Journal of Sensors

Journal of Sensors / 2016 / Article

Research Article | Open Access

Volume 2016 |Article ID 6291216 | 10 pages | https://doi.org/10.1155/2016/6291216

Collision Sensing Using Force/Torque Sensor

Academic Editor: Dong-ning Wang
Received15 Jun 2015
Accepted27 Aug 2015
Published14 Dec 2015

Abstract

Collision sensing including collision position, collision direction, and force size could make robots smoothly interact with environment, so that the robots can strongly adapt to the outside world. Skin sensor imitates principles of human skin using special material and physical structure to obtain collision information, but this method has some disadvantages, such as complex design, low sampling rate, and poor generality. In this paper, a new method using force/torque sensor to calculate collision position, collision direction, and force size is proposed. Detailed algorithm is elaborated based on physical principle and unified modeling method for basic geometric surface. Gravity compensation and dynamic compensation are also introduced for working manipulators/robots in gravity and dynamic environment. In addition, considering algorithm solvability and uniqueness, four constraints are proposed, which are force constraint, geometric constraint, normal vector constraint, and current mutation constraint. In order to solve conflict solution of algorithm in redundant constraints, compatibility solution analysis is proposed. Finally, a simulation experiment shows that the proposed method can achieve collision information efficiently and accurately.

1. Introduction

In recent years, more and more sensors are installed on robots to realize sensing and interacting with environment. These sensors help robots achieve a large amount of information about the environment, which contributes robots to make correct decision and planning. For example, vision sensor assists robots in obtaining appearance information of environment, which is used to realize target tracking and object capture, and so forth.

Collision sensing is also an important environment sensing method, through which robots sense collision point and collision direction to avoid collision again, and makes compliment control come true [1, 2]. In the environment containing human and robots, collision sensing is extremely significant to avoid serious collision. In addition, in [3], collision sensing is also used for compliance assembly. Since that collision sensing has so many applications, realization of whole robotic body sensing is gradually carried out [4, 5].

Skin force sensor like human skin system, which is pasted on the whole surface of robots, could sense force action point, force direction and size [2, 5]. In the research filed, MIT has developed a special compound material called QTC (Quantum Tunneling Composite), which is pressed by metal and nonmetal [2, 6]. This sensor measures force information by resistance change when it is pressed. Similar researches also include organic thin film composed of pentacene molecular (U-Tokyo, Japan) and E-skin (Philips Company), and so forth [1]. The skin force sensor looks like an ideal solution for robot force sensing, but there are many disadvantages that make it hard to be used in real world, such as being easy to damage during collision, expensive price, complex design and high environment requirements, low sampling rate, and poor generality [4, 7]. Moreover, sensitivity of skin sensor system could not achieve information of collision direction and could be influenced by many factors, such as temperature and humidity [1].

Skin force sensor is the direct method to measure force information; on the other way, it also could be checked out through indirect techniques [8, 9]. In [10] Mason and Salisbury have proposed the theory of calculating force information using force/torque sensor and in [11] Bicchi et al. have developed experiments to verify it. Zhou and Han use the theory to realize skin force sense on the one freedom finger [1214]. In this paper, theories of manipulator with multiple degrees of freedom are applied and method of compatibility solution analysis to solve contradiction of solutions is proposed.

The rest of this paper is organized as follows. Section 2 describes detection principle, when point collision happens, unified equation for collision sensing considering gravity and manipulator dynamics, and unified modeling method for basic geometric surface. In the gravity environment, force analysis is proposed in Section 3. In Section 4, force analysis is shown when manipulator is in a working condition. Solvability analysis is provided in Section 5, which includes force constraint, geometric constraint, normal vector constraint, current mutation constraint, and compatibility solution analysis. In Section 6, the simulation experiment and results are shown to prove effectiveness of the algorithm. Finally, the concluding remarks follow in Section 7.

2. Detection Principle

In this section, physical principle about point collision on manipulator is introduced. On the one hand, the whole process of force effect needs meets force analysis principle, and on the other hand, the result of calculation should suit physical laws, such as point which is on the manipulator surface and the angle of force direction and normal vector is less than .

2.1. Force Analysis

Assume that no gravity and manipulator are static; force analysis is shown in Figure 1. In order to apperceive whole system, force/torque sensor is assembled on the base and close to the first joint. The force/torque sensor could measure force in three directions and torque rotated of three coordinate axes.

In Figure 1, point means collision point, which is assumed on th joint. The center of force/torque sensor is expressed as , which is set as origin of coordinate system. Every joint of manipulator is built coordinate system as according to DH parameter method. represents coordinate system of th joint, and , , and , respectively, mean collision force, measured force, and measured torque. represents normal vector of point . could be achieved by translating coordinate system and no rotation. Then coordinate of point in is obtained by coordinate transformation, as shown in the following:where

When collision occurs, the outside force is , and data of force/torque sensor are and . According to force analysis, data of outside force in should be equal to measured data in ideal condition, as shown in the following:where

In (4),and means extraction of elements of the first three rows and the first column.

In (5),

Considering factor of gravity and manipulator dynamics in real world, general equation could be shown as follows:

In (8), and , respectively, express force and torque caused by collision mapping in basic coordinate system ; and , respectively, mean force and torque caused by gravity mapping in basic coordinate system , which will be analyzed in Section 3; and , respectively, express force and torque caused by manipulator dynamics mapping in basic coordinate system , which will be shown in Section 4.

In (8), , , , and could be calculated based on states of manipulator and joint physical properties, such as joint angle, joint velocity, joint acceleration, and joint quality. Collision information is just contented in and , that is, the parameters of , , , , , and .

2.2. Physical Constraint

Normal geometrical surface contains ellipsoid, sphere, cylindrical surface, and plane. They are able to construct all simple surfaces including outline of manipulators. Mathematical description mode of all manipulator surface is achieved through coordinate transformation. From the role of geometrical change, the core of four types of surface is ellipsoid, which is able to change to other three types by changing parameters, as shown in Figure 2.

Assume three axis lengths of ellipsoid are , , and , setting center as origin of coordinate system. When , sphere will be formed; when , cylindrical surface is achieved; and when , , and , plane surface is displayed. In summary, it just needs to build ellipsoid mode to describe all surface, as shown in the following:where

Normal vector of point is set as and could be calculated with equation as follows:where means coordinate values and represents gradient.

3. Gravity Compensation

In the above section, gravity element is sampled as and . In this section, gravity influence on sensor will be analyzed, which relates to joint length, joint angle gravity center of joint, and quality. All joints cause force and torque on sensor, so each of them needs to be calculated. Force analysis is shown in Figure 3 in gravity.

In Figure 3, is gravity center position in coordinate; then means coordinate of gravity center of th joint and is expressed aswhere

Assuming variety of sensors is , , then (14) and (15) are achieved:

In (14), () and is the total number of joints.

In (15), in order to easily calculate with matrix, vector is transformed into matrix :

4. Dynamic Compensation

In Section 3, manipulator dynamic is sampled as and . In this section, dynamic factor is analyzed. When manipulator works, it also causes reaction force to sensor, so calculation is also needed. Dynamic force is very complex, which relates to joint length, joint angle, joint angular velocity, joint angular acceleration, and so on. In Figure 4, dynamic force is analyzed.

In Figure 4, assume is joint angular acceleration and is gravity center position in coordinate. Then, acceleration of gravity center is expressed as

In coordinate, in order to keep moving as in Figure 4, the force and torque are calculated as shown in the following:

In (18), and , respectively, express quality and inertia of th joint, and

Due to the fact that is a motional coordinate, Coriolis force emerges in the whole system, which is expressed as

In (20), and , respectively, mean velocity vector and angular velocity vector of coordinate relative to basic coordinate.

Based on the principle of equivalence, the above forces and torque of joint are transfered to , which could be expressed as

In the above equation, and , respectively, mean acceleration force and Coriolis force in the basic coordinate; and express torque of force transformation; torque could transfer with no other changes, so .

Manipulator contains many joints, so all effect of force of joints on the basic coordinate is shown as

5. Solvability Analysis

At present, problem will be analyzed under the following limits in this subsection:(a)Material of manipulator is rigid, which means no deformation produce.(b)Collision is caused by manipulator and point of object.(c)All sensor is ideal.(d)Gravity is ignored in this subsection, because it has to be calculated in Section 5.3.(e)Manipulator dynamic is discussed in Section 5.4, so assume manipulator is static and motion of outside object causes collision.

In order to ensure solvability and uniqueness, four constraints are provided and compatibility principle is proposed.

5.1. Force Constraint

From Section 2, combine (8) and (9); seven equations are achieved with six variables. Moreover, , , , and are zero under the above assumption.

In order to easily calculate with matrix, vector is transformed into matrix :

Then, part of (8) could be changed to

Combining (1), (8), and (24), the following equation is achieved:where

is relation matrix and it is singular matrix in ideal condition, that is, rank() = 5. A series of solutions about (24) are obtained. There are many states that make rank() = 6, such as noise of sensor, precision of sensor, and deformation. This problem will be solved in Section 5.5.

5.2. Geometric Constraint

Force act on the surface of manipulator, so mathematical direction of whole outline is necessary to constraint solution, that is, means mathematical direction of manipulator surface.

5.3. Normal Vector Constraint

Because that force can only apply to manipulator from outside, the angle of force direction and normal vector is less than . Based on this constraint, equation could be shown as

5.4. Current Mutation Constraint

Strange geometries of manipulator surface and multiple degrees of freedom of manipulator may cause different force action with the same data of force/torque sensor. In this condition, uniqueness solution could not be calculated, so current mutation constraint is drawn in.

Assuming collision point is on the th joint, then the current of this joint will change suddenly. In addition, the current of th () joint also produces mutation, but the current of th () joint will not change suddenly. In this law, collision point will be judged on the th joint.

On the one hand, this constraint avoids multiple solutions, and on the other hand, it could ensure the range of collision point and accelerate the speed of calculation.

5.5. Compatibility Solution Analysis

In Section 5.1, if rank() = 5, then uniqueness solution will be achieved combining with (9) which means compatibility is the best. But many elements cause rank() = 6, such as noise of sensor, precision of sensor, and deformation. There is no solution through combining (8) and (9), so compatibility solution analysis is proposed to ensure an approximate solution. In Figure 5, process of method is shown.

From Figure 5, when rank() = 6, five equations will be chosen from matrix equation (25) and combining with (9); then one group of solution is obtained. Other five groups of solutions will be also achieved by the same way. Every solution includes the information about position and force size in three coordinate axes. Six normal vectors about solution position are achieved through (25). Then singular solutions should be removed by deviation of positions and normal vectors. At this moment, average values of the rest of solutions are calculated, and choose the closest point in outline of manipulator as approximate solution. At last, force size in three coordinate axes will be achieved by (25). This method avoids no solution condition and achieves an approximate solution.

6. Simulation Experiment

One manipulator with three degrees of freedom is established, as shown in Figure 6. In order to simplify analysis, the outline of manipulator is composed of cylindrical surface and semisphere, and the size is set to . In addition, the material of every joint is uniform and set as 1060 alloys ( kg/m3) and geometry of every joint is central symmetry; then gravity center of joint lies on central axis.

When collision occurs, data of force/torque sensor change with time. In engineering application, some signal processing methods will be adopted to achieve effective data. In this paper, our attention is focused on the method of collision sensing, so in order to simplify analysis, assume that manipulator is static. Parameters of links are listed in Table 1.


NameQuality (Kg)Position of gravity center in local coordinate (mm)

Link 01.629(0, 0, 60)
Link 11.786(0, 0, 69.995)
Link 22.565(86.256, 0, 0)
Link 33.180(106.906, 0, 0)

In Figure 6,  mm,  mm,  mm,  mm, and  mm. Due to the fact that joint connected surface is complex, assume collision point is only on link rod. Surface of each joint is described in coordinate of itself as follows:Link 1: Link 2: Link 3: Top of Link 3:

According to coordinate transformation matrix as shown in equations of links’ outline in basic coordinate will be obtained as shown in the following:Link 1:Link 2:Link 3:Top of Link 3:where

Considering gravity compensation, the manipulator is analyzed as shown in Figure 7, where  mm and  mm,

Mode of manipulator is built in ADAMS, and two groups of data are tested to verify our algorithm.

Assume , , and , and 100 N force applies on the surface. Ten points are tested, throughout the entire surface.

In another experiment, assume , , and , but force size is changed at the same position = (206.08 72.79525.46).

In Tables 2 and 3, force size, force direction, and force position are known and set as input conditions; detected force and detected torque express the data of force/torque sensor, which could be achieved by measurement; calculated position and calculated force could be obtained by (8) and coordinate transformation with a series of calculations; force size error, force direction error, and position error are put forward to judge accuracy and validity of the calculation. Equation of each error is shown as follows:Force size error:Force direction error:Position error:


NumberForce size (N)Force direction (N)Force position (mm)Detected force (N)Detected torque (N·m)Calculated position (mm)Calculated force (mm)Force size error (%)Force direction error (°)Position error (%)

110093.8152 
9.9627 
33.158
40 
0 
150
−93.8152 
79.8145 
−33.158
−25.4134 
−12.746 
6.654
40.34 
0.05 
152.38
93.1473 
10.2345 
32.153
0.9302.0871.78

210060.9138 
74.9999 
25.7783
0 
40 
175
−60.9183 
14.7773 
−25.7783
−14.8139 
−10.6599 
9.4891
2.12 
39.83 
176.33
59.2332 
74.5389 
25.2234
1.5072.6572.017

3100−90.4417 
42.0904 
−6.9776
40 
0 
200
90.4417 
47.6868 
6.9776
−18.4897 
17.8092 
5.3689
42.98 
1.46 
197.94
−89.1347 
40.6234 
−7.7463
1.7393.0693.187

410073.5958 
10.5043 
−66.8828
65.02 
37.54 
267.16
−73.5958 
79.2729 
66.8828
−21.5907 
−24.0106 
9.1323
68.58 
40.24 
263.34
71.3748 
9.0657 
−66.1635
2.2554.0193.632

5100−4.7869 
94.594 
−32.0789
83.75 
2.17 
312.5
4.7869 
4.8169 
32.0789
2.7225 
−1.1907 
−0.8801
85.63 
2.37 
324.49
−5.0375 
96.4736 
−34.785
2.6774.8674.349

6100−36.4847 
−68.9913 
62.5226
118.66 
68.51 
302.92
36.4847 
158.7685 
−62.5226
−52.09 
18.4709 
12.7395
124.94 
63.89 
306.35
−35.8134 
−70.7645 
65.386
2.7895.0324.310

7100−81.5353 
44.681 
36.8185
186.93 
61.74 
442.98
81.5353 
45.0962 
−36.8185
−9.3882 
43.001 
−6.3337
174.65 
68.49 
452.76
−83.4756 
44.9652 
39.8583
2.8535.5825.943

810079.8215 
38.4423 
−46.3758
210.36 
121.45 
475.56
−79.8215 
51.3349 
46.3758
−2.9938 
−47.7155 
8.6602
222.08 
131.75 
487.74
82.9467 
40.8643 
−45.7643
3.1716.1116.404

9100−80.1006 
58.8915 
10.7551
206.08 
72.79 
525.46
80.1006 
30.8856 
−10.7551
3.2545 
44.3061 
−10.9144
219.79 
84.86 
539.75
−84.4754 
58.4393 
10.4637
3.2517.4577.041

10100−74.0921 
−18.1331 
−64.665
222.17 
128.27 
587.74
74.0921 
107.9102 
64.665
−29.2707 
29.1803 
1.5773
238.57 
113.45 
572.84
−76.4836 
−21.9574 
−68.4833
4.9857.8867.192


NumberForce size (N)Force direction (N)Force position (mm)Detected force (N)Detected torque (N·m)Calculated position (mm)Calculated force (mm)Force size error (%)Force direction error (°)Position error (%)

160−48.0604 
35.3349 
6.4531
206.08 
72.79 
525.46
48.0604 
54.4423 
−6.4531
−8.8104 
26.5837 
−3.7276
223.53 
85.34 
542.45
−46.4684 
32.2344 
7.1736
2.9938.3848.257

280−64.0805 
47.1132 
8.6041
206.08 
72.79 
525.46
64.0805 
42.664 
−8.0641
−2.7779 
3504449 
−7.321
223.44 
80.32 
543.24
−60.3674 
46.6237 
9.7344
3.1067.7217.498

3100−80.1006 
58.8915 
10.7551
206.08 
72.79 
525.46
80.1006 
30.8856 
−10.7551
3.2545 
44.3061 
−10.9144
219.79 
84.86 
539.75
−84.4754 
58.4393 
10.4637
3.2517.4577.041

4120−96.1208 
70.6698 
12.9062
206.08 
72.79 
525.46
96.1028 
19.1073 
−12.9062
9.287 
53.1673 
−14.5078
216.45 
87.87 
535.64
−99.8348 
70.7982 
10.5374
2.8437.0606.261

5140−112.1409 
82.4482 
15.0572
206.08 
72.79 
525.46
112.1409 
7.329 
−15.0572
15.3194 
62.0285 
−18.1011
213.23 
85.56 
538.97
−113.4532 
87.1726 
13.2736
3.6906.6205.874

6160−128.161 
94.2265 
17.2082
206.08 
72.79 
525.46
128.161 
−4.4493 
−17.2082
21.3519 
70.8898 
−21.6945
213.74 
81.46 
539.53
−123.7562 
95.6352 
17.3845
2.6346.1045.342

7180−144.1812 
106.0048 
19.3593
206.08 
72.79 
525.46
144.1812 
−16.2276 
−19.3593
27.3843 
79.751 
−25.2879
217.36 
76.87 
540.37
−149.2352 
104.8453 
18.4632
3.3155.7265.319

8200−160.2013 
117.7831 
21.5103
206.08 
72.79 
525.46
160.2013 
−28.0059 
−21.5103
33.4168 
88.6122 
−28.8813
223.42 
78.36 
530.75
−155.7297 
119.4328 
20.5643
2.6715.2014.955

9220−176.2214 
129.5614 
23.6613
206.08 
72.79 
525.46
176.2214 
−39.7842 
−23.6613
39.4493 
97.4734 
−32.4747
197.45 
65.32 
535.75
−171.2194 
131.3342 
22.9472
2.9955.1724.637

10240−192.2415 
141.3397 
25.8123
206.08 
72.79 
525.46
192.2415 
−51.5625 
−25.8123
45.4817 
106.3346 
−36.068
199.63 
65.37 
533.74
−196.24387 
140.3484 
29.6547
3.0824.9733.892

In these three equations, , , and mean force size of calculated force and , , and mean calculated position mapping to three axes in basic coordination; , , and mean force size of force and , , and mean calculated position mapping to three axes in basic coordination.

From Tables 2 and 3, collision detection is effective and the relative error is extremely small in simulation environment. In order to intuitively express data relation, Figures 8 and 9 are drawn to show them. In Figure 8, relation between different collision positions and each error is established. In Figure 9, relation between different force sizes and each error is established.

In Figure 8, force size error, force direction error, and position error all become larger with farther distance. Different collision point produces different error and each error will be larger with farther distance. If we use this method to test collision information, it must ensure whether the biggest errors meet accuracy requirements at the farthest point of manipulator.

In Figure 9, force direction error and position error become smaller with bigger force, and force size error is fluctuating. Sensitivity of this method is almost certain at the same point, so force direction error and position error become smaller with bigger force. About fluctuating of force size error, (40) has given our explanation that numerator and denominator influence force size error at the same time and have the same trend.

7. Summary

Both animal’s arm and person’s arm are wrapped by skins, which help them protect their biological organization and apperceive environmental information, such as temperature change and object collision. Researchers except manipulators also have the same function with biological arm, but the method is expensive and easily damaged by distributing sensors on the whole manipulator’s outline, so one indirect method to detect collision point and direction by using force/torque sensor is put forward. Compared to skin force sensor, the force/torque sensor is easy to be installed and maintained. In our method, constraint equations and compatibility solution analysis is used to ensure existence of solution. Moreover, gravity compensation and dynamic compensation are also described, which indicate this theory could be effective in gravity environment and when manipulators are exercising. At last, the simulation experiment is executed to verify our algorithm and the result is perfect.

But there exist a lot of engineering problems, if this method is used in real system, which could be as follows: how to extract more accurate force and torque information, based on the fact that signal of sensor is fluctuant; how to describe manipulator’s outline accurately, because it has complex shape; how to measure force and torque in an instant when manipulator collides; how to realize real-time perception, on the condition that this theory contents a lot of calculations. In order to promote the theory in engineering application some experiments will be done on a real system, especially putting focus on the above problems.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Acknowledgment

This work is supported by National Postdoctoral Foundation of China under Grant 2013M541258, State Key Laboratory of Robotics (2015-Z08).

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Copyright © 2016 Yu-Quan Leng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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