Hardware-in-the-loop simulation (HILS) allows a more realistic evaluation of control approaches than what is possible with pure software simulations, but without the actual complexity of the complete system. This is important for some complex systems such as orbital robots, where testing of the system is typically not possible after its launch, and an on-ground replica is used to validate the performance of such a system. In this article, an impedance-matching approach is presented to match the end-effector dynamics of a fixed-base robot manipulator with that of a target vehicle-manipulator system (VMS), while taking into account the redundant nullspace dynamics in a connected real-time simulation framework. This approach ensures that the forces and torques exerted by the system on the environment matches with that of the simulated system. The contact wrenches used in our approach are not obtained from numerical simulations, but rather from real physical interaction, which is one of the main advantages of our approach. The effectiveness of our method is validated by demonstrating various physical interaction tasks with the environment, using a suspended aerial manipulator as the target system.

In this paper, a method is presented for lowering the energy consumption and/or increasing the speed of a standard manipulator spray painting a surface. The approach is based on the observation that a small angle between the spray direction and the surface normal does not affect the quality of the paint job. Recent results in set-based kinematic control are utilized to develop a switched control system, where this angle is defined as a set-based task with a maximum allowed limit. Four different set-based methods are implemented and tested on a UR5 manipulator from Universal Robots. Experimental results verify the correctness of the method, and demonstrate that the set-based approaches can substantially lower the paint time and energy consumption compared to the current standard solution.

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.

A haptic feedback device is a device that establishes a kinaesthetic link between a human operator and a computer-generated environment. This paper addresses the bidirectional coupling between a commercial off-the-shelf (COTS) haptic feedback device and a general-purpose modelling and simulation environment. In particular, an open-source library is developed to couple the Force Dimension omega.7 haptic device with the 20-sim modelling and simulation environment. The presented coupling interface is also compatible with all the different haptic devices produced by Force Dimension. The proposed integrated haptic interface makes it possible to track the user's motion, detect collisions between the user-controlled probe and virtual objects, compute reaction forces in response to motion or contacts and exert an intuitive force feedback on the user. A real-time one-to-one correspondence between reality and virtual reality can be transparently created. This allows for a variety of possible applications. Stability issues, performance issues, design and virtual prototyping challenges can be addressed and investigated for research purposes. In addition, design and virtual prototyping are also of interest to industry. Realistic training environments can be developed for the user considering different possible operations and stressing the importance of usability and user experience. Experiments based on using haptics technology in the field of education can also be easily performed. To demonstrate the potential of the proposed coupling, a case study is presented. Related simulations and experimental results are carried out.

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 control system for fast cooperative dual-arm manipulation of rigid objects with experimental results. The motivation for multi-arm manipulation comes from the wide range of applications. The possible tasks that can be performed by such a system greatly exceed those of a single manipulator system. The proposed system is flexible with respect to uncertainties in object size. Moreover, it allows for physical human interaction through force/torque sensing. This is especially beneficial in industrial cases where humans and robots work on the same production line. One main goal of this paper is to bridge the gap between current research regarding dual-arm manipulation and the implementation possibilities on current industrial robots and widely available standard hardware.

Increasing efficiency by improving the locomotion methods is a key issue for underwater robots. Consequently, an accurate dynamic model is important for both controller design and for the development of efficient locomotion methods. This paper presents a model of the kinematics and dynamics of an underwater snake robot moving in a vertical plane in 3D. The fluid contact forces (hydrodynamic forces) and torques (fluid moments) are modeled using analytical fluid dynamics. Hydrodynamic forces and torques, i.e. linear and nonlinear drag forces, current effects, added mass and fluid torque effects, are considered. In addition, this modeling approach also takes into account the hydrostatic forces (gravitational forces and buoyancy). The model is given in a closed form and is thus in a form that is well-suited for modern model-based control schemes. The proposed model is easily implemented and simulated, regardless of the number of robot links. Simulation results for lateral undulation and eel-like motion with a ten link robotic system are presented.

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.

The stability of discrete time kinematic sensor-based control of robots is investigated in this paper. A hierarchical inner-loop/outer-loop control architecture common for a generic robotic system is considered. The inner loop is composed of a servo-level joint controller and higher level kinematic feedback is performed in the outer loop. Stability results derived in this paper are of interest in several applications including visual servoing problems, redundancy control, and coordination/synchronization problems. The stability of the overall system is investigated taking into account input/output delays and the inner loop dynamics. A necessary and sufficient condition that the gain of the outer feedback loop has to satisfy to ensure local stability is derived. Experiments on a Kuka K-R16 manipulator have been performed in order to validate the theoretical findings on a real robotic system and show their practical relevance.

The aim of this paper is to investigate the discrete-time stability of robot motion control in the task space. The control system has been modeled as a classical inner-loop/outer-loop architecture, adopted in several industrial robotic systems. The inner-loop is composed of a servo-level joint controller, and higher level kinematic feedback is performed in the outer-loop. Heterogeneous dynamics is considered in the inner-loop, which can for instance describe redundant coordination/synchronization control systems with cooperative robots with non-identical dynamical responses. There are surprisingly few discrete-time stability results in the current state-of-the-art for this popular control architecture. The qualitative effects of the inner-loop dynamics on the overall stability of the system is investigated, and improved outer-loop feedback gain margins are derived.

This paper presents a novel Coriolis/centripetal matrix factorization applicable to serial link rigid manipulators. The computationally efficient Coriolis matrix factorization is explicitly given as a function of the robot's kinematic matrices and their time derivatives which are easily obtained using the Denavit-Hartenberg-convention. The factorization is different from the popular Christoffel symbol representation, but the important skew-symmetry property is preserved. The proposed factorization is used to determine the class of manipulators for which a particular non-minimal representation of the manipulator dynamics exists.

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 this paper, we present a solution and experimental results for real-time control of manipulation tasks considering the alignment of a robots end effector relative to some reference. The developed controller is applicable to industrial manipulators and is based on the pseudoinverse redundancy resolution method. The application considered is the employment of two industrial robots in an offshore remote inspection and maintenance system. A leader robot is controlled freely from onshore, and a follower robot uses an attached camera to provide the onshore operator with live video feed of the ongoing operation. Robot manipulators constitute flexible camera platforms, compared to e.g. simple pan/tilt units, for monitoring offshore operations. We develop a controller for the follower robot such that automatic camera tracking is achieved using pseudoinverse redundancy resolution control. A minimal task space parametrization relying on stereographic projection is constructed which achieves relative end effector alignment tracking without introducing representational or algorithmic singularities. It is shown that singular configurations will only in special cases affect the closed loop behavior. The controller is applicable to tasks such as spray painting or polishing on curved surfaces. The control approach is experimentally validated on two Kuka KR-16 industrial robot manipulators.

Remote controlled robots on offshore oil and gas platforms can potentially reduce costs and improve environment, health and safety issues. A key to successful remote control is to provide onshore operators with a sufficient overview of the processes offshore. To this end, robot manipulators constitute flexible camera platforms, compared to e.g. simple pan-tilt units, for monitoring offshore operations. In this paper, we present a system solution and experimental results for real-time active camera control with obstacle avoidance for industrial manipulators based on weighted pseudoinverse redundancy resolution method. We extend the pseudoinverse solution for joint limit avoidance in combination with obstacle avoidance such that joint limits are gracefully avoided. A novel choice of stereographic projection provides robustness with respect to global stability and singularities. Implementation issues are addressed and the monitoring approach is experimentally validated on two Kuka KR-16 robot manipulators. Experimental results show that a follower robot with a camera is able to monitor and track a leader robot while simultaneously avoiding collisions. In addition, a robot control system architecture which ensures efficient and safe testing of new Matlab-implemented robot controllers is presented.

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 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.

A nonsmooth (hybrid) 3-D mathematical model of a snake robot (without wheels) is developed and experimentally validated in this paper. The model is based on the framework of nonsmooth dynamics and convex analysis that allows us to easily and systematically incorporate unilateral contact forces (i.e., between the snake robot and the ground surface) and friction forces based on Coulomb's law of dry friction. Conventional numerical solvers cannot be employed directly due to set-valued force laws and possible instantaneous velocity changes. Therefore, we show how to implement the model for numerical treatment with a numerical integrator called the time-stepping method. This method helps to avoid explicit changes between equations during simulation even though the system is hybrid. Simulation results for the serpentine motion pattern lateral undulation and sidewinding are presented. In addition, experiments are performed with the snake robot ldquoAikordquo for locomotion by lateral undulation and sidewinding, both with isotropic friction. For these cases, back-to-back comparisons between numerical results and experimental results are given.

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 considers the problem of model based control of the joints of a snake robot without wheels. The potential range of applications for snake robots are numerous, and delicate operations such as inspection and maintenance in industrial environments or performing search and rescue operations require precise control of a snake robot joints. To this end we present a controller that asymptotically stabilizes the joints of the snake robot to a desired reference trajectory. The controller is based on input-output linearization of a control plant model of the snake robot dynamics also developed in this paper. In addition, we provide a formal Lyapunov-based proof of the closed-loop stability, together with simulation results for a smooth dynamical model. Finally, the performance of the controller is tested on a non-smooth snake robot model with set-valued Coulomb friction that offers an accurate description of the stick-slip transitions during locomotion.

Snake robots may one day play a crucial role in search and rescue operations and fire-fighting where it may either be too narrow or to dangerous for personnel to operate. Properties such as high terrainability, redundancy, and the possibility of complete sealing of the body of the robot, make snake robots very interesting for practical applications and hence as a research topic. During the last ten to fifteen years, the published literature on snake robots has increased vastly. However, no thorough review of the theory presented in this period regarding mathematical modeling techniques and locomotion of snake robots has been found. The purpose of this paper is to give such a review. Both purely kinematic models and models including dynamics are investigated. The choice of modeling method is linked to snake robot design characteristics and locomotion approach. Different approaches to biologically inspired locomotion are also discussed