A Dual-Motor Joint Model for Humanoid Robots

A Dual-Motor Joint Model for Humanoid Robots Jingtao Xue1,2,3, Xiaopeng Chen 1,2,3, Ye Tian1,2,3, Zhangguo Yu1,2,3, Fei Meng1,2,3, Qiang Huang1,2,3 1. IRI , School of Mechatronic Engineering, Beijing Institute of Technology, Beijing 100081 E-mail: [email protected] 2. Key Laboratory of Biomimetic Robots and Systems, Ministry of Education, Beijing 100081 E-mail: [email protected] 3. Key Laboratory of Intelligent Control and Decision of Complex System, Beijing 100081 E-mail: [email protected] Abstract: To make humanoid robots walking fast, it’s important to improve driving force of their leg joints. Usually, each joint of humanoid robots is driven by a single motor. Dual-motor joint, on the other hand, is one of the candidate solutions to meet the power requirement needed for fast walking. This paper proposed a new dual-motor control model. In the model, two motors are treated as a single control plant instead of two parallel control plants. With the usage of current distributor, the control model can pump different current to each motor freely so as to eliminate the unbalance of the load imposed on each motor. Simulation and experiment show that the proposed model works well under high joint load and it can be used on a fast walking humanoid robot. Key Words: Humanoid robot, dual motor, control model

1

Introduction

Aging societies in the near future will face a growing need for daily assistance of human activities in the common environments, such as offices, homes and hospitals [1, 2, 3]. Because of the better mobility and human like outlook, humanoid robot becomes the ideal serving assistant. Since humanoid robot needs to keep a compact structure and a light weight for walking, the joint is usually driven by a dc motor with a separate controller. To get a high driving force in a small volume, the famous Maxon BLDC motor and Elmo motion controller have been used in our previous biped robot BHR-4 (as shown in Fig.1). With this joint group, BHR-4 has been able to walk smoothly under the speed of 1km/h. However, when the speed reached 1.5km/h, the leg joint error developed enormously, indicating the lack of driving force. This phenomenon exists in all biped robots. Robot HRP3L (by the University of Tokyo) uses forced water cooling to improve the driving ability and reaches a speed of 4km/h [4]. While, forced water cooling need a separate hydraulic system, which makes the robot body more complicated and less reliable. On the contrary dual motor drive just makes a little change on the joint and keeps a relatively compact structure to get a high driving force. As to dual motor control system, the most common form is to make one motor as the master and the other as the slave [5]. In this form, the slave one receives the master’s speed command and follows the speed, so that the two motor can output torque force together. This strategy works when the load is small and balanced. If the load on the slave is much bigger than the other, speeds will differ seriously between the two motors and cause fatal failure. In addition, the two motors can also be controlled separately when the

synchronization of speed is not so necessary, which obviously cannot be used in humanoid robot joint. Therefore this paper proposed a new dual motor control model, which can make two motors work under the same speed based on synchronous belt and eliminate the unbalancedness of joint load by the innovative current distributor.

2

Humanoid robot BHR-4 is shown in Fig.1. It’s the late achievement of BIT, which can play tai ji and recognize obstacle in front and bypass. The proposed dual motor control model will be tested upon BHR-4. Dual motor driven joint of knee is specially designed, making two motors connected through synchronous belt. And the exact structure is represented in Fig.2.

Fig. 1: Humanoid robot BHR-4

The corresponding author is Xiaopeng Chen. This work was supported by the National High Technology Research of China under Grant 2011AA040202, The National Natural Science Foundation of China under Grants 60925014 and 61273348, Beijing Science Foundation under Grant 4122065, and “111 Project” under Grant B08043.

c 978-1-4673-5532-2 2013 IEEE

System Configuration

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J1 ǃ J 2 : Moment of inertia; TL : Load torque; J L : Moment of load; n : Rotational speed, r/min; The subscript “1” and “2” above represent the motor1 and motor2. As motor1 and motor2 keep synchronous in mechanic, so they have the same rotational speed. The initial condition is assumed to be zero. Through Laplace transformation [7], the dual motor control model is represented as follows:

Fig. 2: Dual motor structure

Due to the synchronous belt, both motor1 and motor2 work under the same speed, so that one velocity loop is enough to control the two motor. And the load distributed to each motor is usually unbalanced, so a separate current loop is added to each motor. The current distributor can distribute different current to each motor on its own to make the two motor bear a balanced joint load. The control scheme is presented in Fig. 3.

I1 1 = U1 -E1 L1s +R1 I2 1 = U 2 -E2 L2 s +R2 n 375 = Te1 +Te 2 -TL 4 g (J1 +J 2 +J L )s

(4) (5) (6)

In this model the joint is treated as an integrated device and the coupling relationship is not necessary to consider. The simulation and experiment have been carried out according to formulas (4), (5) and (6).

4

Simulation and Experiment

4.1

Simulation

For the simulation, Faulhaber DC-micromotor is chosen as the driving motor and the relevant parameters of the motors are listed in Table 1. Both motors have the same specifications. Fig. 3: Dual motor control scheme Table 1: Specifications of Motor

3

Mathematical Model

Motor Specifications

To make the system clear, two common dc motors are used as the simulated machine. And an ideal condition is assumed: the rotor field is constant and created by permanent magnets [6]; the mechanical parts run smoothly; there is no slippage of the synchronous belt. So the electric equations for dual motor joint can be presented as below:

dI U1 =I1 R1 +L1 1 +E1 dt dI U 2 =I 2 R2 +L2 2 +E2 dt 4g dn Te1 +Te 2 -TL = (J1 +J 2 +J L ) 375 dt Where: U1 ǃ U 2 : Armature voltage;

I1 ǃ I 2 : Armature current; R1 ǃ R2 : Armature resistance; L1 ǃ L2 : Armature inductance; E1 ǃ E2 : Induced electromotive force; Te1 ǃ Te 2 : Electric torque; 2622

(1) (2) (3)

Value

Nominal voltage(V)

48

Terminal resistance(ȍ)

2.47

Back-EMF constant(mV/rpm)

7.05

Torque constant (mNm/A)

67.3

Rotor inductance (ȝH)

500

2

Rotor inertia( gcm )

110

Speed up to (rpm)

8000

Torque up to (mNm)

110

Output power(W)

226

Efficiency, max (%)

85

No load speed (rpm)

6700

No load current (A)

0.12

The proposed dual motor control model has been simulated through MATLAB/Simulink with referring the control strategy shown in Fig.3 [8, 9, 10]. This simulation uses the proposed dual motor model established above.

2013 25th Chinese Control and Decision Conference (CCDC)

Fig.3: Dual motor control mode

Fig.4: Mater-slave control model

The current distributor in the model may adjust the proportion of the output current on its own, making the two motors bearing different load. Therefore, the driving force can be distributed more reasonably and the system would be more robust. In the following simulation, speed responses under different conditions are observed. In order to make a contrast, another simulation result of a master-slave dual motor model is also presented as contrast. The master-slave dual motor model [9] is shown in Fig.4. In this model, the motor2 always follows the speed of motor1. Fig.5 shows the mechanical characteristic of the proposed dual motor system and the traditional master-slave dual motor system. At

t=5 × 10-4 s, a load torque ( TL =2Nm) for

both motors had been imposed on ‘Joint’. In figures below, the red line represents the speed command, and the blue curve stands for the measured terminal speed of the proposed dual motor control system and the green one for the master-slave dual motor model. In Fig.5, when the load is imposed at t=0.0005s, the blue curve fluctuates a little and gets back to expected speed in less than

Fig.5 Mechanical characteristic of the two kinds of dual motor system

As a contrast, the green curve drops down dramatically when the load of joint comes and it is hard to get back to the normal value, showing that the master-slave dual motor system is more vulnerable to a heavy load. Therefore the proposed dual motor system works better in the heavy load than the traditional master-slave model.

1×10-4 s, which indicates the proposed dual motor system

responses quickly to a disturbing moment and the adjustment time is short.

Fig.6 Speed response under oscillating and unbalanced load


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Fig.6 shows the speed response of the proposed dual motor system and the master-slave dual motor system under unbalanced and oscillating load which is imitating the working environment of a fast walking humanoid robot. The oscillating load is imposed on both motors. The peak and frequency of this load are 1Nm and 1k Hz. In addition, an extra load is imposed on the motor1 at t=0.15s to act as an unbalanced load. The value of the unbalanced load is 1Nm. The reference speed changes from 1450rpm up to 1500rpm at t=0.1s and then keeps constant. With fluctuation of the terminal load, the speed oscillates in a small range. The meaning of different colors in lines is the same with Fig.5. In Fig.6, when an unbalanced load is imposed on motor1 at t=0.15s the green curve slips down to1475rpm from 1500rpm and cannot catch up to the reference speed ever since. That means if the load is not equal in two motors, the joint speed would fall behind the reference speed, which is not acceptable in a real-time walking robot system. To solve this problem, a creative current distributor is designed in the new dual motor control system. At t=0. 17s when the system sensed the unbalanced load imposed on motor1, the current distributor increases the output current to motor2, making motor2 bearing more loads to decrease the unbalancedness of load imposed on the two motors and getting the system back to normal. As the blue curve shows, the rotational speed recovers to the expected value in less than 0.1s. So the proposed dual motor system works well when the joint comes with unbalanced load. 4.2

Experiment

After simulation, the algorithm of the dual motor controller is developed according to the proposed dual motor control model. And a fast walking experiment is done to test the reliability of this model. The humanoid robot BHR-4 has been shown in Fig.1 of part 2 with the improved knee joint for dual motor drive in Fig.2 of part 2. The joint error of the humanoid robot is tracked through upper computer. Fig.7 to 9 shows the joint error of the humanoid robot’s left knee joint in different walking speed. The red curve represents the joint is driven by one 200W dc motor with an elmo motor controller and the blue curve means the joint is driven by two 100W dc motors controlled by the improved dual motor controller.

Fig.7: Joint error of left knee at v=0.4km/h

In Fig.7, the joint error keeps in a range of 1 degree in both single and dual motor driving strategy, which indicates the load of the leg joint is relatively low in a slow walking speed and both driving strategy can afford this load.

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Fig.8: Joint error of left knee at v=1km/h

Fig.9: Joint error of left knee at v=1.5km/h

As the red curve shows in Fig.9 and 10, the joint error driven by one motor increases dramatically as the walking speed increases. Especially, at the speed of 1.5km/h, the joint error can reach up to 14.5 degree which is unacceptable and may causes deadly instability in a fast walking robot system. That is to say when the humanoid robot walks in a high speed, the load imposed on leg joint is beyond the max limitation that the motor can afford. On the contrary, the blue curve shows joint error of the dual motor control system keeps in a range of 3 degree at the speed of both 1km/h and 1.5km/h. So the improved dual motor control system is able to bear the high load caused in fast walking pattern comparing to the one motor driven system of the same power. With the study of humanoid robot going deep, walking speed will become faster and faster. When the walking speed goes up to 2km/h, the load of knee joint imposed on motors can be as large as 2.3Nm, which is beyond the tolerance that any small size dc servo motor can afford. So another experiment is done to observe the joint error under the speed of 2km/h with dual motor drive method. In this walking experiment, the robot is slung up to avoid falling down. The joint error acts as the criterion to the model.

Fig.10: Joint error of left knee with two driving motor (v=2km/h)

Fig.14 shows that the joint error reaches up to 3.8 degree when the left leg land on ground every time. That is an acceptable error range which can be decreased further more through trajectory planning strategy. So the proposed dual motor control model will satisfy the need of future study on improving waking speed of humanoid robots.


5

Conclusion

The new dual motor control model using current distributor algorithm and synchronous speed model based on robot joint is presented. It has been designed for the fast walking humanoid robots. This technology shows good mechanical property and excellent adaption to unbalanced and oscillating load. The simulation result indicates this dual motor control model can recover to the reference speed rapidly when a high load was imposed. And the current

[5]

References [1]

[2]

[3] [4]

distributor works well to eliminate the unbalancedness of joint load. The fast walking experiment shows the proposed dual motor control system has a good reliability. And the joint error drops dramatically when using the improved dual motor drive joint in high waking speed under the same power. So the proposed dual motor control system can make the walking pattern more stable and can afford the high joint load in the future study of fast walking humanoid robots.

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