Dynamic Modeling and Experimental Validation of a Water Hydraulic Soft Manipulator Based on an Improved Newton-Euler Iterative Method

Abstract

Compared with rigid robots, soft robots have better adaptability to the environment because of their pliability. However, due to the lower structural stiffness of the soft manipulator, the posture of the manipulator is usually decided by the weight and the external load under operating conditions. Therefore, it is necessary to conduct dynamics modeling and movement analysis of the soft manipulator. In this paper, a fabric reinforced soft manipulator driven by a water hydraulic system is firstly proposed, and the dynamics of both the soft manipulator and hydraulic system are considered. Specifically, a dynamic model of the soft manipulator is established based on an improved Newton-Euler iterative method, which comprehensively considers the influence of inertial force, elastic force, damping force, as well as combined bending and torsion moments. The dynamics of the water hydraulic system consider the effects of cylinder inertia, friction, and water response. Finally, the accuracy of the proposed dynamic model is verified by comparing the simulation results with the experimental data about the steady and dynamic characteristics of the soft manipulator under various conditions. The results show that the maximum sectional error is about 0.0245 m and that the maximum cumulative error is 0.042 m, which validate the effectiveness of the proposed model.

Keywords: Newton–Euler iterative method; dynamic modeling; soft manipulator; water hydraulic system.

Figure 1

(a) Physical image of the soft manipulator. (b) Three-dimensional model of the soft manipulator. (c) Schematic diagram of the components of the soft manipulator.

Figure 2

(a) Schematic diagram of the structure of two adjacent soft manipulators. (b) The shape parameters of the i-th segment of the soft manipulator and the coordinate transformation between two adjacent coordinate systems.

Figure 3

Force diagram of the soft manipulator in segment i.

Figure 4

Schematic diagram of the hydraulic system for driving the soft manipulator. At the left is the schematic representation of the servo motor, and at the right is the representation of the piston and hydraulic cylinder. Above is a schematic representation of the soft manipulator and connecting pipes.

Figure 5

(a) The 3D working space of the single-section soft manipulator. (b) The bending state of the single-section soft manipulator in the XOZ plane. (c) The limit posture of the soft manipulator in space when the pressure on each soft unit of the two-section soft manipulator reaches the limit value (1 mpa).

Figure 6

Simulation results of the soft manipulator when the first, fifth and sixth actuators are actuated by step torque. (a) Soft manipulator trajectory versus time. (b) Curves of the bending curvature versus time. (c) Curves of speed versus time.

Figure 7

Simulation results of the soft manipulator when the first and fourth actuators are actuated by step torque. (a) Soft manipulator trajectory versus time. (b) Curves of the bending curvature versus time. (c) Curves of speed versus time.

Figure 8

Simulation results of the soft manipulator when the first, fifth and sixth actuators are actuated by ramp torque. (a) Soft manipulator trajectory versus time. (b) Curves of the bending curvature versus time. (c) Curves of speed versus time.

Figure 9

Soft manipulator test platform.

Figure 10

The steady state posture of the soft manipulator under different driving pressures.

Figure 11

(a) The comparison of experimental results and simulation results when the second section of the soft manipulator is actuated by different torque to reach a steady state. (b) The comparison of experimental results and simulation results when the first section of the soft manipulator is actuated by different torque to reach a steady state.

Figure 12

Final pose comparison of the dynamic model and prototype continuum arm for in plane bending of all sections. (a) The final posture of the soft manipulator simulation model. (b) The final posture of the prototype continuous arm.

Figure 13

Sequential planar bending of all the sections. Comparison of the dynamic section tip coordinate evolution (solid line) vs. the corresponding coordinate values of the prototype arm (X, Y, and Z experimental data are denoted by o, +, and × marks, respectively). Position errors, ERR_i = ||ψ_i^e-ψ_i|| ∀i ϵ {1,2}, are denoted by a dashed line in each subplot.

Figure 14

Sequential planar bending of all the sections. Comparison of the dynamic section tip coordinate evolution (solid line) vs. the corresponding coordinate values of the prototype arm (X, Y, and Z experimental data are denoted by o, +, and × marks, respectively). Position errors, ERR_i = ||ψ_i^e-ψ_i|| ∀i ϵ {1,2}, are denoted by a dashed line in each subplot.