This paper proposes and experimentally validates a straight line path following controller for underwater snake robots in the presence of constant irrotational currents of unknown direction and magnitude. An integral line-of-sight guidance law is presented, which is combined with a sinusoidal gait pattern and a directional controller that steers the robot toward and along the desired path. The stability of the proposed control scheme in the presence of ocean currents is investigated by using Poincaré map analysis. Simulation results are presented to illustrate the performance of the proposed path following controller for both lateral undulation and eel-like motion. In addition, the performance of the path following controller is investigated through experiments with a physical underwater snake robot. The experimental results show that the proposed control strategy successfully steers the robot toward and along the desired path in the presence of an unknown constant irrotational current in the inertial frame.

Biological snakes can gracefully traverse a wide range of different and complex environments. Snake robots that can mimic this behaviour could be fitted with sensors and also transport tools to hazardous or confined areas that other robots and humans are unable to access. To carry out such tasks, snake robots must have a high degree of awareness of their surroundings (i.e. perception-driven locomotion) and be capable of efficient obstacle exploitation (i.e. obstacle-aided locomotion) to gain propulsion. These aspects are important to realise the large variety of possible snake robot applications in real-life operations such as fire-fighting, industrial inspection, search-and-rescue and more. In this paper, an elaborate review and discussion of the state-of-the-art, challenges and possibilities of perception-driven obstacle-aided locomotion for snake robots is presented for the first time. Pertinent to snake robots, we focus on current strategies for obstacle avoidance, obstacle accommodation, and obstacle-aided locomotion. Moreover, we put obstacle-aided locomotion into the context of perception and mapping. To this end, we present an overview of relevant key technologies and methods within environment perception, mapping and representation that constitute important aspects of perception-driven obstacle-aided locomotion.

Increasing efficiency by improving the locomotion methods is a key issue for underwater robots. Hence, an accurate dynamic model is important for both controller design and efficient locomotion methods. This paper presents a model of the kinematics and dynamics of a planar, underwater snake robot aimed at control design. Fluid contact forces and torques are modeled using analytical fluid dynamics. The model is derived in a closed form and can be utilized in modern model-based control schemes. The proposed model is easily implemented and simulated, regardless of the number of robot links. Simulation results with a ten link robotic system are presented.

This paper presents a general motion planning framework for body shape control of snake robots. We demonstrate the applicability of the framework for straight line path following control, and for implementing body shape compliance in environments with obstacles. Compliance is achieved by assigning mass-spring-damper dynamics to the shape curve defining the motion of the robot. The performance of the control strategies is illustrated with simulation results.

This paper considers straight line path following control of wheel-less planar snake robots using sliding mode techniques. We first derive the Poincaré representation of the equations of motion of the robot using the techniques of differential geometry. Furthermore, we use partial feedback linearization to linearize the directly actuated part of the system dynamics. Subsequently, we propose an analytical solution to the robust path following control problem in two steps. In the first step, we use sliding mode techniques to design a robust tracking controller for the joints of the robot to track a desired gait pattern. In the second step, we stabilize an appropriately defined sliding manifold for the underactuated configuration variables of the robot, thereby guaranteeing convergence of the robot to the desired straight path. The paper presents simulation results which validate the theoretical results.

This paper presents a motion planning framework for three-dimensional body shape control of snake robots. Whereas conventional motion planning approaches define the body shape of snake robots in terms of their individual joint angles, the proposed framework allows the body shape to be specified in terms of Cartesian coordinates in the environment of the robot. This approach simplifies motion planning since Cartesian coordinates are more intuitively mapped to the overall body shape of the snake robot. The paper demonstrates the applicability of the framework for realizing different types of three-dimensional motion patterns.

This paper presents the snake robot Mamba, which is a modular, reconfigurable, and waterproof experimental platform developed to support the ongoing research on snake robot locomotion, including underwater locomotion. A novel contribution of the snake robot is its ability to measure environment contact forces acting along its body, which is achieved by isolating the actuator inside each joint module with a custom-designed force/torque sensor. The paper describes the design of this sensor and presents experimental results which illustrate its performance.

This paper presents a control framework for shape control of snake robots for the purpose of locomotion. An advantage of the framework is that it allows the macroscopic shape of a snake robot to be controlled explicitly and intuitively. The framework is based on specifying the desired shape of the snake robot as a continuous shape curve defined by a set of shape control points interconnected by Bézier curves. We propose a novel approach for motion generation in which the shape curve is repeatedly extended according to a desired gait pattern while a virtual snake robot is progressed along the shape curve to retrieve joint reference angles for the physical snake robot. Practical applications of the proposed control framework are exemplified along with simulation results.

This paper presents the design of a waterproof and mechanically robust joint module for the snake robot Mamba. The main contribution of the module is a custom-designed force/torque sensor based on strain gauges, which enables the module to measure forces and torques acting on its joint shaft. The ability to measure joint constraint forces and torques enables a snake robot to estimate the external contact forces from its environment, which is important for intelligent and adaptive snake robot locomotion. The paper presents experimental results which illustrate the performance of the force/torque sensor.

This paper considers path following control of snake robots and has two contributions. The first contribution is a description of how a straight line path following controller previously proposed by the authors can be extended to path following of general curved paths. The second contribution of this paper is a waypoint guidance strategy for steering a snake robot along a path defined by waypoints interconnected by straight lines. The waypoint guidance strategy builds on the straight line path following controller previously proposed by the authors. The paper presents simulation results that illustrate the performance of the proposed guidance strategy.

As a step towards enabling snake robots to move in unstructured environments, this paper considers control strategies where environment adaptation is combined with directional control of snake robot locomotion. The first contribution of the paper is a general framework for motion control of snake robots, which allows the motion to be specified in terms of a body wave component, an environment adaptation component, and a heading control component. As a second contribution, we employ the controller framework to propose a control law for straight line path following control of snake robots in environments with obstacles. The paper presents simulation results where the path following controller is combined with a waypoint guidance strategy in order to steer the snake robot between waypoints in an obstacle environment.

In a recent paper, the authors have proposed a control strategy for a snake robot during obstacle-aided locomotion. In this paper, experimental results are presented where the controller is shown to successfully maintain the forward propulsion of a physical snake robot in a course with different obstacle configurations.

This paper considers path following control of snake robots along straight paths. A controller is proposed which, under the assumption that the forward velocity of the snake robot is nonzero and positive, guarantees K-exponential stability of the distance between the snake robot and the desired path and also K-exponential stability of the heading of the robot with respect to the direction of the path. The performance of the path following controller is investigated through experiments with a physical snake robot. The experiments show that the proposed controller successfully steers the snake robot towards and along the desired straight path.

This paper derives and experimentally investigates fundamental properties of the velocity of a snake robot conducting lateral undulation. In particular, the derived properties state that the average forward velocity of the snake robot 1) is proportional to the squared amplitude of the sinusoidal motion of each joint of the robot, 2) is proportional to the angular frequency of the sinusoidal motion of each joint, 3) is proportional to a particular function of the constant phase shift between the joints, and 4) is maximized by the phase shift between the joints that also maximizes the particular phase shift function. The paper presents an experimental investigation of the validity of these derived properties by measuring the forward velocity of a physical snake robot during lateral undulation. The experimental results support the theoretical findings.

A snake robot can traverse cluttered and irregular environments by using irregularities around its body as push-points to aid the propulsion. This is denoted obstacle-aided locomotion and requires the snake robot to have two features: 1) a smooth exterior surface combined with 2) a contact force sensing system. These two features are characteristic of biological snakes, but have received limited attention in snake robot designs so far. This paper describes the development of a new snake robot aimed at meeting both these requirements. The paper details the design and implementation of the snake robot, presents experimental results that validate the function of the contact force measurement system, and demonstrates some of the motion capabilities of the robot.

A snake can traverse cluttered and irregular environments by using irregularities around its body as push-points to aid the propulsion. This characteristic feature of biological snake locomotion, denoted obstacle-aided locomotion, is investigated for snake robot locomotion purposes in this paper. The paper presents a hybrid model of the dynamics of a planar snake robot interacting with obstacles in its environment. Obstacle contact forces are calculated by formulating and solving a linear complementarity problem (LCP). The existence and uniqueness properties of the state evolution of the hybrid model are investigated. Simulation results validate the hybrid modelling approach.

This paper presents a model of the kinematics and dynamics of a planar, wheelless snake robot aimed at control design and stability analysis purposes. The proposed model is significantly less complex than existing models of planar snake robot locomotion. The paper presents an analysis of an existing complex snake robot model which reveals a set of essential properties that characterize the overall motion of a planar snake robot. The proposed model is developed to capture only these essential properties of snake locomotion, thereby significantly reducing the complexity compared to the original model used in the analysis. The paper presents simulation results that indicate that the qualitative behaviour of the proposed model and the original complex model are similar, and that a quantitative similarity is achieved with a proper choice of numerical values of the friction coefficients in the two models.

This paper presents a set of fundamental properties of the velocity of a snake robot conducting lateral undulation on a planar surface. In particular, the derived properties state that the average forward velocity of the snake robot 1) is proportional to the squared amplitude of the sinusoidal motion of each joint of the robot, 2) is proportional to the angular frequency of the sinusoidal motion of each joint, 3) is proportional to a particular function of the constant phase shift between the joints, and 4) is maximized by the phase shift between the joints that also maximizes the particular phase shift function. The paper presents simulation results that support the validity of the derived properties.

A snake can traverse cluttered and irregular environments by using irregularities around its body as push points to aid the propulsion. This characteristic feature of biological snake locomotion, which is denoted as obstacle-aided locomotion, is investigated for snake robot locomotion purposes in this paper. The paper presents a hybrid model of the dynamics of a planar snake robot interacting with obstacles in its environment. Obstacle contact forces are calculated by formulating and solving a linear complementarity problem (LCP). The existence and uniqueness properties of the state evolution of the hybrid model are investigated. The paper also presents a hybrid control strategy employing measured contact forces to maintain propulsion while simultaneously preventing the snake robot from being jammed between obstacles in its path. The simulation results validate the hybrid modelling approach and the effectiveness of the proposed control strategy.

A snake robot can traverse cluttered and irregular environments by using irregularities around its body as push-points to aid the propulsion. This is denoted obstacle-aided locomotion and requires the snake robot to have two features: (1) a smooth exterior surface combined with (2) a contact force sensing system. These two features are characteristic of biological snakes, but have received limited attention in snake robot designs so far. This paper presents a joint mechanism for a snake robot aimed at meeting both these requirements. The paper details the design and implementation of the joint mechanism and presents experimental results that validate the function of the contact force measurement system.

A snake robot can traverse cluttered and irregular environments by using irregularities around its body as push-points to aid the propulsion. This characteristic feature of snake locomotion, denoted obstacle-aided locomotion, has received limited focus in previous literature. This paper presents a model of this phenomenon and a control strategy employing measured contact forces to maintain propulsion while simultaneously preventing the snake robot from being jammed between obstacles in its path. The simulation results validate the contact modelling approach and the effectiveness of the proposed control strategy.

This paper presents a mechanism for navigating complex pipe structures, both horizontally and vertically. The mechanism consists of a series of identical modules interconnected by two degree of freedom active joints. A set of active wheels on each module provides propulsion. Horizontal motion is achieved through a train-like scheme, while vertical motion is achieved through spanning the pipe alternatingly with the modules. The design and the capability of horizontal and vertical motion is validated through experiments.

This paper investigates the controllability properties of planar snake robots influenced by viscous ground friction forces. The paper provides three contributions: 1) A partially feedback linearized model of a planar snake robot is developed. 2) A stabilizability analysis is presented proving that any asymptotically stabilizable control law for a planar snake robot to an equilibrium point must be time-varying. 3) A controllability analysis is presented proving that planar snake robots are not controllable when the viscous ground friction is uniform, but that a snake robot becomes strongly accessible when the viscous ground friction is non-uniform. The analysis also shows that the snake robot does not satisfy sufficient conditions for small-time local controllability (STLC).

This paper presents an analysis of snake locomotion that explains how non-uniform viscous ground friction conditions enable snake robots to locomote forward on a planar surface. The explanation is based on a simple mapping from link velocities normal to the direction of motion into propulsive forces in the direction of motion. From this analysis, a controller for a snake robot is proposed. A Poincare¿ map is employed to prove that all state variables of the snake robot, except for the position in the forward direction, trace out an exponentially stable periodic orbit.

Snakes utilize irregularities in the terrain, such as rocks and vegetation, for faster and more efficient locomotion. This motivates the development of snake robots that actively use the terrain for locomotion, i.e., obstacle-aided locomotion. In order to accurately model and understand this phenomenon, this paper presents a novel nonsmooth (hybrid) mathematical model for wheel-less snake robots, which allows the snake robot to push against external obstacles apart from a flat ground. The framework of nonsmooth dynamics and convex analysis allows us to systematically and accurately incorporate both unilateral contact forces (from the obstacles) and isotropic friction forces based on Coulomb's law using set-valued force laws. The mathematical model is verified through experiments. In particular, a back-to-back comparison between numerical simulations and experimental results is presented. It is, furthermore, shown that the snake robot is able to move forward faster and more robustly by exploiting obstacles.

The paper considers the problem of obstacle aided locomotion for snake robots, as taking advantage of obstacles for locomotion is an enabling technique for snake robots to enter challenging environments like earthquaked areas and mines for search and rescue missions. To this end, the paper presents a novel non-smooth (hybrid) 2D mathematical model for snake robots which incorporates that the snake robot can come in contact with external obstacles apart from flat ground. The mathematical model is verified through a back-to-back comparison between numerical simulations and experimental results. It is furthermore shown that the snake robot is able to move forward faster and more robustly by exploiting obstacles, and that the locomotion in this case is not as dependent on the ground surface.

This paper presents the SnakeFighter concept and describes the generic element within this concept in the form of a water hydraulic snake robot. Applications of a SnakeFighter system are presented with focus on fire intervention tasks. The development of a water hydraulic snake robot that demonstrates the concept is described. The robot is the first water hydraulic snake robot ever constructed. The paper identifies design challenges of a complete SnakeFighter system and describes future research on this concept