An OOSEM-Based Design Pattern for Developing AUV Controllers

1. Introduction

Water vehicles have been strongly studied and used in defense in the last century. Autonomous underwater vehicles (AUVs) are especially being developed for civilian applications, e.g., maritime monitoring and patrol, disaster and tsunami warnings, ocean exploration, etc. [1,2,3,4].

Control systems for AUVs always have a challenge because they must be connected to dynamic models of the AUVs in water environments with complex disturbances, e.g., nonlinear waves and sea currents. The control system of an AUV can be implemented as a wrapper that associates discrete and continuous blocks and their interactions, called a HDS (Hybrid Dynamic System), and its control behaviors can be visually modeled by specializing in HA (Hybrid Automata) [5,6,7]. Traditional control techniques, in combination with soft-computational methods, have often been used for unmanned vehicles or robots [8,9,10,11,12,13,14,15]. This combination has also been used for building up control systems for AUVs; for instance, Table 1 summarizes the assessments on key control techniques used for controller design and implementation of AUVs.

The above-assessed points let us choose the backstepping technique combined with the PID regulator, which is named the integral backstepping (IB) method, for performing the continuous behavior evolutions of controllers of UAVs. In addition, development costs and reusability need to be considered when constructing an application. Reusability plays a vital role in the process of developing different applications for AUVs. To achieve this objective, the UML will be standardized to visually analyze and design different system components of a system in the software industrial field. Furthermore, the SysML (System Modeling Language) [37], which is based on UML and standardized by OMG, is utilized to perform different steps (analyzing, designing, verification, and validation) in realizing industrial systems in different domains. A drawback of UML/SysML is the lack of parts for modeling the internal continuous behavior evolution of developed systems. Besides, OOSEM [38,39,40] was originally based on the MBSE approach, which is standardized by INCOSE [41,42], for modeling requirements, designing, analyzing, validating, and verifying artifacts of developed systems. The OOSEM is a development method at the system level that allows facilitating the combination of systems engineering, OO (object-oriented) software engineering, and applying object-oriented technology in a way that profits from the systems engineering process. OMG also formalized MDA (the Model-Driven Architecture) [43,44] to separate specifications of systematic operations from their details related to the way of using the capabilities of the system platform. Up to date, many industrial applications of RealTime UML and SysML for complicated control systems with the above model-based approaches are shown in [44,45,46,47,48,49,50,51,52].

Hence, the OOSEM and MDA could be specified in combination with the RealTime UML [53,54,55,56] and SysML (denoted as RealTime UML/SysML) to particularly describe the artifacts of the implemented AUV controller. Based on the above assessments, this study emphasizes developing a hybrid model wrapper that combines the dynamic model of AUV specified for the OOSEM with the MDA components consisting of CIM (Computation Independent Model) considered as the analysis model, the PIM (Platform Independent Model) represented as the design model, and the PSM (Platform Specific Model) carried out as the implementation model, followed up by the RealTime UML-SysML, the algorithm based on UKF and HA (hybrid automata), which allows us to intensively deploy the controller for AUV. On the basis of this hybrid model, an AUV controller for horizontal trajectory tracking dedicated to turtle-shaped AUVs is deployed and tested.

2. Overview of AUV Dynamic Modeling and Control Structure

2.1. Dynamics of Underwater Vehicles for Control

The motional parts of underwater vehicles are specified as surge, sway, heave (position components), and roll, pitch, and yaw (attitude components) by SNAME [57] (see Table 2).

Based on the model of the general control structure (navigation, guidance, and control) for an underwater vehicle, the AUV kinematics in the navigation frame and the AUV dynamics in the body frame can be respectively described as the first and second equations in (1) [58].

$$\left\{\begin{array}{l}\dot{\mathit{\eta }}=\mathit{J}(\mathit{\eta })\mathit{v}\\ \mathit{M}\dot{\mathit{v}}+\mathit{C}(\mathit{v})\mathit{v}+\mathit{D}(\mathit{v})+\mathit{g}(\mathit{\eta })=\mathit{\tau }(\mathit{v},\mathit{u})\end{array}\right.$$

(1)

Here: η₁ = [x,y,z]^T denotes the position, η₂ = [ϕ,θ,ψ]^T – the orientation, η = [η₁^T,η₂^T]^T; v₁ = [u,v,w]^T depicts the linear velocities, v₂ = [p,q,r]^T - angular velocities, ν = [v₁^T,v₂^T]^T; M, D(ν), C(ν) respectively describe inertia, damping and Coriolis matrices; g(η) represents the buoyancy forces and gravity; τ(v,u) – control forces and torques, while u -the inputs of the controller.

A discrete state-space model is required to deal with the evolution of continuous behaviors of the developed AUV that can estimate the vehicle movements through filters, such as particle filters, extended Kalman filters, etc. [59,60]. The evolution of continuous states of the AUV controller is then developed by (2).

$$\left\{\begin{array}{l}{\mathit{x}}_{\mathit{k}}={\mathit{f}}_{\mathit{k}-1}({\mathit{x}}_{\mathit{k}-1},{\mathit{u}}_{\mathit{k}-1})+{\mathit{w}}_{\mathit{k}-1}\\ {\mathit{y}}_{\mathit{k}}={\mathit{h}}_{\mathit{k}}({\mathit{x}}_{\mathit{k}})+{\mathit{v}}_{\mathit{k}}\end{array}\right.$$

(2)

Where: $\mathbf{x}=\left[\begin{array}{c}\mathit{\eta }\\ \mathit{\nu }\end{array}\right]$; x_k denotes the k^th state variables; u_k is control inputs to the system, y_k is its outputs; w_k, v_k, h_k denote the supplementary process, measured disturbance and the measurement function, respectively.

2.2. General Architecture of an AUV Controller

An autonomous underwater vehicle often has three sub-systems. The first sub-system (guidance) prepares parameters of the desired trajectory for the AUV controller to reach and follow up on; the second navigation sub-system has a responsibility to predict the actual AUV states; and the control sub-system is mainly responsible for creating the control torques and forces for acting on and conducting the AUV. Each sub-system has its own individual tasks to be performed, yet they must coordinately work on the same purpose, allowing the AUV to perform its missions. Figure 1 brings out a BBD (block definition diagram) formatted in the conventions of SysML that describes the interactions of the sub-systems. As previously mentioned, control systems can be seen as a combination of continuous and discrete behaviors, which are called HDSs (Hybrid Dynamic Systems). As shown by the above AUV dynamic models (1)–(2) and the three sub-systems, and together with the HDS’s features, AUV controllers are thus presumed to be HDSs, of which dynamic models can be implemented by hybrid automata.

3. OOSEM/MDA-Based Development for an AUV Controller

In this section, the MDA concepts in the OOSEM are specialized for realizing the control parts of an AUV that overall consists of PIM, CIM, and PSM components. All the modeling elements in CIM, PIM, and PSM when realizing AUV controllers will be shown in the following sub-sections.

3.1. CIM realization for AUV Controllers

In CIM, the use case model of RealTime UML-SysML, the functional block diagram, in combination with the PID and IB techniques, and HA are defined to model in detail the requirements of control. Based on the dynamic models and control architecture of AUVs, the key use-case model is defined in Figure 2. The control-oriented modes of an AUV are then modeled by using the state machine extracted from the “Track a desired trajectory” use case. This local state machine is then depicted in Figure 3. Here: MES stands for the Marine Environment System, including various disturbances, for example, waves, wind, ocean current, etc. MDS stands for Measurement Display Systems, which include both guidance and navigation sub-systems.

In the paper, a supplemented FBD (Functional Block Diagram) is defined to provide support to model evolutions of the continuous parts of AUV controllers, as it is hard to utilize the RealTime UML/SysML version, which does not have the standardized notations to visually model complex evolutions of internal continuous behaviors combining with control laws, such as the Integrator Backstepping technique. Thus, a supplemented FBD (Figure 4) was specified for capturing the internal continuous evolution of the control parts of the AUV.

Here, depth and desired trajectory are external events respectively providing the desired position, desired depth to the reference input of the control blocks. Ω_di, $\mathrm{i}=\overline{1,\mathit{n}}$ are requisite rotation velocity, which are used to conduct motors of the i actuator of the AUV, for example, the motors of rudders, propellers and sail plan. τ_φ,θ,Ψ and ΣT represent the output torques and forces allocating on the actuators.

In the analysis model as the CIM, HA is applied to globally represent the discrete/continuous models of the AUV controller considered as a HDS that is written as Equation (3).

H_AUV = (Q, X, ∑, A, Inv, F, q_o, x_co)

(3)

Here: Qis the global states (or situations) of AUVs; q_o ∈ Q - init of Q; X denotes the space of continuous state for describing continuous elements of AUVs, X⊂°ⁿ; x_co ∈ X- the init of X; ∑ - external discrete events, which triggers the transform from the current global state to the target global state. These events are generated from operating environment, external systems, or users, for example, MES, MDS, Users described in the use case diagram (Figure 2); Arepresent a set of transitions from situations to situations, which are often accompanied by the internal/external discrete events (σ ∈ ∑); Inv(q) stands for invariant, it is an application dedicated to verification if the global state of the system is q. In this case, if the continuous element x_c belongs to the global state q, it must be ensured that x_c ∈ inv(q); F are the continuous parts followed up by Equations (1)-(2) that depict the whole continuous evolution to a new situation of the developed AUV. The detailed specializations of HA and evolution hypotheses for the control parts of AUVs can be seen in the report [61].

3.2. PIM Realization for AUV Controllers

As mentioned above, the IB (integrator backstepping) technique, in integration with the CLF (candidate Lyapunov functions), is well performed in various control applications of AUVs. In the PIM, these techniques are used in the Position Control block, Depth Control block, and Attitude Control block (Figure 4), which take part as continuous elements of the AUV controller. The control algorithm based on PID is also applied to the motor control block. However, we will not deal with the details of these control methods because they can be found in a wide range of applications of AUV control [16,17,28,29,62,63,64,65,66].

In addition, the discrete state-space model as described in (2) is used for estimating the states of the AUV. In this study, the state predictions and estimations can be implemented by the standard navigation filter [59], followed by the UKF algorithm as shown in Algorithm 1. Here, $\widehat{.}$ represents its estimation; P denotes the covariance matrix of the state space; R, Q represent the measured noise and covariance matrices of the process. The state estimation is performed by the initial conditions: ${\widehat{\mathbf{x}}}_{0|0}={\mathbf{x}}_0$ and ${\mathrm{P}}_{0|0}=0_{12\times 12}$.

Algorithm 1. Navigation filter followed up by an UKF filter

Function UKF-based algorithm Step UKF prediction   Data : ${\widehat{\mathbf{x}}}_{\mathrm{i}-1|\mathrm{i}-1},{\mathrm{P}}_{\mathrm{i}-1|\mathrm{i}-1},{\mathbf{f}}_{\mathrm{i}-1}(.)$   Result : ${\widehat{\mathbf{x}}}_{\mathrm{i}|\mathrm{i}-1},{\mathrm{P}}_{\mathrm{i}|\mathrm{i}-1}$   $\left({\widehat{\mathbf{x}}}_{\mathrm{i}|\mathrm{i}-1},{\overline{\mathrm{P}}}_{\mathrm{i}|\mathrm{i}-1}\right)=\mathrm{U}\mathrm{T}\left({\widehat{\mathbf{x}}}_{\mathrm{i}-1|\mathrm{i}-1},{\overline{\mathrm{P}}}_{\mathrm{i}-1|\mathrm{i}-1},{\mathbf{f}}_{\mathrm{i}-1}\left(.\right)\right);$   ${\mathrm{P}}_{\mathrm{i}|\mathrm{i}-1}={\overline{\mathrm{P}}}_{\mathrm{i}|\mathrm{i}-1}+{\mathrm{Q}}_{\mathrm{i}-1};$ end Step UKF updating Data : ${\widehat{\mathbf{x}}}_{\mathrm{i}|\mathrm{i}-1},{\mathrm{P}}_{\mathrm{i}|\mathrm{i}-1},{\mathbf{h}}_{\mathrm{i}}(.)$ Result : ${\widehat{\mathbf{x}}}_{\mathrm{i}|\mathrm{i}},{\mathrm{P}}_{\mathrm{i}|\mathrm{i}}$ $\left({\widehat{\mathbf{y}}}_{\mathrm{i}|\mathrm{i}-1},{\overline{\mathrm{S}}}_{\mathrm{i}},{\mathrm{P}}_{\mathrm{i}}^{\mathrm{x}\mathrm{y}}\right)=\mathrm{U}\mathrm{T}\left({\widehat{\mathbf{x}}}_{\mathrm{i}|\mathrm{i}-1},{\mathrm{P}}_{\mathrm{i}|\mathrm{i}-1},{\mathbf{h}}_{\mathrm{i}-1}\left(.\right)\right);$ ${\mathrm{S}}_{\mathrm{i}}={\mathrm{R}}_{\mathrm{i}}+{\overline{\mathrm{S}}}_{\mathrm{i}};$ ${\mathrm{L}}_{\mathrm{i}}={\mathrm{P}}_{\mathrm{i}}^{\mathrm{x}\mathrm{y}}{\mathrm{S}}_{\mathrm{i}}^{-1};$ ${\mathbf{e}}_{\mathrm{i}}={{\mathbf{y}}_{\mathrm{i}}-\widehat{\mathbf{y}}}_{\mathrm{i}|\mathrm{i}-1};$ ${\widehat{\mathbf{x}}}_{\mathrm{i}|\mathrm{i}}={\widehat{\mathbf{x}}}_{\mathrm{i}|\mathrm{i}-1}+{\mathrm{L}}_{\mathrm{i}}{\mathbf{e}}_{\mathrm{i}};$ ${\mathrm{P}}_{\mathrm{i}|\mathrm{i}}={\mathrm{P}}_{\mathrm{i}|\mathrm{i}-1}-{\mathrm{L}}_{\mathrm{i}}{\mathrm{S}}_{\mathrm{i}}{\mathrm{L}}_{\mathrm{i}}^{\mathrm{T}};$ end

Subsequently, the PIM is conventionally designed to generate a pattern of a real-time capsule, which permits visually capturing the control elements in the object collaboration of RealTime UML-SysML. From the CIM components defined above, a set of five capsules of control elements were designed to take part in the HA evolution of the control parts for the developed AUV: the capsule of discrete part, the capsule of continuous part, the capsule of ICGB (Instantaneous Global Continuous Behavior), the capsule of internal interface, and the capsule of external interface. Figure 5 and Figure 6 show the design pattern of various capsules for the AUVs following the conventions of real-time UML-SysML structure and class diagrams.

Here: the capsule of discrete part is dedicated to the implementation of transitions A and states Q; the capsule of IGCB is used to form an instant of the continuous models, for example, f∈F is created from the supplemented FBD (Figure 4); the capsule of internal interface uses invariant module (Inv) to generate discrete events appeared in the continuous and discrete evolutions of the HA; the capsule of the continuous component deal with continuous evolution going on in the state space X; the capsule for external interface exchanges continuous signals and discrete events between this designed AUV controller and the external elements, for example, the MDS, MES, or system of User depicted in the use case diagram (Figure 2).

In addition, the capsules of discrete parts and IGCB have their own local state machines, as shown in Figure 7 and Figure 8, to cooperatively synchronize and validate the realization evolution of HA for the five main control capsules in this pattern.

As mentioned in Section 1, the ability to reuse plays an important role in developing a control system as it mitigates time, cost, and resources. In the cycle of controller development, the reusability can be expanded by the control capsule-based pattern and its components, e.g., the protocols, ports, connectors, internal structures, and local state machines described in Figure 5, Figure 6, Figure 7 and Figure 8.

3.3. PSM Implementation for an AUV Controller

For realizing AUV controllers, PIM is transformed into a model of implementation. This process can be performed by using various object-oriented software platforms, such as C++, C#, Java, which support completely performing the model on industrial-specific platforms (EPC, MCU, PLC). The ultimate-designed model by PIM is first tested by the simulation model. There are various software tools that can perform this simulation, such as IBM Rational Rose Real-time [67] and Open-Modelica [68]. From the simulation results, we can estimate the performance of the designed controller. In the next step, the design artifacts of the model can be optimized before realization. These optimized elements, after simulation, are utilized to adapt PIM to get the updated design model. In the final step, the optimized PIM is converted into a deployment model embedded on available and compatible hardware via IDE tools. Here, round-trip engineering is used to perform the transformations. These techniques are, for example, backward and forward techniques in intermediate programming, with responses of 80% and 20%, respectively, for generated codes and handcrafted codes.

4. Application

On the basis of this new model, a controller for tracking a surface trajectory is designed and then deployed on the hardware platform. This controller manipulates a small-scale T-AUV (turtle-shaped autonomous underwater vehicle) to track a desired trajectory on the water surface. The functions of the T-AUV are shown in Table 3.

According to the AUV dynamic models described in Equations (1)–(2), in combination with the assumption that the vertical and lateral motions are negligible because the T-AUV possesses a turtle shape, the dynamic model of the T-AUV can only be concerned with the longitudinal axis line.

The UKF algorithm (Algorithm 1) is mapped to sensors attached to the T-AUV. These sensors can be the GPS Ublox Neo 6M [69] and the IMU MPU6000 [70]. In this study, MCUs of types ATMEGA32-U2 and STM32 Cortex-M4 [71] were utilized to embed the control program for the AUV controller. The whole physical M-AUV was built in order to test the controller, as shown in Figure 9. For a practical test, we predefined different course angles, trajectories, and velocities. The trial results are displayed in Table 4. Figure 10a–b illustrate the trial results, where the T-AUV is controlled to follow given triangle-shaped and rectangle-shaped trajectories with an average velocity of 1.5 m/s, respectively. Table 5 and Table 6 show the trajectory-tracking errors based on the RMS (root mean square) calculation as well as peak values.

In comparison to the previous experimental results of the author’s research [61] with PID control and the same AUV model, the new proposed controller improves the tracking error and time stabilization, which show a drop of 1.5% and 5.5%, respectively. For this new controller, the IB control law and UKF implementations were combined to build the control blocks for depth, attitude, and position. It is shown that the new proposed controller, accompanied by IB and UKF techniques, improves the control performance over using a single PID regulator.

5. Conclusions and Future Work

This paper introduces a hybrid control model that effectively supports deploying control parts of AUVs. The proposed model is followed by OOSEM specialization combined with MDA concepts, the RealTime UML/SysML, Hybrid Automata, and the UKF algorithm to closely deploy AUV controllers. The dynamics and control architecture of AUV were first used for the inputs of the development lifecycle and integrated with the OOSEM/MDA’s features (CIM, PIM, and PSM). In CIM, we define the use case model, which is then combined with continuous models such as the FBD (supplemented functional block) diagram and HA for capturing control requirements in detail. The PIM was equipped with the UKF algorithm to create the design pattern of the control capsules. Next, the designed PIM was transformed into a PSM that deployed the controller with compatible hardware. Finally, a controller for planar trajectory-tracking dedicated to a real model of T-AUV was implemented and tested with trial cruises. Following the above OOSEM/MDA specialization and the RealTime UML/SysML, system developers can handle complex systems by utilizing developed model artifacts and traceability in a visual way. Nevertheless, as the RealTime UML/SysML version does not have notations to model complex continuous evolutions combined with control laws in developing control systems, a supplemented FBD could thus be added to the CIM of the developed AUV.

In the future, we plan to develop this proposed framework and application equipped with compatible physical sensors and industrial microcontrollers to create a control system that could permit the M-AUV to be used for monitoring and patrolling the marine environment of our country (Vietnam).