Planar Snake Robot Research Articles

Improved Jacobian matrix estimation applied to snake robots.

Two manipulator Jacobian matrix estimators for constrained planar snake robots are developed and tested, which enables the implementation of Jacobian-based obstacle-aided locomotion (OAL) control schemes. These schemes use obstacles in the robot's vicinity to obtain propulsion. The devised estimators infer manipulator Jacobians for constrained planar snake robots in situations where the positions and number of surrounding obstacle constraints might change or are not precisely known. The first proposed estimator is an adaptation of contemporary research in soft robots and builds on convex optimization. The second estimator builds on the unscented Kalman filter. By simulations, we evaluate and compare the two devised algorithms in terms of their statistical performance, execution times, and robustness to measurement noise. We find that both algorithms lead to Jacobian matrix estimates that are similarly useful to predict end-effector movements. However, the unscented filter approach requires significantly lower computing resources and is not poised by convergence issues displayed by the convex optimization-based method. We foresee that the estimators may have use in other fields of research, such as soft robotics and visual servoing. The estimators may also be adapted for use in general non-planar snake robots.

Virtual holonomic constraints based super twisting sliding mode control for motion control of planar snake robot in the uncertain underwater environment

In this article, the snake robot having nine links with eight joints is considered for serpentine motion in the underwater environment. The movement of a snake robot occurs due to nonlinear drag forces and fluidic torque in underwater conditions. The uncertainties in drag forces and fluidic torque are considered to track the head angle and tangential velocity in this work. The virtual holonomic constraints are formulated to track all the joints by designing a controller for single joint. The parameters of gait pattern are obtained using the sliding surface. The sliding surface is formulated for head link angle and velocity tracking. Super twisting sliding mode control approach is proposed to deal with uncertainties, and results are compared with sliding mode control and adaptive sliding mode control. The robustness of controller is verified by inputting measurement noise. The significant improvement has been observed in chattering indicator and control effort by using the proposed super twisting sliding mode control. The investigation of this research article focuses on how to get almost chattering free operation in underwater uncertain environmental conditions with minimum control effort.

Robust control of a planar snake robot based on interval type-2 Takagi–Sugeno fuzzy control using genetic algorithm

This paper presents trajectory tracking control of a snake robot in the presence of system uncertainty such as disturbances and parameter uncertainties. First, we derive a realistic dynamic model of the snake robot in the framework of the bond graph technique. Next, we present an interval type-2 Takagi–Sugeno fuzzy proportional–derivative (IT2FPD) control scheme, whose parameters are tuned using a genetic algorithm (GA) optimization approach. An improved optimization formulation with randomness is employed for robust near-optimal parameters. Under the assumption that forward velocity of the robot is always positive, we apply the proposed IT2FPD controller to the snake robot model so that the robot can have locomotion along the desired trajectory against uncertainties. To validate the performance of the proposed robot model and control scheme, we conduct in-depth numerical experiments using 20-sim software. Experimental results demonstrate that the snake robot embedded with the IT2FPD controller achieves a straight-line locomotion with the serpenoid gait function despite infiltration of external disturbances and parameter changes.

Optimal Path Following Control With Efficient Computation for Snake Robots Subject to Multiple Constraints and Unknown Frictions

This letter proposes a real-time optimal robust path following control scheme for planar snake robots without sideslip constraints using model predictive control (MPC). One of the features is that a linear double-integrator model rather than the complex dynamic model of snake robots is used for the MPC design to improve calculation efficiency. Moreover, in addition to constraints on joint angles, velocity, and acceleration for security, constraints on the joint offset and velocity are also considered to keep the snake robot moving forward efficiently. And the multiple inequality constraints are handled by a novel constraints translator. Furthermore, to achieve robust path following control subject to unknown and varied friction forces and disturbances, two reduced-order structure-improved extended state observers are designed to avoid complex environmental modeling. Extensive comparative experiments were conducted to verify the constraints design and the effectiveness of the proposed control scheme.

A Muscle-Driven Mechanism for Locomotion of Snake-Robots

This paper presents the concept of muscle-driven locomotion for planar snake robots, which combines the advantages of both rigid and soft robotic approaches to enhance the performance of snake robot locomotion. For this purpose, two adjacent links are connected by a pair of pneumatic artificial muscles wherein an alternate actuation of these soft actuators causes a rotational motion at the connecting joints. The muscle-based actuated linkage mechanism, as a closed six-linkage mechanism, was designed and prototyped. The linear motion and force generation of the pneumatic artificial muscle was experimentally characterized using isotonic and isometric contraction experiments. A predictive model was developed based on the experimental data to describe the relationship between the force–length–pressure of the PAMs. Additionally, the muscle-driven mechanism was kinematically and dynamically characterized based on both theoretical and experimental studies. The experimental data generally agreed with our model’s results and the generated joint angle and torque were comparable to the current snake-like robots. A skx-link planar snake robot with five joints, five pairs of antagonistic muscles, and an associated pneumatic controller was prototyped and examined for simple movements on a straight-line. We demonstrated the muscle-driven locomotion of the six-link snake robot, and the results show the feasibility of using the proposed mechanism for future explorations of snake robot locomotion.

Redundant Control of a Planar Snake Robot with Prismatic Joints

Redundant Control of a Planar Snake Robot with Prismatic Joints

Maneuvering control of planar snake robot: An adaptive robust approach with artificial time delay

AbstractThis article proposes an adaptive‐robust maneuvering control framework for a planar snake robot under the influence of parameter uncertainties. The entire control objective of maneuvering control can be viewed as the simultaneous establishments of two goals: one to maintain a time‐varying body shape of the snake robot for consistent motion (called the outer layer) and the other dealing with the velocity and head‐angle tracking of the same (called the inner layer). Unknown variations in the ground friction coefficients have been considered to be the primary source of time‐varying uncertainties which affects the control performance in both the layers. Accordingly, an artificial time delay‐based adaptive‐robust control (ARC) framework, dual adaptive‐robust time‐delayed control (ARTDC), is proposed. The term dual signifies simultaneous application of ARTDC for the outer as well as the inner layer. ARTDC comprises of two segments: an artificial time delay‐based time‐delayed estimation (TDE) part and an ARC part. While TDE approximates the completely unknown friction forces, the ARC tackles the approximation error arising from the TDE. More importantly, compared with the existing ARC methodologies, the proposed ARTDC neither presumes the overall uncertainty to be upper bounded by a constant nor requires any prior knowledge of the bound of uncertainty to implement the controller. A Lyapunov function‐based method has been adopted for analyzing the stability of the closed‐loop system. Simulation studies affirm the improved performance of the ARTDC in contrast to the classical artificial delay‐based methodology.

Plate-Springed Parallel Elastic Actuator for Efficient Snake Robot Movement

The design methodology of a plate-springed parallel elastic actuator (PSPEA) for the efficient movement of planar snake robots is presented. The stiffness, which refers to the relationship between the resilience moment and the joint angle, of the plate spring was first designed using a rigid body spring model. The modeled stiffness was then verified via a simple test rig. Combinations of spring stiffnesses that minimize the energy consumption of each joint at different velocities were obtained using dynamic simulation. Experiments using a planar six-link PSPEA-based snake robot were performed via sensors installed in the servomotors to measure torque and speed, and a motion-tracking system was utilized to measure the moving distance. True efficiency was evaluated using the cost of transport criterion, which was later compared with the dynamic simulation results. Despite its compact design, it was observed that the proposed PSPEA improved the energy efficiency of the snake robot by a maximum of approximately 50%.

Head-Trajectory-Tracking Control of a Snake Robot and Its Robustness Under Actuator Failure

This brief considers the problem of trajectory tracking of a planar snake robot without a lateral constraint. The reference trajectory of the head position and the orientation of link 1 are given, and torque control is determined to reduce tracking errors. The performance of the controller was tested in a number of simulations. The robustness during actuator failure was also studied. We assumed that one of the actuators was broken and the corresponding joint became passive. Furthermore, as a more realistic situation, we considered an instance when some of the states were not readily accessible from the sensor readings and needed to be estimated by an observer. The extended Kalman filter was employed for this purpose, and the performance of the closed-loop system with the observer was also tested in simulations.

A Double-Layered Artificial Delay-Based Approach for Maneuvering Control of Planar Snake Robots

Uncertainty and disturbance are common in a planar snake robot model due to its structural complexity and variation in system parameters. To achieve efficient head angle and velocity tracking with least computational complexity and unknown uncertainty bounds, a time-delayed control (TDC) scheme has been presented in this paper. A Serpenoid gait function is being tracked by the joint angles utilizing virtual holonomic constraints (VHCs) method. The first layer of TDC has been proposed for stabilizing the VHC dynamics to the origin. Once the VHCs are satisfied, the system is said to be on the constraint manifold. The second layer of TDC has been applied to an output system defined over the reduced order dynamics on the constrained manifold. To establish the robustness of the control approach through simulation, uncertainty in the friction coefficients is considered to be time-varying emulating change in the ground conditions. Simulation results and Lyapunov stability analysis affirm the uniformly ultimately bounded stability of the robot employing the proposed approach.

Stiffness Design of a Resonance-Based Planar Snake Robot With Parallel Elastic Actuators

This letter proposes an $N$ -link snake robot with parallel elastic actuators (PEA) and a stiffness property that reduces the energy consumption during fast movement. Each PEA couples the actuator output to a spring element, enhancing the periodic gait as demonstrated in previous studies of walking robots. The PEA can mimic each joint of a typical snake robot, which is also controlled by sinusoidal periodic signals. If the actuator output is synchronized with the resonance frequency of the spring, the PEA can greatly reduce the actuator torque and power. Therefore, this letter proposes PEAs to reduce the energy consumption of $N$ -link snake robots. After analyzing the robot dynamics, we explain how the torque of each joint is minimized. The energy consumption is evaluated by measuring the motor current in experimental tests. During fast movement of the robot, the PEA reduced the current consumption by 72%.

Sliding Mode Control of Planar Snake Robot With Uncertainty Using Virtual Holonomic Constraints

In this paper, we present a sliding mode control (SMC) based approach to address the velocity tracking and head-angle control problem of a planar snake robot. The motion characteristics of a snake exhibit the generation of propulsive force as a result of anisotropic friction with respect to the ground. To imitate the motion of a snake, all the joints of the snake robot are tracked to a serpenoid gait function utilizing virtual holonomic constraints. The parameters of the gait function are obtained from the SMC resulting in head-angle control and velocity tracking. SMC has been chosen to ensure robustness and stability of the system in the presence of uncertainties arising from variation in the friction force coefficients between the robot and the ground. Lyapunov's stability analysis proves the finite-time stability of the system. The control scheme has also been verified and compared with an existing approach through simulation studies.

Maneuvering Control of Planar Snake Robots Using Virtual Holonomic Constraints

This paper investigates the problem of maneuvering control for planar snake robots. The control objective is to make the center of mass of the snake robot converge to a desired path and traverse the path with a desired velocity. The proposed feedback control strategy enforces virtual constraints encoding a lateral undulatory gait, parametrized by the states of dynamic compensators used to regulate the orientation and forward speed of the snake robot.

Analysis and heading control of continuum planar snake robot based on kinematics and a general solution thereof

This paper presents a kinematic calculation and control method for an inextensible continuum planar snake robot. The snake robot is assumed to move without side slipping; this constraint makes it easy to construct its kinematic model based on which we can analyze the movement of the robot. The kinematic model is expressed as a semi-linear partial differential equation (PDE). We discuss the general solution of the PDE and a calculation method based on it. However, the constraint also raises the problem of singular posture. The problem of singularities has been addressed for a snake robot with a serial link structure; however, for a continuum snake robot, much less research has been carried out. In this paper, we propose a method for controlling the direction of movement while avoiding singularities. The validity of our method is tested through simulations and experiments.

Path following control of planar snake robots using virtual holonomic constraints: theory and experiments.

This paper considers path following control of planar snake robots using virtual holonomic constraints. In order to present a model-based path following control design for the snake robot, we first derive the Euler-Lagrange equations of motion of the system. Subsequently, we define geometric relations among the generalized coordinates of the system, using the method of virtual holonomic constraints. These appropriately defined constraints shape the geometry of a constraint manifold for the system, which is a submanifold of the configuration space of the robot. Furthermore, we show that the constraint manifold can be made invariant by a suitable choice of feedback. In particular, we analytically design a smooth feedback control law to exponentially stabilize the constraint manifold. We show that enforcing the appropriately defined virtual holonomic constraints for the configuration variables implies that the robot converges to and follows a desired geometric path. Numerical simulations and experimental results are presented to validate the theoretical approach.

Path Following Control of a Planar Snake Robot with an Exponentially Stabilizing Joint Control Law

This paper considers the problem of path following control of a planar snake robot without sideslip constraints. We use Lagrangian mechanics to derive the dynamical equations of motion of the system. The possibility of controlling the orientation of the robot in the absence of external dissipative forces is investigated. An exponentially stabilizing joint control law for the actuated shape dynamics of the robot is presented. We analytically design a guidance-based path following control law for the snake robot, and we show that the trajectories of the heading error dynamics are ultimately bounded with a bound that can be made arbitrarily small. The efficiency of the control design is shown with simulations.

Snake Robots From Biology to Nonlinear Control

Inspired by the motion of biological snakes, this paper presents an overview of recent results in modelling and control of snake robots. The objective of the research underlying this paper is to contribute to the mathematical foundation of the control theory of snake robots. To this end, the paper presents two mathematical models of planar snake robot dynamics, which are employed to investigate stabilisability and controllability properties of snake robots. Furthermore, averaging theory is used to derive properties of the velocity dynamics of snake robots. Moreover, a straight line path following controller is proposed and cascaded systems theory is employed to prove that the controller K -exponentially stabilizes a snake robot to any desired straight path.

Controllability and Stability Analysis of Planar Snake Robot Locomotion

This paper contributes to the understanding of snake robot locomotion by employing nonlinear system analysis tools for investigating fundamental properties of snake robot dynamics. The paper has five contributions: 1) a partially feedback linearized model of a planar snake robot influenced by viscous ground friction is developed. 2) A stabilizability analysis is presented proving that any asymptotically stabilizing 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 isotropic, but that a snake robot becomes strongly accessible when the viscous ground friction is anisotropic. The analysis also shows that the snake robot does not satisfy sufficient conditions for small-time local controllability (STLC). 4) An analysis of snake locomotion is presented that easily explains how anisotropic viscous ground friction enables 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. 5) A controller for straight line path following control of snake robots is proposed and a Poincaré map is investigated to prove that the resulting state variables of the snake robot, except for the position in the forward direction, trace out an exponentially stable periodic orbit.

Path Following Control of Planar Snake Robots Using a Cascaded Approach

This paper considers path following control of snake robots along straight paths. Under the assumption that the forward velocity of the snake robot is nonzero and positive, we prove that the proposed path following controller K-exponentially stabilizes a snake robot to any desired straight path. The performance of the path following controller is investigated through simulations and through experiments with a physical snake robot, where the controller successfully steers the snake robot toward and along the desired straight path.

Hybrid Modelling and Control of Obstacle-Aided Snake Robot Locomotion

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.