The paper focuses on the design and nonlinear control of the humanoid wrist/shoulder joint based on the cable-driven parallel mechanism which can realize roll and pitch movement. In view of the existence of the flexible parts in the mechanism, it is necessary to solve the vibration control of the flexible wrist/shoulder joint. In this paper, a cable-driven parallel robot platform is developed for the experiment study of the humanoid wrist/shoulder joint. And the dynamic model of the mechanism is formulated by using the coupling theory of the flexible body’s large global motion and small flexible deformation. Based on derived dynamics, antivibration control of the joint robot is studied with a nonlinear control method. Finally, simulations and experiments were performed to validate the feasibility of the developed parallel robot prototype and the proposed control scheme.
Live working is a better option for executing related tasks of the electric system. In consideration of the fact that traditional live working is mainly accomplished by the labour, it is dangerous and easy to cause personal casualty accidents. In order to avoid the accident in the artificial live working, it has urgent realistic meaning and important research value that the robot replaces the labour to execute live working. The traditional live working robot [
Structure design of the cable-driven wrist/shoulder joint.
Prototype of the cable-driven parallel robot with a flexible spring.
Due to large workspace, high quality of load ratio, and small inertia, the cable-driven robot technology which stems from the crane system has become a research hot spot in the field of the robot [
The designed cable-driven parallel robot with a flexible spring belongs to the cable-driven parallel robot with an upholder. Little research highlights how to design and control a robotic wrist/shoulder joint which moves smoothly like the people’s wrist/shoulder joint. In light of the inspiration of people’s wrist/shoulder joint structure, we elaborate a 2-DOF (roll and pitch) cable-driven parallel robot with a flexible spring. It includes a cable-driven parallel mechanism and the auxiliary mechanisms which consist of three guide mechanisms, four pillars, three driving mechanisms, a pedestal, an attitude measuring mechanism, three cable force measuring mechanisms, three cable length measuring mechanisms, and so on. The cable-driven parallel mechanism is the key mechanism of the proposed parallel robot. The spring replaces the articular bone in people’s wrist/shoulder joint to support the moving platform and bends to one side to produce 2-DOF (roll and pitch) movements. Three driving cables are equally spaced at 120° on both the fixed base and the moving platform. The wrist/shoulder joint’s 2-DOF (roll and pitch) movements are actuated by three cables which replace people’s wrist/shoulder joint muscle. Three cables are pulled by three driving mechanisms mounted on the pedestal via three guide mechanisms on the pedestal.
Seeing that the proposed parallel robot has some flexible bodies such as the cylindrical compression spring and three cables, the moving platform must generate the flexible vibration during the parallel robot moves. In view of short length, light weight, and small diameter of the cables, cables are assumed to be linear elements that can only work in tension and the dynamical characteristics of cables themselves, such as the vibration and elongation, can be neglected [
The issues of the flexible body’s dynamics attract the researchers’ attentions [
The rest of this paper is organized as follows. In Section
This section will elaborate the parallel robot design which includes mechanical design and electrical design.
The solid model of the parallel robot is illustrated in Figure
Solid model of the cable-driven parallel robot with a flexible spring.
Local mechanical design of the parallel robot: (a) cable force transmission mechanism, (b) perspective 1 of the cable force measuring mechanism, and (c) perspective 2 of the cable force measuring mechanism.
As shown in Figure
Each driving mechanism is made up of a direct current (DC) motor and a reducer. The parameters of the DC gear motor are given in Table
Parameters of the DC gear motor.
Parameter (units) | Value | Description |
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|
40 | Rated power of DC motor |
|
24 | Rated voltage of DC motor |
|
2.1 | Rated current of DC motor |
|
1800 | Rated speed of DC motor |
|
180 : 1 | Reduction ratio of the reducer |
Each cable force is a very important measurand in cable-based architectures. In order to perform a measurement, a low-cost mechanism is presented for the cable force measuring in the proposed parallel robot. The mechanical design of the cable force measuring mechanism is illustrated in Figures
Each cable length is also such an important measurand in cable-based architectures. To perform a measurement, a simple mechanism is presented for the cable length measuring in the proposed parallel robot. The cable transmission system is depicted in Figure
For such a cable force transmission system which is shown in Figure
The DC motor’s electromagnetic torque
If we neglect the DC motor’s friction torque and the reducer’s friction torque, the reducer’s output torque
Based on (
Considering that
The architecture of the control system for the parallel robot is shown in Figure
Architecture of the control system.
The motion control card (USB9010) which is powered by the main computer can control three motor drivers through the analog output mode and collect the data from three incremental encoders. The data acquisition card (USB 8AD) which is powered by the main computer can capture the data from three current sensors and three force transducers.
The sensors contain three incremental encoders, three current sensors, three force transducers, and an AHRS (attitude heading reference system) module. The resolution of each incremental encoder which is powered by the motion control card is 1000 lines per rev. The incremental encoder resolution denotes the output pulse number of the encoder during each rev. Each current sensor is powered by a switching power supply whose output voltage is 5 V. Each force transducer is powered by a signal amplifier (DYBSQ-001) which can be powered by a switching power supply whose output voltage is 24 V. The AHRS module contains a control chip (STM32F103T8), a MPU6050 (a triaxis accelerometer and a triaxis gyroscope), a HMC5883 (a triaxis magnetometer), and a BMP180 (an atmospheric pressure altimeter). The AHRS module which is powered by the main computer can measure the moving platform’s posture.
Each motor driver which is powered by a switching power supply whose output voltage is 24 V can drive a DC motor through the torque control mode. The switching power supply can power the objects within the dashed box in Figure
This part illustrates the cable-driven parallel mechanism’s schematic which is depicted in Figure
Schematic of the cable-driven parallel mechanism.
The flexible spring is supposed to crook in the same lateral plane and the moving platform will have no torsional behavior with respect to the
The workspace analysis of the proposed flexible parallel humanoid arm joint robot is presented in [
Deformation principle and force equivalent.
The velocity of the point
The velocity of the point
Therefore, the energy of the flexible spring which includes the kinetic energy
The energy of the moving platform containing the kinetic energy
Based on (
As described in Figure
We denote
In conclusion, the system’s Lagrange function is given as
We denote the generalized mass matrix as
In view of the existence of the system damping, we add Rayleigh viscous damping model
This part aims to design a nonlinear controller which can be used to track the position of the center for the moving platform while suppressing vibration of the flexible spring and to validate the effectiveness of the design for the cable-driven parallel robot and the proposed control strategy.
Equation (
Equation (
Referring to (
Multiplying (
Our main goal is to achieve a small tracking error at the moving platform while suppressing the vibration in the flexible spring. To this end, we define the output as
As shown in Figure
Substituting (
Let
We choose
Substituting (
Based on (
Based on (
We define
Based on (
Considering that each cable only produces pull force, each element in
The controller given in (
After we obtain the flexible spring’s mode coordinates and the mode velocities, the controller given by (
We provide simulation and experimental results to illustrate the practical feasibility of the design for the cable-driven parallel robot and to test the effectiveness of the dynamical model for control and the proposed control scheme in this section. The simulation and experimental parameters of the moving platform and the fixed base are given in Table
Simulation and experimental parameters of the moving platform and the fixed base.
|
|
|
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0.09 | 0.43 | 0.09 |
Simulation and experimental parameters of the spring.
|
|
|
|
---|---|---|---|
1.095 | 0.1016 | 196.5 |
|
During the flexible spring crooks in the lateral plane, the flexible vibration of
In (
Desired trajectory of
The results of the simulation and the experiment are shown in Figures
Responses of the system under open-loop: (a) theoretical results of all cable forces under open-loop, (b) experimental results of all cable forces under open-loop, (c) experimental results of all motor armature currents under open-loop, (d) theoretical transverse deformation result of the point
Responses of the system under closed-loop: (a) theoretical results of all cable forces under closed-loop, (b) experimental results of all cable forces under closed-loop, (c) experimental results of all motor armature currents under closed-loop, (d) experimental results of all cable lengths under closed-loop, (e) theoretical result of
Variation results of
Variation results of
The system responses under open-loop are shown in Figure
The system responses under closed-loop are shown in Figure
Figure
It can be concluded that we validate the robot prototype, the theoretical model for control, and the proposed control method by the simulation and experiment results.
This paper carries out the mechanical design and electrical design of the cable-driven parallel robot. Meanwhile, the theoretical and experimental studies on the vibration control of the center of the moving platform for the trajectory tracking movement are executed. First, we elaborate a cable-driven parallel robot device that can efficiently be applied to the experimental research. Then, the dynamic model of the system is derived by AMM and Lagrange’s equation. After that, system nonlinear controller is designed to control the spring-induced vibration of the moving platform’s trajectory tracking. Eventually, we provide the simulation study and analyze the experiment result of the vibration control to validate the usability of the cable-driven parallel robot prototype and to verify the proposed control scheme. The approximate consistency for the vibration control results of the simulation and experiment in Section
Based on the study of the design and control of a 2-DOF flexible parallel humanoid arm joint robot, our future work will focus on the experimental study of antivibration control of the whole humanoid arm system.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This study was supported by the Excellent Young Teachers Program of Southeast University (2242015R30024) and Six Talent Peaks Project of Jiangsu Province (2014-ZBZZ-001).