## Off-Shore Robotics: Robust and Optimal Solutions for Autonomous Operation

##### Abstract

The vast majority of research in the field of robotics has over the last few decades shifted from industrial robots—in the sense of robots mounted in a structured environment such as a factory floor—to robots operating in unstructured and harsh environments. Even though industrial robotics has become a mature research field we believe that there is still room for progress and improvement. In fact, we show this through both theoretical advances and experimental results in this thesis. However, the main focus of most researchers today has shifted towards autonomous robots and robots in unstructured environments, and this is also the main focus of the work presented here.
This thesis is concerned with the borderline between the mature technology that includes conventional industrial robots and robots operating in unstructured and harsh environments, an area that is still undergoing considerable advances. The oil fields of the future will have to adopt solutions from both mature and evolving technologies—including the borderline between them—and we will use this application to illustrate the practical importance of the theoretical results throughout the thesis. Several tasks to be performed by the robot on the oil fields of the future resemble the tasks performed by industrial robots on the factory floor in thousands of factories around the world today. In this sense we may consider this a mature and robust technology. At the same time the robots will have to work in an unstructured environment with little or no direct human intervention and autonomous operation is required also for non-routine tasks. In this sense, the oil platforms of the future present us with an interesting case study.
We believe there to be two main issues that need to be addressed before partially or completely robotised oil platforms will see the light of day. The first is concerned with robustness. Robotic solutions will only be applied to tasks where the efficiency, accuracy, repeatability, and robustness surpass those of the human operator performing the same tasks. Remotely located oil platforms, and especially the ones located in sensitive areas such as the Barents Sea, are characterised by strict legislative standards to protect the environment and the wildlife. Any installation involving petrochemicals such as oil and gas will have to show for robust and reliable solutions at every stage of the operation. Thus, any operation involving robots will have to meet very high standards when it comes to robustness and fault tolerance. This imposes great challenges on the oil companies that are to operate in these areas.
The second issue is concerned with the effectiveness and cost efficiency of the operation. An experienced human operator has an incredible capability to find efficient solutions to both routine tasks and unexpected occurrences. The robotics system should also strive to solve any task in an optimal manner. Effective and cost efficient operation is vital to be able to justify the high investment in research and installation related with robotised oil fields. Thus, for these systems to be interesting for the oil companies the daily operation should not only be more robust compared to human operators, it should also be more cost efficient to guarantee that the investment in expensive robotic equipment pays off.
When it comes to remotely located oil fields, effectiveness and robustness are very much related. The main economical risk involved with the operation of oil platforms today is unscheduled shutdowns. Unscheduled shutdowns, as well as planned maintenance shutdowns, should be made as short as possible and if possible avoided. A robust solution with less chance of failure is thus something the oil companies strive for also with the economical gain as a motivation.
This thesis is divided into four main parts. Part I is concerned with a large class of robotic systems that will play a very important role in the operation of remotely located oil platforms, namely vehicle-manipulator systems. One application of such systems is subsea installations where humans do not have direct access. The use of robots mounted on a underwater vehicles is believed to be the on-shore operator’s main tool for surveillance and operation of these fields. We are mainly concerned with the mathematical modelling of a large class of systems, including vehicle-manipulator systems. The main contribution of this part is the derivation of the dynamics of a general class of vehicle-manipulator systems that also allows for joints that cannot be represented with generalised coordinates. These types of joints are often subject to singularities in the representation, but we use Lie groups and Lie algebras to represent the transformation between the local and global velocity variables and thus obtain a singularity-free formulation of the dynamics. The papers that are published in this part serve as a detailed study of vehicle-manipulator systems and are also intended to introduce these results to some relevant research areas where a singularity-free formulation is not normally adopted. We show that with our formulation we obtain a set of dynamic equations with the same complexity as the conventional Lagrangian approach but without singularities. The joints are classified depending on what Lie group we use to represent the configuration space so we can easily build a library of joints types for easy implementation in a simulation environment.
While Part I is mainly concerned with robustness in the sense that a suitable mathematical representation is chosen, Part II deals with robustness of the manipulator design. Specifically we address the problem of joint failure, i.e. when the joint loses its actuation and becomes a passive joint. This is an extremely serious situation as the passive joints in general cannot be controlled, and external forces, such as gravity or inertial forces, may cause the manipulator to collapse. This can result in severe damage to the robot’s surroundings. Based on a geometric approach, we thus analyse in detail the effects of joint failure on serial and parallel manipulators. We find that for serial manipulators this should be dealt with in the control of the robot once a joint failure is identified. For parallel manipulators, however, this should be dealt with in the design of the manipulator. We present a complete set of rules on how to choose the active and passive joints in a parallel manipulator in order to guarantee fault tolerance.
Maintenance tasks on oil platforms are very important and especially for platforms situated in high sea, cold locations, and rough environments in general. The corrosion due to the salt water is for example very damaging to both the platform construction and the process area of the platform. High pressure water blasting is thus essential for maintenance and cleaning of the equipment. High pressure water blasting is also used for removing ice and preparing the surfaces to be painted. Painting the huge surfaces of the platform with frequent intervals is another very time consuming task that needs to be performed by the robots. In Part III we show how we can improve efficiency for robots that are to perform these tasks by introducing an extended definition of functional redundancy. All the tasks above are so called pointing tasks, i.e. tasks where only the direction of the robot tool is of concern and not the orientation. We extend this definition to also allow a small error in the orientation of the robot tool. For these tasks a small error in the orientation will not affect the quality of the job, but—as we illustrate through both theoretical and experimental results—this allows us to substantially reduce the time needed to perform the task. We show how to cast the problem of finding the optimal orientation error into a convex optimisation problem that allows us to find the solution in real time. This makes the approach suitable for several tasks performed by the robotic systems on oil platforms, but also for spray paint and welding applications in factory installations.
The process area on an oil platform is very complex and the use of redundant manipulators to get access to every part of the robot is inevitable. The inverse kinematics of redundant robots, however, is challenging due to the infinite number of solutions to the problem. There are also other robots that do not have a known analytical solution to the inverse kinematics problem. One example is robots with complex geometry, which often occurs when we put the cables connecting the tool and the base on the inside of the manipulator structure. Similarly to kinematically redundant manipulators there is in this case no known solution to the inverse kinematics problem, which thus needs to be solved numerically. In Part IV we present a set of iterative solutions to the inverse kinematics problem. We divide the problem into several sub-problems that can be solved analytically. Due to the analytical solution of every sub-problem we are able to solve the inverse kinematics problem very efficiently. The approach is also very robust compared to conventional Jacobian-based methods when the initial point is far from the solution. We also present an alternative formulation of the gradient method where we solve both the problem of finding the gradient and the search along the gradient analytically. Even thought our “gradient” is only an approximation of the actual gradient, the approach is computationally very efficient and a solution is found very quickly.
This thesis addresses several different topics in robotics. All the results presented can be applied to off-shore robotics, but there are also other applications where the results are indeed applicable. As the project has progressed we have discovered several of these alternative applications and in some cases the theory presented is just as relevant in areas other than where it was originally intended. We have included several examples including space robotics and industrial spray paint robots to illustrate this, and we believe this diversity in terms of applications strengthens the theoretical results presented throughout the thesis.

##### Has parts

From, Pal J.; Duindam, Vincent; Pettersen, Kristin Y.; Gravdahl, Jan T.; Sastry, Shankar. Singularity-free dynamic equations of vehicle-manipulator systems. Simulation (San Diego, Calif.). (ISSN 1569-190X). 18(6): 712-731, 2010. 10.1016/j.simpat.2010.01.012.From, P. J.; Duindam, V.; Gravdahl, J. T.; Sastry, S.. Modeling and motion planning for mechanisms on a non-inertial base. IEEE International Conference on Robotics and Automation: 3320-3326, 2009. 10.1109/ROBOT.2009.5152666.

From, P. J.; Gravdahl, J. T.; Lillehagen, T.; Abbeel, P.. Motion Planning and Control of Robotic Manipulators on Seaborne Platforms. .

From, P. J.; Schjølberg, I.; Gravdahl, J. T.; Pettersen, K. Y.; Fossen, T. I.. On the Boundedness Property of the Inertia Matrix and Skew-Symmetric Property of the Coriolis Matrix for Vehicle-Manipulator Systems. .

From, P. J.; Pettersen, K. Y.; Gravdahl, J. T.. Singularity-Free Formulation of the Dynamically Equivalent Manipulator Mapping for Free-Flying and Free-Floating Space Manipulators. .

From, P. J.; Gravdahl, J. T.. A Geometric Approach to Handling Torque Failure in Serial and Closed Chain Manipulators with Passive Joints. .

From, P. J.; Gravdahl, J. T.. Representing Attitudes as Sets of Frames. American Control Conference: 2465-2472, 2007. 10.1109/ACC.2007.4282319.

From, P. J.; Gravdahl, J. T.. On the equivalence of orientation error and positive definiteness of matrices. Proceedings of the 10th International Conference on Control, Automation, Robotics and Vision: 2089-2094, 2008. 10.1109/ICARCV.2008.4795853.

From, P. J.; Gravdahl, J. T.. A Real-Time Algorithm for Determining the Optimal Paint Gun Orientation in Spray Paint Applications. IEEE Transactions on Automation Science and Engineering. (ISSN 1545-5955). 7(4): 803-816, 2010. 10.1109/TASE.2009.2033567.

From, P. J.; Gunnar, J.; Gravdahl, J. T.. Optimal Paint Gun Orientation in Spray Paint Applications—Experimental Results. IEEE Transactions on Automation Science and Engineering. (ISSN 1545-5955). 8(2): 438-442, 2011. 10.1109/TASE.2009.2033567.

From, Pål Johan; Gravdahl, Jan Tommy. Iterative Solutions to the Inverse Geometric Problem for Manipulators with no Closed Form Solution. Modeling, Identification and Control. (ISSN 0332-7353). 29(3): 77-92, 2008. 10.4173/mic.2008.3.1.