Control and Stability Analysis of Snake Robot Locomotion
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Snake robots are inspired by biological snakes in both shape and dynamical behavior. A snake robot is constructed by a chain of links, interconnected by revolute joints. By imitating gaits of biological snakes, the snake robot is able to move in rough terrains. The great maneuverability of biological snakes has inspired researchers to develop snake robots for future use within different applications where great mobility in various terrains is required. A lot of research has been made within the field of snake robot construction. Open loop control strategies have been proposed in snake robot literature, but still a lot of work remains on a theoretical level in providing stability proofs for snake robot control systems. Additionally, a higher degree of automation is desirable within snake robots in order to fulfill high level control objectives in future applications. In this thesis, control and stability analysis of snake robot locomotion is considered. Initially, a description of biologically inspired snake robots is given, including brief presentations of the most common gaits for biological snakes. Future applications like fire fighting and search and rescue is briefly presented in order to get an overview of possibly future usages of snake robots. Mathematical models of snake robot motion is presented. A somewhat simplified process plant model describes a snake robot with revolute joints, while a model based on a snake robot with prismatic joints is used as control plant model. Averaged system equations for the control plant model are presented based on a snake robot performing the gait lateral undulation. Simulations are carried out to investigate the validity of the averaged system equations during turning motions. Good correspondence between the averaged model and the original control plant model is seen as long as the steering input is not varying too rapidly. Control objectives for a planar snake robot moving in a horizontal plane are discussed. To which degree the snake robot is to be autonomous is highly dependent on the application within which it is used. It is proposed that a suitable way of controlling a snake robot can be for the operator to define certain points of interest within the planar space. The snake robot should be able to navigate autonomously through these points. Inspired by way-point guidance known from marine applications, a solution involving path following strategies by means of guidance laws and orientation control is considered. Next, the control plant model is used for design of orientation controllers for the snake robot. Simulations are made to show tracking performance of time-varying reference trajectories. The proposed controllers show good performance, but a drawback is that the controllers are all singular when the tangential velocity of the snake robot is zero. Boundedness of the snake robot state space is ensured when constraints are set on the steering input. However, simulations show that such constraints on the input give highly conservative bounds on the tangential velocity. It is desirable in the future to calculate actual bounds of tangential velocity when the snake robot is steered by a non-constrained orientation controller. In order to fulfill the higher control objective of steering the snake robot through points of interest in the horizontal plane, guidance laws are used to ensure that the snake robot is able to follow straight-lines and curved paths. By employing cascaded systems theory, the complete control system, including guidance laws and orientation controllers, is proven to be asymptotically stable. The theoretical results are verified through simulations of the control plant model, while simulations of the process plant model investigate the likelihood of successful control of a real snake robot. The control strategies for straight-line following are seen to successfully steer the process plant model to the desired straight-line, but for curved path following some deviations are observed. Better results for curved path following of the process plant model may be obtained by performing system identification and including integral control. The thesis briefly presents experimental results where the proposed path following controller is implemented on a physical snake robot. These experiments show that the path following controller successfully steer the physical snake robot towards a desired straight path.