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Ocean Engineering

# Continuous Collision Detection of Cubic-Spline-Based Tethers in ROV Simulations

[+] Author and Article Information
André Roy

Department of Mechanical Engineering, University of New Brunswick, Fredericton, NB, E3B 5A3, Canadaandre.roy@unb.ca

Juan A. Carretero1

Department of Mechanical Engineering, University of New Brunswick, Fredericton, NB, E3B 5A3, Canadajuan.carretero@unb.ca

Department of Mechanical Engineering, University of Victoria, Victoria, BC, V8W 3P6, Canadabbuckham@uvic.ca

Ryan S. Nicoll

Dynamic Systems Analysis Ltd., Victoria, BC, V8W 3W2, Canadaryan@dsa-ltd.ca

Take note that here, the circles surrounding the points $r(s1)$ and $r(s2)$ do not represent the tether’s cross sections but simply a circle of radius $r1$ or $r2$, which is used to symbolize the distance required to initiate a collision.

1

Corresponding author.

J. Offshore Mech. Arct. Eng 131(4), 041102 (Sep 08, 2009) (10 pages) doi:10.1115/1.3124128 History: Received March 27, 2008; Revised December 18, 2008; Published September 08, 2009

## Abstract

Improving the efficacy of the pilot remotely operated vehicle (ROV) interaction through extensive training is paramount in reducing the duration, and thus expense, of ROV deployments. To complete training without sacrificing operational windows, ROV simulators can be used. Since the ROV tether, which provides power and telemetry, will at times dominate the ROV motion, the tether must be accurately modeled over the full duration of a simulated ROV maneuver. One aspect of the tether dynamics that remains relatively untouched is the modeling of tether self-contact, contact with other tethers, or entanglement. The aim of this work is to present a computationally efficient and accurate method of detecting tether collisions. To this end, a combinatorial global optimization method is first used to determine the approximate separation distance minima locations. Then, a local optimization scheme is used to find the exact separation distances and the locations of the closest points. The first combinatorial stage increases the speed at which the minima can be found. The minimum separation distance information and its change with respect to time can then be used to continuously determine whether a collision has occurred. If a collision is detected, a contact force is calculated from the interference geometry and applied at the collision site.

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## Figures

Figure 1

Examples of contacting tethers (contacting portions highlighted): (a) tether-self-contact, (b) tether-tether contact, and (c) tether-environment contact

Figure 2

Tethered underwater vehicle system

Figure 3

Example of MLSDist with three different starting node pairs

Figure 4

Tether lay used to generate the distance solution space in Fig. 5

Figure 5

The 3D surface of the distance between a point on the tether at s1 and a point on the tether at s2

Figure 6

The tether with (a) minimum distances found and (b) exact minimum found on the cubic-spline segment

Figure 7

A two-dimensional representation of (a) the nine minimum separation distance pairs and (b) the initial pairs prior to being minimized

Figure 8

(a) Defining βmin to determine if a collision has occurred between time steps t and t+1. (b) Defining β and Pstart to determine if a collision has occurred between time steps t and t+1.

Figure 9

Case where the time step was too large and the tether traveled too far past the point of initial contact to be considered accurate where Finitial is the contact force at start of contact and Factual is the contact force that will be generated on the real-time step

Figure 10

The minimum separation distance between two tether segments to which r(s1) and r(s2) belong, and their tangents V1 and V2 at s1 and s2 (a) before the tether crosses itself and (b) after the tether has crossed itself

Figure 11

Continuous collision detection flow diagram

Figure 12

A tether forming a knot showing four minima

Figure 13

Close-up of the shortest minimum (right) prior to the collision

Figure 14

The shortest minimum (right) during the collision. The two added dark lines represent the forces being applied at the contact points.

Figure 15

The shortest minimum (right) after the collision

Figure 16

The minimum separation distances of the three shortest minima, the shortest of which showing a collision at time ≈0.21 s. Distances have been adjusted to account for the tether radius.

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