Trajectory Following Control of an Unmanned Vehicle for Marine Environment Sensing

Abstract

An autonomous surface vehicle is indispensable for sensing of marine environments owing to its challenging and dynamic conditions. To accomplish this task, the vehicle has to navigate through a desired trajectory. However, due to the complexity and dynamic nature of a marine environment affected by factors such as ocean currents, waves, and wind, a robust controller is of paramount importance for maintaining the vehicle along the desired trajectory by minimizing the trajectory error. To this end, in this study, we propose a robust discrete-time super-twisting second-order sliding mode controller (DSTA). Besides, this control method effectively suppresses the chattering effect. To start with, the vehicle's model is discretized using an integral approximation with nonlinear terms including environmental disturbances treated as perturbation terms. Then, the perturbation is estimated using a time delay estimator (TDE), which further enhances the robustness of the proposed method and allows us to choose smaller controller gains. Moreover, we employ a genetic algorithm (GA) to tune the controller gains based on a quadratic cost function that considers the tracking error and control energy. The stability of the proposed sliding mode controller (SMC) is rigorously demonstrated using a Lyapunov approach. The controller is implemented using the Simulink^® software. Finally, a conventional discrete-time SMC based on the reaching law (DSMR) and a heuristically tuned DSTA controller are used as benchmarks to compare the tracking accuracy and chattering attenuation capability of the proposed GA based DSTA (GA-DSTA). Simulation results are presented both with or without external disturbances. The simulation results demonstrate that the proposed controller drives the vehicle along the desired trajectory successfully and outperforms the other two controllers.

Keywords: Lyapunov stability; chattering; estimation; genetic algorithm; marine; sensing; sliding mode control; trajectory following; vehicle.

Figure 1

Guidance, navigation and control (GNC) block diagram.

Figure 2

Block diagram of the proposed control method.

Figure 3

Illustration of body-fixed and earth-fixed reference frames of a surface vehicle.

Figure 4

Flowchart of the Genetic algorithm for gain optimization.

Figure 5

Illustration of convergence of genetic algorithm using fitness, stopping criteria, and average distance between individuals.

Figure 6

Surge speed trajectory following comparison of the GA-DSTA, DSTA, and DSMR controllers for Scenario 1.

Figure 7

Sway speed trajectory following comparison of the GA-DSTA, DSTA, and DSMR controllers for Scenario 1.

Figure 8

Yaw rate trajectory following comparison of the GA-DSTA, DSTA, and DSMR controllers for Scenario 1.

Figure 9

Comparison of RMSEs of GA–DSTA, DSTA, and DSMR controllers for surge, sway, and yaw rate for Scenario 1.

Figure 10

Comparison of the total energy expenditure of the GA–DSTA, DSTA, and DSMR controllers for Scenario 1. RPM is revolutions per minute.

Figure 11

Control signals for surge, sway, and yaw rate of GA-DSTA, DSTA, and DSMR controllers for Scenario 1. RPM is revolutions per minute.

Figure 12

Surge speed trajectory following comparison of the GA-DSTA, DSTA, and DSMR controllers for Scenario 2.

Figure 13

Sway speed trajectory following comparison of the GA-DSTA, DSTA, and DSMR controllers for Scenario 2.

Figure 14

Yaw rate trajectory following comparison of the GA-DSTA, DSTA, and DSMR controllers for Scenario 2.

Figure 15

Comparison of the RMSEs of the GA-DSTA, DSTA, and DSMR controllers for the surge, sway, and yaw rate Scenario 2. RPM is revolutions per minute.

Figure 16

Comparison of total energy expenditure of the GA-DSTA, DSTA, and DSMR controllers in revolution for Scenario 2. RPM is revolutions per minute.

Figure 17

Control signals for surge, sway, and yaw rate of GA-DSTA, DSTA, and DSMR controllers for Scenario 2. RPM is revolutions per minute.