x$ position error; (c) $y$ position error; (d) Percentage of $y$ position error; (e) $z$ position error; (f) Percentage of $z$ position error.

Figure 14

Position errors and histograms of position errors in Case 2 (a) $x$ position error; (b) Percentage of $x$ position error; (c) $y$ position error; (d) Percentage of $y$ position error; (e) $z$ position error; (f) Percentage of $z$ position error.