Formation Control of Autonomous Underwater Vehicles under Communication Delay and Actuator Saturation

Abstract

Autonomous Underwater Vehicles (AUVs) are robots which autonomously carry out desired underwater operations. With the advancements in efficient sensors, actuators and processors, AUVs can be deployed for various applications such as underwater mineral detection, studying life patterns of aquatic plants and animals so that measures can be taken to protect endangered species, scanning deep sea beds for installing underwater pipelines, overhauling and repair of installed pipelines and defence applications which includes carrying as well as detecting warheads. In order to accomplish the aforementioned applications, various sensors are necessary to be installed with the AUV. Thus, deploying a group of AUVs with a distributed sensor configuration, helps in reducing the payloads on a single AUV. Moreover, when AUVs are deployed in a group, larger areas can be scanned in less time and it also makes the mission redundant in case a single AUV fails. There are various approaches of formation control such as behaviour based, synchronization based, virtual structure based and leader-follower based approach. The leader-follower approach is one of the most widely used formation control approaches owing to its simple structure. In this approach, the leader AUV states are sent to the follower AUVs for maintaining the formation. These states are transferred in underwater via acoustic modem. However, the low data rate of acoustic medium introduces communication delay into the AUV motion control system. This delay varies as the distance between the leader and follower AUVs varies with the ocean currents. In the literature [1, 2], most often, this delay is minimized by either transferring least number of AUV states or accurately estimating these states. However, the communication delay can still increase as well as vary significantly due to change in distance between the AUVs with the ocean current. Hence, in this thesis, a leader-follower approach is considered for studying the effects of this variable communication delay on the performance of follower AUVs. Optimal control facilitates path following by optimizing the error between the desired and actual AUV positions [3, 4]. Moreover, when this control is employed for formation control while considering the communication delay among multiple AUVs, it also provides an optimal control law which can handle the effects of delay along with ensuring smooth path following during formation control. Thus, in the thesis, an optimal kinematic control is developed to deal with the communication delay during formation control. In this approach, a linear augmented system comprising the kinematics of both leader as well as the follower AUVs is constructed. This co-operative AUV system also takes into consideration the leader AUV states received by the follower AUVs. Further, an optimal control law is derived for both the leader and follower AUVs. By using these optimal gains, the leader AUV converge to the desired path and also the follower AUVs maintain the formation under the effects of communication delay without yielding oscillations. The performance of the optimal control scheme is compared with a Linear Quadratic Regulator (LQR) based formation controller. The results clearly show that the follower AUVs in case of proposed controller follows the path without oscillations, whereas, in case of LQR, for a chosen set of Qlqr and Rlqr matrices, the response is oscillatory. The simulation results also show that though the steady state error occurs in case of the proposed controller, it is significantly less than LQR. To minimize the aforesaid steady-state error, a convex optimization based modified constrained adaptive control is then proposed in the thesis considering non-linear kinematics and dynamics of AUV. In this approach, the cost function comprising communication delay information based position and velocity error equations is minimized in every iteration. Thus, the effect of communication delay is considered in every sampling time and adaptive control is developed to deal with these effects. This proposed controller also resolves the issue of actuator saturation. However, the results in this case are compared to a backstepping control based formation controller. The backstepping controller is one of the most widely adopted control paradigms for non-linear systems as it considers all the system non-linearities while calculating the control input. Moreover, as backstepping is a Lyapunov function based approach, it also guarantees asymptotic stability of the system. Nevertheless, from the results, it is clearly evident that, under the effects of communication delay, in case of the constrained adaptive control, the AUVs follow the desired path within an accuracy of 5cm, thereby reducing the steady-state error. But in case of backtepping control, with stamping based technique is used in this approach to determine the communication delay. In this technique, the packet of leader AUV states also contains time information at which it is sent. When this packet is received by the follower AUV, the time at which it is received is also noted. The time-difference between these two time-stamps gives the actual delay which is used for controller design. This technique not only increases the packet-size, which subsequently increases the communication delay, it also necessitates that all the clocks pertaining to every AUV to be synchronized. To address increased communication delay and clock synchronization issues, next, a gradient descent method based delay estimator is designed to handle the effects of the time stamping of every sent packet of the leader AUV states. It also does not necessitate time synchronization of AUV system clocks. This estimator is employed along with the developed constrained adaptive controller to reduce the delay and achieve the desired formation control performance. The results show that the gradient-descent method based estimator accurately estimates the communication delay. Moreover, employing the proposed estimator also helps in significantly reducing the communication delay occurring in each sampling-time. The formation control of AUVs considering small or negligible communication delay has been widely studied in the available literature. However, in this thesis, a leader-follower approach based formation control of AUVs under the effects of significantly large variable communication delay has been investigated. Simulations were conducted by implementing a group of a leader AUV and two follower AUVs using MATLAB/Simulink. In case of all the aforementioned proposed algorithms, it is observed that, the AUVs follow the desired formation with accuracy and without oscillations. To verify the efficiency of all the developed control schemes for formation of AUVs, in real-time, an experimental setup is developed. A torpedo-shaped prototype AUV is designed for implementation of proposed control algorithms. Moreover, the hydrodynamic parameters of the developed prototype AUV are also determined. Since, in the proposed constrained adaptive technique which is employed to handle varying communication delay between the AUVs, the determination of the hydrodynamic parameters a priori helps in minimizing the computational burden. Moreover, the determined parameters can also be used for controller design in the future applications. Furthermore, a virtual AUV is considered as the leader AUV and the prototype AUV with Robot Operating System which supports python based programming is employed as the follower AUV. The experimental results also support the observations from the simulation studies. In case of all the aforesaid proposed algorithms such as optimal and constrained adaptive control, the follower AUV follows the desired orientation, under communication delay without oscillations. Moreover, the designed estimator helps in estimating the communication delay accurately and also helps in reducing the delay which occurs due to time-stamping. Thus, from the results it is evident that for small linearization errors or slowly changing paths (as the linearization errors depend on angular velocity of the desired path), the proposed optimal kinematic control law can be employed to deal with communication delay during formation control. Since, the optimal control gains in this case are calculated off-line, it helps in reducing the computation burden, while achieving smooth formation between the AUVs. As the linearization error increases, the constrained adaptive control can be employed for the aforementioned objective. This control adapts on-line to the variable communication delay occurring during formation control and also helps in avoiding actuator saturation. This proposed control being adaptive in nature, still computes the control law within the considered sampling time, thereby adhering to the limit of computation time. Moreover, this adaptive control law when employed along with the gradient descent method based estimator helps in accurately estimating and reducing the communication delay by avoiding time-stamping. However, based on these aforesaid advantages, it is evident that, with the advancements in the processor speed, the adaptive control algorithm offers better performance and the delay estimator can appropriately replace time-stamping technique.