The force control and path planning of electromagnetic induction-based massage robot

2.1Structure of the massage robot

The structure of the presented wheeled massage robot is demonstrated in Fig. 2, which is mainly composed of tapping head, left and right driving wheels, front and rear driving wheels and sensors. The tapping head based on electromagnetic induction is mainly used to achieve tapping massage operation, and the driving wheels achieve rolling and kneading massage. Infrared distance sensors and crash sensors are placed around the wheeled massage robot (see Fig. 2) to detect environmental information of human back and achieve direction control of the massage robot.

Figure 1.

Schematic configuration of massage robot.

Figure 2.

Massage head structure.

In the previous work, tapping massage head (see Fig. 2) was designed and mounted on a mobile platform, which could change the massage area by moving the platform. During movement, the massage head should avoid touching human body to improve comfort. Therefore, a spring-based structure was design to balance the gravity of massage head. Massage head taps down with the action of springs, a yoke was added to increase the electromagnetic force which overcomes the spring force to achieve tapping operation.

The massage head works as follows: the winding coil is placed around the yoke, the movable core is magnetized when the coil is energized and it linearly moves under the action of the electromagnetic force. When the coil is powered off, the electromagnetic force disappears, the movable core return to the original position with the spring force. Tapping operation periodically takes place as the coil is periodically powered on.

2.2Model analysis of the massage head

The model of robot massage head includes three parts, namely the electrical circuit, the magnetic circuit and the mechanics.

Windings and moving iron core part can be simplified as a resistance-inductance model. The driving voltage is

The equivalent inductance is

Where, R is the equivalent resistance, ψ is the flux generated by the coil in a magnetic field, N is the number of turns, Rm is the equivalent magnetic resistance, Rδ is the equivalent working air gap reluctance, Rl is the equivalent non-working air gap reluctance.

To simplify the calculation, we assume that the coil inductance L will not change during movement, then the Eq. (1) can be simplified as

To solve Eq. (3), the coil current of massage head could be calculated as

Where, τ=L/R, i0 is the initial current.

Where, Φ is magnetic flux, A is the interaction area of the electromagnetic, δ is the initial distance, μ0 is the air permeability, x is the displacement of the movable core, 0⩽x⩽δ, Fm is the electromagnetic force of the moving iron core.

The magnetized moving iron core taps down with the action of electromagnetic force. It moves under the interaction of electromagnetic force, spring force and body back resistance. The motion equation is

The differential equation of motion by combining Eqs (2.2) and (6) is

Where, Fk is the spring load force, Ff is the back resistance.

The equations from Eqs (1) to (6) show the factors which affect the dynamic characteristics of the massage head.

3.1Parameterization analysis

The orthogonal experiment method was used to analyze the sensitivity in this paper. Orthogonal experiment is the mathematical method which organizes and analyzes multi-factor scientifically [11]. In this paper, tapping intensity design scheme was made by orthogonal experiment method. Factors such as magnetic materials and the mass of massage head are generally pre-selected, so their influence on the electromagnetic force does not need to be analyzed. The main factors which affect the massage head pounding strength can be identified as:

To investigate the influence from the above factors, three levels (three values) were chosen for each factor, then there are totally 27 kinds of programs for the three chosen factors. However, it is not necessary to calculate all programs according to the aforementioned method. The maximum and minimum tapping force programs can be quickly and accurately determined by a few programs with the theory of orthogonal experiment method.

The number of turns can be determined between 2000 and 2200 turns depending on the size of the yoke and the coil. Accordingly, three levels of factor A⁢(A1,A2,A3) were choose as 2000 turns, 2100 turns, 2200 turns respectively. With the previous simulation experience, the electromagnetic force is too small for the designed coil when the coil current is less than 0.30 A, the moving iron core springs rebound without touching the human back, which causes failing of massage function. The diameter of coil wire chosen in our work is 0.41 mm, the limit of coil current is 0.40 A when it works long time. Thus, the range of coil current should be controlled between 0.30 A and 0.40 A. As a result, three levels of factor B⁢(B1,B2,B3) were chosen as 0.300 A, 0.325 A, 0.350 A respectively. When the robot is not working, the moving iron core needs to maintain a certain distance from the human back to avoid touching the back which may cause discomfort. However, too small electromagnetic force cannot overcome the spring resistance when the distance between the moving iron core and the back is more than 12 mm. Therefore, three levels of factor C⁢(C1,C2,C3) were chosen as 10 mm, 11 mm, 12 mm respectively.

3.2Analysis of orthogonal experiment

The finite element simulation method was used to calculate the initial electromagnetic force F0 of these nine programs, and the results are listed in Table 2. For the electromagnetic force calculated in Table 2, we tried to determine which factor has more important influence on the electromagnetic force. The influence extent of each factor on the design value was calculated by the difference of the calculated values at different levels, namely the difference between the average values is more, the influence is bigger.

Comparing the results shown in Table 2, it indicates that the deviation of factor B is much larger than factors A and C, which is 0.0461. So the coil current is the most important factor for electromagnetic force compared to the other two factors. Therefore, the number of turns and the distance between the moving iron core and the yoke could be determined based on the requirements of massage operation. Then, massage intensity could be controlled by adjusting the coil current value.

4.1Requirements of path planning

There are two massage paths based on the wheeled massage robot, tapping path and rolling/kneading path. Tapping path is the motion area of the tapping head of electromagnetic induction, rolling/kneading path is the motion area of the two driving wheels.

To get better massage effect, the requirements for path planning of massage robot were discussed and summarized as follows:

4.2The improved reciprocating path planning algorithm

The goal of complete coverage path planning is to make mobile robot efficiently move on the whole planned area and avoid obstacles, which requires the robot to traverse all the reachable area of human back area [12, 13]. Massage path planning of the designed wheeled massage robot belongs to the range of typical complete coverage path planning. The TCM massage order generally cycles from top to bottom, and from inside to outside. Therefore, this paper chose reciprocating path planning algorithm to complete motion control of the massage robot.

The object of this study is a new wheeled massage robot which works on the human back, and it cannot be considered as a particle compared to the back area. For tapping massage path, only the middle path of the massage area is valid. For rolling/kneading and other massage path, only the path of two wheels is valid. It can be calculated that the effective massage area is about one-third or two-thirds of the whole massage area when the massage robot moves along a circle. Therefore, this paper proposed the improved reciprocating path planning algorithm to improve regional coverage rate and massage effect.

The diagram of the improved reciprocating path planning algorithm is depicted in Fig. 3, the basic principle is described as follows: taking the reciprocating path planning algorithm as the foundation, the massage robot uses the infrared distance sensors and crash sensors to determine if there is a cliff (edge) or an obstacle during moving. When an obstacle or a cliff is detected, the massage robot immediately turns right 90∘. Meanwhile, the A* algorithm was used to search the nearest uncovered area.

Figure 3.

Principle description of the improved reciprocating path planning algorithm.

Figure 4.

Control system model of massage robot.

Figure 5.

Relationship between the electromagnetic force and the displacement of the moving iron core.

Figure 6.

Vector distributions of magnetic induction B of the moving iron core at different time.

Figure 7.

Relationship between velocity and displacement of the moving iron core.

Figure 8.

Visual interface of massage robot movement.

Figure 9.

Comparison before and after improving of tapping path.

Figure 10.

Comparison before and after improving of rolling/kneading path.

4.3Modeling of control system

This paper established the control system model of the wheeled massage robot based on Simulink (see Fig. 4), it includes control subsystem of the motor, path algorithm control subsystem, parameter module of the massage robot and virtual reality interface module. The control signal is directly outputted to a virtual operating environment by virtual reality (VR) Sink block, and the operation of the massage robot could be observed through a browser window.

5.1Structure optimism of massage head

Considering factors like massage comfort and electromagnetic force, the distance between moving iron core and the yoke was chosen as 12 mm. the massage percussion depth is about 4 mm according to TCM massage and the maximum movement stroke of the moving iron core is 8 mm. Considering factors like the size of the yoke and coil diameter, the number of coil turns was chosen as 2100. The relationship between the electromagnetic force and displacement of moving iron core under the current of 0.3 A, 0.325 A, 0.35 A are given in Fig. 5. It shows that massage force varies from 10 N to 20 N. Tapping intensity usually varies between 10 N and 30 N according to TCM massage theory. It indicates that all the chosen current values satisfy the requirements.

When the coil current is 0.35 A, the vector distributions of magnetic flux density B of the moving iron core are illustrated in Fig. 6. It indicates that the distance between the moving iron core and the yoke gradually reduces with time but the magnetic flux density gradually increases.

5.2Control of massage intensity

From the simulation results, it can be inferred that the coil current is the most important factor which affects massage intensity based on orthogonal experiment. Compared to other factors, the coil current is more flexible to control the massage intensity. The relationship between velocity and displacement of the moving iron core with the coil current 0.3 A, 0.35 A and 0.4 A are illustrated in Fig. 7. The electromagnetic forces are between 10 ∼ 20 N at the initial time for all three current values. It was found that the electromagnetic force is too small when the coil current is less than 0.30 A, the moving iron core was bounced back without touching the human back due to the spring force. Coil diameter was chosen as 0.41 mm, and the operating current should not exceed 0.4 A if it works long time. Thus the coil current must fluctuate between 0.3 A and 0.4 A to guarantee the safety of the device and massage comfort. Different massage intensity and tapping rate can be produced by adjusting the coil currents to achieve different massage effect ultimately.

5.3Simulation of path planning

The actual movement of the massage robot in virtual operating environment can be observed after completing the above modeling work (see Fig. 8). The simulation results of the proposed algorithm before and after improving tapping path are presented in Fig. 9. It can be calculated that the coverage rate is only 35.27% by using the traditional reciprocating path planning algorithm, while the coverage rate reaches up to 60.27% with the improved reciprocating path planning algorithm.

For rolling/kneading path, the corresponding results are shown in Fig. 10. It can be seen that the coverage rate is only 58.82% using the traditional reciprocating path planning algorithm as shown in Fig. 10a, it is improved to 84.93% using the improved reciprocating path planning algorithm as shown in Fig. 10b.