Development of a Modular Tensegrity Robot Arm Capable of Continuous Bending

Abstract

In this study, we present a tensegrity robot arm that can reproduce the features of complex musculoskeletal structures, and can bend like a continuum manipulator. In particular, we propose a design method for an arm-type tensegrity robot that has a long shape in one direction, and can be deformed like a continuum manipulator. This method is based on the idea of utilizing simple and flexible strict tensegrity modules, and connecting them recursively so that they remain strict tensegrity even after being connected. The tensegrity obtained by this method strongly resists compressive forces in the longitudinal direction, but is flexible in the bending direction. Therefore, the changes in stiffness owing to internal forces, such as in musculoskeletal robots, appear more in the bending direction. First, this study describes this design method, then describes a developed pneumatically driven tensegrity robot arm with 20 actuators. Next, the range of motion and stiffness under various driving patterns are presented as evaluations of the robot performance.

Keywords: continuum robot; modular design; musculoskeletal robot; soft robotics; tensegrity.

FIGURE 1

Proposed design rule of a tensegrity robot arm. The tensegrity module constituting the tensegrity robot arm has two types of cables: a stiff cable and a flexible cable. Because the flexible cables allow deformation of the module, two modules can be connected by the closed path composed of stiff cables. To make the connected structure a tensegrity, each end on the closed path needs an additional connection with an end belonging to the different module, not being on the closed path, and does not have an opposite neighboring end. The proposed design rule utilize actuators for these additional cables. The addition of a third or subsequent module is considered to be the insertion of the module into the closed path connecting two modules. To keep this a tensegrity, cables that connect ends on the two new closed paths, but don’t belong to the inserted module are needed. These additional cables mean actuators in the proposed method similar to the two module connections.

FIGURE 2

The tensegrity robot arm mock-up fabricated by the proposed design rule and the verification results. The mock-up was fabricated utilizing a simple tensegrity comprising four struts as a module, and connecting five of them based on the proposed design rule. Each of the five modules can be viewed as a layer of the arm-like tensegrity. By applying an external force, a variety of continuous bending postures can be observed. As expected, the closed path comprising stiff cables suppresses changes in the longitudinal length, and external forces contribute solely to changes in the bending direction.

FIGURE 3

The overview of the developed tensegrity robot arm capable of continuous bending. In this robot, five tensegrity modules are connected by the proposed design rule, and 20 pneumatic cylinders are employed as actuators. Note that two types of modules with different twisting directions are utilized, and they are connected alternately. The instruments for the control system are implemented in the box frame that the robot is mounted.

FIGURE 4

The developed cable fixing part attachable at the ends of struts. The fixing part comprises the body part and the cover. The body part has slits in four directions for attaching the cable, and the clamps or knots on the cable can be caught in the gaps to fix the cable firmly. Because there are closed paths with stiff cables in the proposed design rule, as an alternative, it allows the stiff cables to pass through the body part via slits, and the cover can firmly fix it. These parts are fabricated by the FDM 3D printer (Mark Two, Markforged).

FIGURE 5

The schematic of the control system. Pressure control valves supply compressed air to the pneumatic cylinders and measure the actual pressures in their chambers. The pressure control valves are connected to the embedded control device having AD/DA converter modules. Also, stable compressed air of 0.5 MPa is supplied to the pressure control valves. The base box of the developed tensegrity robot arm encloses the pressure control valves and the embedded control device.

FIGURE 6

The numbering rule for 20 pneumatic cylinders in the developed tensegrity robot arm. The pneumatic cylinders are numbered counterclockwise in each layer, starting from the cylinder at the extreme back right. All the 20 pneumatic cylinders are numbered by following this procedure for all five layers from the tip to the base.

FIGURE 7

The overview of the measuring system utilizing the optical motion capture system. A total of 24 markers, four for each of the six closed paths of stiff cables, are attached to the developed tensegrity robot. The centers of the six closed paths are calculated from the marker positions, and the robot posture is expressed, i.e., a serial link mechanism with five links connected by multi-degree-of-freedom joints. The base coordinate system is defined as a right-handed system, with the origin at the bottom closed path’s center. The tip coordinate system, which eases understanding the posture, is defined as a right-handed system. The Z and X axes are defined as the normal of the least-squares plane of marker 1 to marker 4, and the projection of marker 2 onto the least-squares plane, respectively.

FIGURE 8

The examples of postures and their corresponding measurements. The developed tensegrity robot arm can not only bend in one direction, but also in different directions twice. The postures are successfully measured by the measuring system utilized in this study.

FIGURE 9

The time series of the hand-tip position during a motion to the maximum bending posture. It shows that the steady-state is reached in about 5 s. Supplementary Video S1 shows this motion.

FIGURE 10

The scatter plot of the tip positions of the developed tensegrity robot arm. The definition of the coordinate system corresponds to that illustrated in Figure 7. The tip position is widely distributed in a hemispherical manner. If viewed in the horizontal plane, the distribution is isotropic. The maximum/minimum tip positions are −857 (mm)/803 (mm) in the x direction, −777 (mm)/854 (mm) in the y direction, and 581 (mm)/1,206 (mm) in the z direction, respectively.

FIGURE 11

The sequential snapshots of the dynamic swing motion of the developed tensegrity robot arm. This swing motion was generated by grouping all the 20 pneumatic cylinders into ten cylinders each on similar and opposite sides, and giving each group a pulse wave with a maximum value of 0.5 (mm), a minimum value of 0.1 (mm), a duty ratio of 0.5, and a period of 3 (sec) in reverse phase. At 0 (sec), the robot arm was stationary, and these sequential snapshots indicate the beginning of the swing motion. Supplementary Video S2 shows this motion.

FIGURE 12

The comparison between most bent postures in the dynamic and static motions. (A): Most bent postures in the static motions. From the postures of the tip coordinate system, it can be observed that there is no significant torsion in the robot arm. (B): Most bent postures in the dynamic motions. The amount of bending is more significant than that in the static case. Furthermore, in contrast to the static motion, significant torsion in the robot arm can be observed.

FIGURE 13

The three different sets of desired pressure values that result in almost the same posture of the developed tensegrity robot arm. The desired pressure values for pneumatic cylinders No. 1 to No. 12, which are not indicated in this graph, were set to (0.24, 0.48, 0.24, 0, 0.48, 0.48, 0, 0, 0.15, 0.3, 0.15, 0) (MPa), respectively, similarly for the three different sets. These values were configured manually.

FIGURE 14

The postures of the tensegrity robot arm under no-load and loaded conditions. (A): the postures by three different desired pressures illustrated in Figure 13 under the no-load condition. The three different desired pressures resulted in similar postures. The average tip position of the robot arm is (x, y, z) = (432.4, 78.7, 1037.3) and the standard deviation is (STD _x , STD _y , STD _z ) = (30.3, 37.6, 21.1). (B): the postures by three different desired pressures illustrated in Figure 13 under the loaded condition where a 130 (g) mass was attached at the tip. The amount of bending was reduced by higher desired pressures, compared to that of lower desired pressures. The average tip position of the robot arm is (x, y, z) = (652.2, 178.2, 797.0) and the standard deviation is (STD _x , STD _y , STD _z ) = (81.0128.1147.2). These results indicate that the developed tensegrity robot arm has variable stiffness.

FIGURE 15

The comparison of displacements by the loading among three different desired pressures. Welch’s t-test was performed in the multiple comparison procedure among the three groups. The number of samples was 10 for each group. Each comparison shows p < 0.001, indicating a significant difference with a probability of significance of less than 1%, even after considering the Bonferroni correction.