A Snake-Inspired Layer-Driven Continuum Robot

Abstract

Continuum robots with redundant degrees of freedom and postactuated devices are suitable for application in aerospace, nuclear facilities, and other narrow and multiobstacle special environments. The development of a snake-inspired continuum robot is presented in this study. The morphological skeleton structure of the snake body is simulated using underactuated continuum joints, which include several rigid-body joints in series. Each rigid-body joint is driven by the traction of a wire rope. Based on the layered-drive principle, angular synchronous motion can be realized in space with multiple rigid-body joints in a single continuous joint, which can considerably reduce the complexity of the inverse kinematics solution, terminal drive box, and control system. The static and dynamic characteristics of the snake-inspired robot are obtained through torque balance and an equivalent transformation. Finally, we demonstrate trajectory planning and load capacity testing in two robot prototypes with arm lengths of 1500 and 2300 mm (including two and four continuous joints, respectively). The rationality of the structure and the correctness of the control of the layered-drive snake-inspired robot are verified.

Introduction

Compared with the discrete robotics associated with industrial robots^1,2 and hyper-redundant robots with more kinematically executable degrees of freedom,³⁻⁵ continuous robots exhibit a large number of kinematic degrees of freedom; however, not all of them can be driven directly.⁶⁻⁸ The design of continuum robots is mainly inspired by natural vertebrates such as snakes and their trunks and tails, as well as invertebrates such as octopuses.⁹⁻¹³ A continuous robot is more flexible than a classical rigid linkage robot when performing a specific task in a highly limited working environment. It can be used in complex environments involving multiple obstacles by means of encircling and other techniques,¹⁴ offering a simpler, smoother, and more real-time motion than those offered by the hyper-redundant robot structure, kinematic solution, or terminal drive box and control system.¹⁵⁻¹⁷ Therefore, such robots are suitable for application in nuclear power and other high-risk or narrow-space operations.¹⁸

A continuum robot can be continuously bent along its length. It is usually manufactured using soft and flexible materials that can be deformed by external forces and that are highly adaptable to the environment.^19,20 The local bending and rotating movement of the continuum is realized using the driving system, mainly comprising the stretching deformation of ropes, tendons, and pneumatic muscles.^21,22 This is still a new field and can meet the needs of special environments in applications such as search and rescue, radioactive waste disposal, outer-space assistance, and minimally invasive surgery.²³⁻²⁹ This study focuses on the detection requirements of a small operating space within the dense environment of the China Fusion Engineering Test Reactor (CFETR) vacuum chamber and the upper window pipe.³⁰ An underactuated continuum robot with a layered-driven configuration is designed by analyzing the snake's skeletal characteristics and its body morphology. Multisegmented rigid joints are used to form a continuum. Subsequently, this continuum is connected in series to form the whole snake-inspired continuum robot, exhibiting high space curvature, position accuracy, and load capacity. The driving system, control system, and kinematic model are also simplified.

The inverse kinematics solution and trajectory planning of the snake-inspired robot are realized by establishing an accurate kinematic model. The working space and cable drive signal of the snake robot are calculated, and the static and dynamic characteristics of the snake robot are then obtained using torque balance and an equivalent transformation. Finally, trajectory planning and load experiments are conducted on snake-inspired robots with different arm lengths (1500 and 2300 mm).

Design of the Layer-Driven Continuum Robot

Snake-crawling bionic mechanism

The skeleton structure of a snake is presented in Figure 1A. It mainly comprises vertebrae, ribs, and a skull, and its winding movement is mainly completed using the skeleton structure of the body, ventral scales, and related muscles. Most of the time, the body morphology of a snake exhibits multiple continuous “S”-shaped geometric configurations during movement. Therefore, for the body morphology of a segment of snake skeleton bending into a single “S” shape, the segment can be regarded as a continuum robot comprising two segments of continuous spine with the same curvature and opposite bending directions. The morphological characteristics of a whole snake can be simulated by the motion path of a snake-inspired robot comprising multiple continuous joints in series.

FIG. 1.

Design of the snake-inspired continuum robot configuration. (A) The skeletal structure of a snake shows an “S” motion configuration. (B) The snake-inspired continuum robot prototype model, which comprises a terminal drive box and a multiarticulated arm (including two continuum joints, each of which comprises three rigid-body joints, and the layered drive principle is adopted to realize angular synchronization design in space). (C) The composite capstan mounted on the motor can simultaneously pull multiple wire ropes to control the spatial angular synchronization of the continuum. Color images are available online.

In this study, a new snake-inspired continuum robot was designed by structurally analyzing the snake skeleton and bionic design of the muscle traction, as shown in Figure 1B. This robot adopts a layered-drive design. A single continuous joint contains three rigid-body joints. Through the composite capstan, as shown in Figure 1C, three steel wires are driven to pull the three rigid-body joints in a single continuous joint to achieve angular synchronous movement in space.

Prototype

In response to the actual use requirements of the CFETR fusion reactor, the prototype of the new continuum snake robot (arm length = 2300 mm) was designed as shown in Figure 2A; the prototype mainly comprises a terminal drive box and several continuum joints. The entire snake arm contains 10 rigid joints, which are divided into four continuum joint groups according to the ratio of 3:3:2:2 for layered-drive design.

FIG. 2.

Structure of the snake-inspired continuum robot. (A) Prototype model, including snake arm (a), drive box (b), power cabinet (c), and motion control card (d). (B) Joint group 2 contains three rigid joints (f), the distribution diagram of the traction cable along the joint unit section (e), the composite capstan traction cable (g). Color images are available online.

We take the joint group 2 in Figure 2A as an example to analyze the principle of layer driving, as shown in Figure 2B. The wire rope layout is shown in Figure 2e, where blue, red, and green represent the positions at which the wire rope is fixed for each joint. As shown in Figure 2f, the outermost green wire rope is fixed at the first rigid-body joint, the intermediate red wire rope is fixed at the second rigid-body joint, and the innermost blue wire rope is fixed at the third rigid-body joint. To realize the angular synchronous motion in the space of three rigid-body joints in a single continuous joint, a composite capstan with different diameters was used to drive it, as shown in Figure 2g. The capstan is arranged along the axis with three winding slots having different diameters. The capstan drives the green, red, and blue wire ropes from top to bottom. The wire rope passes through a continuous joint, and the green, red, and blue wire ropes are fixed successively on the first, second, and third rigid-body joints in the continuous joint, respectively. Thus, angular synchronous motion of the single continuous joint group is realized.

Kinematic and Dynamic Characteristics

Forward kinematic modeling

In this study, the forward kinematic solution of the snake robot adopts the method shown in Figure 3A, where $α_{i}$ is defined as the rotation of the continuous joint around the y_i axis and $3 β_{i}$ is defined as the rotation of the continuous joint around the $x_{i + 1}$ axis. A coordinate system was established for the universal joints between each rigid-body joint for solving the inverse kinematics of the snake robot, as shown in Figure 3B. The motion of the universal joint is defined as the rotation of $δ_{i}$ around the z_i axis and $γ_{i}$ around the $x_{i + 1}$ axis.

FIG. 3.

Method for establishing the coordinate system for the kinematic solution of the continuum robot. (A) Method for establishing the coordinate system for a single continuum joint. (B) Method for establishing the coordinate system for a single universal joint in a single continuous joint. Color images are available online.

The kinematic matrix transformation from joint i + 1 to joint i and the transformation rule are as follows: $\begin{matrix} D_{i} & = T r a n s (x_{i}, y_{i}, z_{i}) \cdot R o t (y_{i}, α_{i}) \cdot R o t (x_{i + 1}, 3 β_{i}) \\ = [\begin{matrix} c α_{i} & s a_{i} s 3 β_{i} & s α_{i} c 3 β_{i} & x_{i} \\ 0 & c 3 β_{i} & - s 3 β_{i} & y_{i} \\ - s α_{i} & c a_{i} s 3 β_{i} & c α_{i} c 3 β_{i} & z_{i} \\ 0 & 0 & 0 & 1 \end{matrix}] \end{matrix}$ (1)

where $T r a n s (x_{i}, y_{i}, z_{i})$ denotes translation transformation, $R o t (y_{i}, α_{i})$ and $R o t (x_{i + 1}, 3 β_{i})$ denote rotation transformation, c denotes cos, and s denotes sin. This convention will be adopted in future studies as well. Then, the corresponding coordinate can be given as follows: $P_{i} (x_{i}, y_{i}, z_{i}, 1) = D_{i} \cdot [\begin{matrix} x_{i + 1} \\ y_{i + 1} \\ \begin{matrix} z_{i + 1} \\ 1 \end{matrix} \end{matrix}] .$ (2)

Thus, the relationship between the base coordinate system of the snake robot and the end coordinate system of the i-th continuum joint can be written as $P_{1} (x_{1}, y_{1}, z_{1}, 1) = D_{1} \cdot D_{2} \cdot \dots D_{i} \cdot [\begin{matrix} x_{i + 1} \\ y_{i + 1} \\ \begin{matrix} z_{i + 1} \\ 1 \end{matrix} \end{matrix}] .$ (3)

Based on the rotation angle $[α_{i}, β_{i}]$ of each continuous joint in real time, the end position $[x_{1}, y_{1}, z_{1}]$ of the corresponding snake robot with respect to the coordinate system of the base can be calculated to complete the forward kinematic solution.

Algorithm of wire rope elongation

For the general case in which neither $δ$ nor $γ$ is zero, the wire ropes $l_{1}, l_{2}, a n d l_{3}$ are line segments in different planes. Estimating the real-time changes using traditional planar and space geometric methods is difficult. Therefore, we introduce the rule of matrix transformation and establish the coordinate system, as shown in Figure 4. Let us assume that the continuum joint shown in Figure 4A is the first continuum joint near the terminal drive box. The lengths of $l_{1}, l_{2}, a n d l_{3}$ of the first set of wire ropes in Figure 4B will be solved next.

FIG. 4.

Coordinate systems of a single continuum joint of the continuum robot. (A) A single continuum joint. (B) Coordinate systems of a single universal joint within a single continuum joint. Color images are available online.

We set point A as the base coordinate system ( $x_{0} - y_{0} - z_{0}$ ). The H point associated with the coordinate system of point C ( $x_{3} - x_{3} - x_{3}$ ) can be transformed to the base coordinate system ( $x_{0} - y_{0} - z_{0}$ ) of point A through matrix transformation. $\begin{matrix} T_{A C} = T r a n s (0, h, 0) R (z_{1}, - δ) R (x_{2}, - γ) T r a n s (0, h, 0) \\ = [\begin{matrix} c δ & s δ c γ & \begin{matrix} s δ s γ & h s δ c γ \end{matrix} \\ - s δ & c δ c γ & \begin{matrix} c δ s γ & h + h c δ c γ \end{matrix} \\ \begin{matrix} 0 \\ 0 \end{matrix} & \begin{matrix} - s γ \\ 0 \end{matrix} & \begin{matrix} c γ & - h s γ \\ 0 & 1 \end{matrix} \end{matrix}] \end{matrix}$ (4)

P_{A H} (x_{A H}, y_{A H}, z_{A H}, 1) = T_{A C} P_{C H} .

(5)

In this study, the coordinates of point D in the base coordinate system A ( $x_{0} - y_{0} - z_{0}$ ) and those of point H in the coordinate system of point C ( $x_{3} - x_{3} - x_{3}$ ) are $\begin{matrix} P_{A D} (x_{A D}, y_{A D}, z_{A D}, 1) & = P_{C H} (x_{C H}, y_{C H}, z_{C H}, 1) \\ = {[\begin{matrix} r & 0 & \begin{matrix} 0 & 1 \end{matrix} \end{matrix}]}^{T}, \end{matrix}$ (6)

where r is the distance between the cable hole and the midline of the joint. Using Equation (6), the coordinates of point H in the base coordinate system A ( $x_{0} - y_{0} - z_{0}$ ) can be obtained as follows: $P_{A H} (x_{A H}, y_{A H}, z_{A H}, 1) = T_{A C} P_{C H} = [\begin{matrix} r c δ + h s δ c γ \\ - r s δ + h (1 + c δ c γ) \\ \begin{matrix} - h s γ \\ 1 \end{matrix} \end{matrix}],$ (7)

According to the distance formula between two points, the length of l₁ can be obtained as $l_{1} = \sqrt{{(x_{A H} - x_{A D})}^{2} + {(y_{A H} - y_{A D})}^{2} + {(z_{A H} - z_{A D})}^{2}} .$ (8)

$l_{2}, l_{3}$ and the other wire rope lengths are obtained analogously to l₁.

Snake robot workspace

Setting the extreme rotation angle of each joint of the snake robot to $2 0^{\circ}$ , we solved the work space of the snake robot using the Monte Carlo and geometric methods. The results are shown in Figure 5, where the curves and dots of different colors represent the fully extended end-effector locations for various arm joint configurations solved using the geometric method and the Monte Carlo method. As the working space of the snake robot is symmetric, it can be projected onto the X–Y and Y–Z working planes. The maximum working space of each joint group of the snake robot can then be visualized in these planes. Comparing the results of solving the snake robot workspace with those of the geometric and Monte Carlo methods, the correctness of the solution can be determined.

FIG. 5.

Geometric and Monte Carlo calculations in the workspace: (A) X–Y plane projection, (B) Y–Z plane projection. Color images are available online.

Snake robot statics

The cable distribution of each joint group of the snake robot is shown in Figure 6A. Assuming that the minimum traction force of any joint cable is 1 N, the cable can be kept tight at all times, ignoring friction and flexible deformation everywhere. The end limit load was set to 5 kg, and the static analysis of each traction cable of the snake-shaped robot was performed through the force balance, torque balance, and equivalent transformation, as shown in Figure 6D. The static force characteristics can guide the selection of joint components and the research of extreme force optimization.

FIG. 6.

Static force analysis of each cable of the snake robot. (A) Joint cable distribution cross section, (B) Synchronous movement of joint group angles. (C) Setting of the end load, (D) The force of each joint cable. Color images are available online.

Snake robot dynamics

Because of the strong coupling characteristics among the joints, end effectors, and drive motors of the snake robot, the mapping relationships among these components cannot be directly obtained. Therefore, an accurate dynamic model that calculates the real-time driving force of the rope is difficult to establish, especially when the arm is long and the number of degrees of freedom becomes high. This article proposes a twice-equivalent transformation method for calculating the cable driving force of the snake robot. First, the traction force of the cable is considered equivalent to the joint torque, and the dynamic equation is established using a traditional approach such as the Lagrangian method. The dynamic equation of the joint torque is then converted using the force balance, torque balance, and equivalent transformation. The joint torque is converted into the driving force of each cable to realize the decoupling calculation.

Figure 7 shows the force analysis of the end joint. The cable traction forces $F_{1}^{10}, F_{2}^{10}, F_{3}^{10}$ are equivalent to the joint driving torques $T_{1}^{10}, T_{2}^{10}$ , which are solved using the Lagrangian method. Through inverse transformation of $T_{1}^{10}, T_{2}^{10}$ , we then obtain $F_{1}^{10}, F_{2}^{10}, F_{3}^{10}$ . We first solve the direction vectors of $F_{1}^{10}, F_{2}^{10}, F_{3}^{10}$ and then decompose them into the coordinate system of point $A_{2}$ . Finally, we compute the values of $F_{1}^{10}, F_{2}^{10}, F_{3}^{10}$ using the equal torque method.

FIG. 7.

Force analysis of end joints in any posture. Color images are available online.

The coordinates of points B and E in the coordinate system $A_{2} (x_{2}, y_{2}, z_{2})$ are $(x_{B x 2}, y_{B y 2}, z_{B z 2})$ , $(x_{E x 2}, y_{E y 2}, z_{E z 2})$ : $P (x_{B x 2}, y_{B y 2}, z_{B z 2}) = T r a n s (0, - h, 0) [\begin{matrix} - r s α_{1} \\ 0 \\ \begin{matrix} r c α_{1} \\ 1 \end{matrix} \end{matrix}],$ (9) $\begin{matrix} P (x_{E x 2}, y_{E y 2}, z_{E z 2}) \\ = R o t (x_{2}, γ) R o t (z_{3}, δ) T r a n s (0, h, 0) [\begin{matrix} - r s α_{1} \\ 0 \\ \begin{matrix} r c α_{1} \\ 1 \end{matrix} \end{matrix}], \end{matrix}$ (10)

where $2 h$ is the length of the universal joint in a horizontal state, $γ$ is the rotation angle of the universal joint around the x₂ axis, $δ$ is the rotation angle of the universal joint around the z₃ axis, r is the distance from the joint cable hole to the axis, and $α_{1}$ is the rotation angle of point B around the y₁ axis.

The unit direction vector of $F_{1}^{10}$ in the coordinate system $A_{2} (x_{2}, y_{2}, z_{2})$ can be obtained as $W_{F 1} = \frac{(x_{B x 2} - x_{E x 2}, y_{B y 2} - y_{E y 2}, z_{B z 2} - z_{E z 2})}{\sqrt{{(x_{B x 2} - x_{E x 2})}^{2} + {(y_{B y 2} - y_{E y 2})}^{2} + {(z_{B z 2} - z_{E z 2})}^{2}}} .$ (11)

Decomposing $F_{1}^{10}$ into the parallel lines of each axis of the coordinate system $A_{2} (x_{2}, y_{2}, z_{2})$ according to the vector decomposition rule of force, we have $F_{x 2 F 1} = \frac{(x_{B x 2} - x_{E x 2})}{\sqrt{{(x_{B x 2} - x_{E x 2})}^{2} + {(y_{B y 2} - y_{E y 2})}^{2} + {(z_{B z 2} - z_{E z 2})}^{2}}} F_{1}^{10},$ (12)

F_{y 2 F 1} = \frac{(y_{B y 2} - y_{E y 2})}{\sqrt{{(x_{B x 2} - x_{E x 2})}^{2} + {(y_{B y 2} - y_{E y 2})}^{2} + {(z_{B z 2} - z_{E z 2})}^{2}}} F_{1}^{10},

(13)

F_{z 2 F 1} = \frac{(z_{B z 2} - z_{E z 2})}{\sqrt{{(x_{B x 2} - x_{E x 2})}^{2} + {(y_{B y 2} - y_{E y 2})}^{2} + {(z_{B z 2} - z_{E z 2})}^{2}}} F_{1}^{10} .

(14)

By analogy, $F_{2}^{10}, F_{3}^{10}$ can be decomposed into the coordinate system $A_{2} (x_{2}, y_{2}, z_{2})$ . The results are $[F_{x 2 F 2}, F_{y 2 F 2}, F_{z 2 F 2}]$ and $[F_{x 2 F 3}, F_{y 2 F 3}, F_{z 2 F 3}]$ .

The torque produced by $F_{1}^{10}, F_{2}^{10}, F_{3}^{10}$ on the x₂ axis in the coordinate system of point $A_{2} (x_{2}, y_{2}, z_{2})$ can be obtained as $T_{x 2 F 1} = F_{y 2 F 1} z_{E x 2} + F_{z 2 F 1} y_{E x 2},$ (15)

T_{x 2 F 2} = F_{y 2 F 2} z_{F x 2} + F_{z 2 F 2} y_{F x 2},

(16)

T_{x 2 F 3} = F_{y 2 F 3} z_{G x 2} + F_{z 2 F 3} y_{G x 2} .

(17)

From the equivalent transformation of $T_{1}^{10}$ on the x₂ axis of coordinate system $A_{2} (x_{2}, y_{2}, z_{2})$ , we get $T_{1}^{10} = T_{x 2 F 1} + T_{x 2 F 2} + T_{x 2 F 3} .$ (18)

By analogy, the equivalent torque of $F_{1}^{10}, F_{2}^{10}, F_{3}^{10}$ along the z₃ axis in coordinate system $A_{2} (x_{3}, y_{3}, z_{3})$ can be obtained. From the equivalent transformation of $T_{2}^{10}$ on the z₃ axis of coordinate system $A_{2} (x_{3}, y_{3}, z_{3})$ , we get $T_{2}^{10} = T_{z 3 F 1} + T_{z 3 F 2} + T_{z 3 F 3} .$ (19)

Combining Equations (18) and (19), we can solve $F_{1}^{10}, F_{2}^{10}, F_{3}^{10}$ in real time. Similarly, the cable force of any other joint can be obtained.

Performance Tests and Validation

Trajectory-planning experiment

Two prototypes with different arm lengths (1500 and 2300 mm) were designed for open-loop trajectory planning through the layered-drive principle. According to the snake robot arm length from short to long, the generalized inverse matrix and backbone curve methods were used to perform inverse kinematics solution and trajectory planning.^31–34 See Supplementary Videos S1–S6 for the captured simulation and experimental results. The tracking accuracy of the snake robot was measured using a Leica laser-tracking measurement system, as shown in Figure 8. The position error and repeated-position accuracy were measured under different loads. The experimental results are shown in Figure 9. The trajectory-tracking errors of the end points of the snake robots with the 1500- and 2300-mm arm lengths were maximized at 12 mm in the space of the circular trajectory-planning process and at 18 mm in the rectangular trajectory-planning process.

FIG. 8.

Snake robot end position accuracy experiment. (A) Test system, (B) laser tracker target ball installation position, (C) end position accuracy test under different loads. Color images are available online.

FIG. 9.

Trajectory planning and error analysis of snake robots with different arm lengths: (A, B) 1500 mm and (C, D) 2300 mm. Color images are available online.

Joint-angle measurement experiment

Figure 10A shows the space-rotation angle data of each joint group of the snake robot with an arm length of 2300 mm. The backbone curve method was used to conduct the rectangular and sinusoidal trajectory experiments, and the data recorded using a gyroscope angle sensor are shown in Figure 10b and c. The snake robot moved smoothly, and no oscillations developed in the joint angles. In several experiments, the maximum repeated joint-angle error along the three coordinate axes in the end joint group of the snake arm (measured by the gyroscope) was $(0.6 3^{\circ}, 0.8 1^{\circ}, 0.3 1^{\circ})$ .

FIG. 10.

Snake robot positioning accuracy experiment. (A) Joint angle measurement experiment, where (a) is the distribution of each angle sensor, (b) and (c) are the angles of each angle sensor on the rectangular trajectory and the sinusoidal trajectory. (B) Error experiment under different loads, where (d) position error of the end point of the snake arm; (e) repeat positioning accuracy of the snake arm. Color images are available online.

Load test of continuum joints

The end-position errors and repeated-position accuracies of the snake robot with an arm length of 1500 mm were measured under different loads using the laser-tracking measurement system. The initial position of the snake robot is shown in Figure 8C. We set the snake robot to perform multiple horizontal sine trajectory tests. The position error of the end along the Z axis is shown in Figure 10d. The position error was maximized (15 mm) at the swing limit corner. Set the snake robot to perform multiple horizontal and vertical sinusoidal trajectory tests; the repeated-position error of the end is shown in Figure 10e. The maximum absolute position error was 11 mm.

The abovementioned experimental results and Supplementary Videos S1–S6 confirm that the entire trajectory control processes were smooth, fluent, and free of oscillations or noise. In the trajectory-planning process of the open-loop inverse kinematics, the maximum position errors of the end points of the snake robots with arm lengths of 1500 and 2300 mm were 12 and 18 mm, respectively. The error has several likely causes. First, the continuum-designed robot based on the layered drive is an underactuated configuration, so each joint group needs high-precision coordinated motion capability. The position error is increased by the flexible deformation of the steel wire rope and the slight change in the diameter of the composite capstan. Second, under the action of gravity, the uneven forces in the cables of the snake robot introduce static position errors in each joint. In addition, errors in the open-loop inverse solution affect the coordinated motion of multiple motors, amplifying the end-position error. When the end-position error of the snake robot is large, it can be compensated using a nonlinear least-squares algorithm to improve the position accuracy.³⁵ In general, the layered-drive snake robot has a simplified drive and control system but stronger load capacity and position accuracy than traditional flexible continuum robots. Therefore, it realizes accurate kinematics models and meets the requirements of CFETR's narrow-space visual navigation.

Conclusion

In this study, we developed an underactuated continuum robot with layered-driven configuration. The continuous joints of this robot comprised several rigid-body joints in series, and angular synchronization was achieved in the spaces of these rigid-body joints. The robot combines the structural characteristics of a hyper-redundant robot and a continuum robot and has the characteristics of high freedom of movement, strong carrying capacity, and simple driving and control systems. The end-drive system of the layered-drive snake robot is designed based on the driving principle of the composite capstan. The motion-control system is designed based on a high-performance motion-control card, and robotic motion control and video image data transmission are realized. The snake robot workspace is calculated using the kinematics model. The static and dynamic force characteristics of the cables are analyzed. The rationality of the structural design and the accuracy of the control system of the snake robot are verified through open-loop trajectory planning and load tests. The maximum trajectory-tracking errors of the end points of the snake robots with arm lengths of 1500 and 2300 mm are 12 and 18 mm, respectively. The position error mainly comes from cable flexibility, initial position error, external force imbalance, and insufficient multimotor coordinated movement ability. In general, compared with the flexible continuum robot, the motion process of the proposed robot is smooth, and without oscillation, position accuracy and load capacity are significantly improved.

In the future, the application of the snake-inspired continuum robot will be improved. Furthermore, a compensation mechanism will be added based on the open-loop position error of the robot to improve the position accuracy. Furthermore, trajectory tracking and a master–slave teleoperation control algorithm of the layer-driven snake robot will be further developed for operational capability in extremely narrow working environments.

Footnotes

Acknowledgments

The authors are very grateful to the editors and reviewers for their valuable comments, which have improved the article.

Author Disclosure Statement

No competing financial interests exist.

Funding Information

This work is supported by the National Key R&D program of China (grant nos. 2019YFB1309600), National Natural Science Foundation of China (grant nos. 11802305, 51875281, and 51861135306), and China National Special Project for Magnetic Confinement Fusion Science Program (grant no. 2017YFE0300503).

Supplementary Material

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