## 4 Tether Simulation  
The previous section was dealt with the dynamics of the ROV and was simulated using a force based method from the mechanical engineering domain. Simulation of dynamic systems in computer graphics mainly use force-based methods, where linear and rotational accelerations are computed from forces and torques. A time integration method is then used to update the velocities and positions of the object as shown in the previous section. In contrast, geometry-based methods work directly on vertex positions, modifying them using iterative update equations. The main advantage of a position-based approach is its controllability. In force-based systems, overshooting problems associated with explicit integration schemes can be avoided. In addition, collision constraints can be handled easily and penetrations can be resolved completely by moving points to valid locations [19]. In our research, we found the tether simulation to be particularly useful in cases were the robot sees its own cable as presented in Figure 4. This fact may disrupt computer vision algorithms--especially those based on tracking using landmark features from the images and assume that these landmarks are not moving in the scene. With this type of simulation, that kind of behaviour can be simulated in a manner close to real cable behaviour. New computer vision algorithms can be developed to mitigate that behaviour and new control algorithms can be developed to manage the cable configuration. The position based simulations which were originally developed for the simulation of solids were also extended to the area of fluid dynamics [20] where it is not reasonable to simulate the interacting forces between the particles in real-time. In contrast to force based simulation, position based models can scale up and can be used today to simulate large multi-body systems such as fabric or fur in real-time. While force based systems tend to be physically accurate under certain assumptions,  
Figure 4: The underwater ROV sees its own tether in the camera view. On the **left** is an image taken from our simulation and on the **right** an image taken from one of our dives with the OpenROV in Port Levy, New Zealand. position based systems aim to be visually realistic. For example, a set of simulation parameters may not correspond to real physical values, but may generate realistic object behaviour as the output. The stiffness parameter implemented in the Unreal Engine, which we will later discuss, is an example of a parameter that influences the dynamic behaviour of the position based cable model but has no meaningful physical value (such as mass or length). Our tether cable simulation method, in terms of number of particles, lies between the forced based system and the position based system. In simulating a long cable with a large number of segments, we aim for real time performance by applying constraints and also use position based models. In our underwater cable implementation, we take the existing Verlet integration suggested by [PERSON] [21] and modify it to simulate a realistic underwater cable. The existing rope simulation in Unreal Engine 4 platform, which we will discuss later, performs in a convincing way only in a light density environment like air but looked quite non-realistic in the aquatic medium. This motivated us to return to the original assumptions of the simulated implementation and modify it in order to create visually convincing underwater rope/cable simulation. In our work, we added extensive damping and random displacements to the particles and experimentally analysed and verified the resulting behaviour. Specifically, we were interested in the behaviour of variable length long cables attached to the ROV at one end and to a spool in the other end.That kind of cables have some unique physical characteristics that could not be addressed by the current features in existing simulation frameworks. Most of the underwater cable modelling was done in the mechanical engineering domain using force based methods.