Impact Sound Control of Robotic Manipulators

Copyright © IFAC Intelligent Components and Instruments for Control Applications. Malaga. Spain. 1992

ROBOT ARM CONTROL

IMPACT SOUND CONTROL OF ROBOTIC MANIPULATORS H. Wada*, T. Fukuda**, K. Kosuge**, F. Arai**, H. Matsuura** and K. Watanabe*** ·Toyoda Automatic Loom Works Lld .. 2-1 Toyota-cho . Kariya 448. Japan ··Department of Mechanical Engineering. Faculty of Engineering. Nagoya University. Furocho-1. Chikusa-ku. Nagoya 464. Japan ·"Department of Mechanical Engineering, Faculty of Science and Engineering, Saga University , Honjomachi-1. Saga 840. Japan

Abstract . This paper presents a robotic control method to reproduce the impact sound emitted by the collision between the endpoint of the robotic manipulator and the object . Because the impact phenomenon occurs in a very short period of time, the feedback control of impact sound in very difficult. Instead of a feedb ac k control method, a learning control algorithm is proposed to control the impact phenomena. Th e learning control algorithm modifies the reference signal to the servo controll er of the robot manipulator so that the desired impact sound is reproduced. The algorithm is based on the optimization of the least-squares criterion of learning error and does not require the dynamic model of the impact phenomena. The algorithm is applied to th e planar manipulator with one d .o.f. driven by a pneumatic actuator. Experimental results illustrate the effectiveness of the proposed algorithm. Keywords. Robots ; Impact force; Impact sound control; Learning systems; Itera tive methods. end-effector and objects. 1\1ills( 1990) developed a INTRODUCTION dynamic model including the effect of impact , and proposed a discontinuous control for th e transition 1I1uch research has been done for the control of from noncontact to contact of robotic manipularobotic manipulators, which is position control or tor . Shoji and Fukuda et .al.(l990 ,1991) adopted force control et.a\. Little attention has been paid a Heltz-type model with energy loss to collision to the transi ent phenomena from position control dynamics, and proved th e stability with resp ect to force control and vice versa. The transient pheto control system of robotic manipul ator with nomena involve the collisions between the manipphenomena. In redu cing impact force, collision ulator endpoint and its working environment, and Walker(1990), Gertz. et .al.( 1991) proposed the th e control of the collisions is one of the key issues strategy using the redund a ncy. In t.his pa per , we for the practical applications of force control. propose a control algorithm to repr odu ce th e impact phenomenon so that we can utili ze the imRece ntly, some research works have been perpact phenomena in the appli cations of robotic maformed with respect to the control problem of colnipulators , such as hammering a nd na iling. Imlision ph enomena . In modeling of impact, Wang pact control is very important for th e tasks that a nu 1IIason(1987) studied the planer impact of two require impulsive forces. In gener al, an imp act objects. and Kahng and Aminouche(1988) derived phenomenon is not easy to observe . In this pat.h e maximum impact force equation for two-body per, the impact phenomenon is controlled based

collision problems. Zheng and Hemami(1985) derived th e mathematical model of a robot collisi on, and proposed the assembly method of two arms using impulsive information(Zheng,1987) . Yousef- Toumi et.a\.( 1989) valideted an analytical mod el of impact experimentally. In stable con-

on the impact sound .

t rol of robotic manipulator with impact, Khatib

The feedback control of impact ph enomena is very difficult , since the collision phenomena occur in a very short period of time. Moreover , it is very difficult to identify th e dynamics of the impact phe-

and Burdick(1986) adopted velocity damping to dissipate excessive impact energy arising between

nomena. The control algorit.hm ,which we propose in this paper, is based on the learning con trol. The

389

in this paper, is based on the learning control. The learning control algorithm modifies the reference signal to the servo controller so that the desired impact phenomenon is reproduced.The algorithm controls the collision, without using the real time feedback of the impact phenomena. The algorithm is based on the optimization of the leastsquares criterion of learning error and is designed based on the impulse response of the system. The design of the control law does not require the dynamic model of the impact phenomena(Watanabe et .al.,1991). The proposed control algorithm is experimentally applied to the impact sound control between a manipulator with one d .o.f. and its environment. Experimental results illustrate the effectiveness of the proposed control algorithm.

.~

Input

o

~

Learning Control System

Fig.1 Impact Sound Control

[y(r), y(r + 1), ... , y(N

+ 1)]

(3)

L E !R(N+l)Xl is a vector, whose element is a Markov parameter, and yE !R(N+l)Xl is the output signal of impact sound. Note that r is a positive integer which denotes the delay of responses . v is the magnitude of the impulse input to the system. Given the desired setpoint or reference values such that

An impact phenomenon is not generally easy to observe, because it occurs in a very short period of time. The impact phenomena are often accompanied with sounds. In this paper, the impact phenomenon is controlled based on the sound emitted by the impact. It is assumed that only the magnitude of impact sound is dealt with, but that the frequency and tone are not dealt with. The realtime feedback control is one way to control the collision, but the extremely high sampling rate is required to do so. We propose a learning control algorithm to control the phenomena in this paper. A learning control algorithm controls the output of the system by repetitively modifying the reference signal to the system so that the output error vanishes. It controls the output of the system in a feedforward manner and does not require the real-time feedback of variables related to the impact phenomenon. Fig.1 shows the structure of the proposed control system of the impact phenomena based on impact sounds.

Yd T

T [Yd T (r),Yd T (r+l)'''',Yd (r+N)] (4)

and the accurate value of L, we can determine a unique input to make v as follows: (5)

v

=

(6)

However we cannot determine it because L generally contains uncertainties . Therefore we apply to solve v in a recursive form. In order to use the weighted least-squares method, we assume that the unknown input is constant at any learning stage, so that we can introduce an identification model given by :

(7)

CONTROL ALGORITHM

(8)

In this section, a learning control algorithm for the impact sound control is proposed. The algorithm is based on the method proposed in [7] . Let the input-output relation of the impact phenomena be described as follows: Lv

Outpu t

Object

IMPACT SOUND CONTROL

Y

.......-

7fi~ ~

where k is the number of trials. Then, the optimal input that minimizes the weighted least-squares criterion J

(9)

is given by

(1)

where

(10)

[J(O), J(I), ..., J(N)]

o

(2)

390

(11)

Ok-l

= Yd -

(12)

Yk-l

where

where Yk_lis an actual output, i.e. LVk_l. The matrix Kk E ~lx(N+l) is the gain, which is obtained iteratively from the following relations: Kk P- 1

P k - 1 L T[ LPk_1L T

+ V -lr

1

aI

L

J(O)

0

J(k)

0 J(O)

(13)

J(/)

(14)

J(N)

0

0 J(O) J(N-k)

J(N - I) (24)

(15) Y

The system expressed by eqs.(7), (8) IS timeinvariant, and is not stabilizable, because an uncontrollable mode exists on the unit circle. Therefore, we add a zero mean noise processes Wk with positive definite covariance W to eq.(7) :

=

v

[y(r),y(r+1), ... ,y(r+N)]

(25)

[v(l), v(2), ... , v(M)]

(26)

where L E ~(N+l)xM is a matrix, and M denotes the number of times of impact . v E ~1 xM show's velocity just before impact in each time. Thus, following the same manner as shown in the case of impact of once, the learning control low is derived as follows :

(16) Defining

(27)

( 17)

o

(18)

(28)

where and assuming that (I,G) is reachable and (F,I) is detectable, a unique positive definite stabilizable solution p.(> 0) is obtained from the following in algebraic Riccati equation:

PSLT {LPsLT

K

Ps -

Ps

+ V-I} -1 (29) 1 psFT{LTPsL + V- }-I Fps +GG T (30)

p. _ p.FT{FTP.F+I-l}-IFP.

Note here that the dimensions of matrices K and Ps is ~Mx(N+1) and ~MxM ,respectively.

+GGT (19) Therefore, the steady-state gain is given by

v

Plant

(20)

K

Consequently, the learning rule in steady-state is obtained by: (21)

o

(22)

Learning Controller

The structure of the present learning controller system is shown in Fig.2, and the block diagram of learning controller is also shown in Fig.3 .

Fig.2 Structure of learning control system New we explain the method of a learning control for impact sound control in the case of impact of M times. In this case, the matrix L shown in eq.(1) is transformed into eq.(23).

EXPERIMENT Experimental Setup

Y

= Lv

(23)

391

nOises . We analyzed the signal from the microphone. Fig.5 shows the power spectrum of the impact sound of our experimental system. In our system, the sound was characterized by the frequency around 244Hz. Throughout the experiments, the sound signal was filtered using band pass filter . The control algorithm was calculated based on filtered signal.

+ +

K

Fig.3 I3lock diagram of learning controller Th e experimental setup is shown in Fig.4 . The two pneumatic actuators (Rubbertuator, Bridgestone) are used to drive th e arm, that is the difference of the output torqu es generated by these actuators through the pulley is used to drive the arm. We assume that the torque generated by an actuator is proportional to the input voltage to the con troller of the actuator. The difference of the input voltages, dv

34.0

iO

:3-

~ ~

Do VI

Et0

0..

0

Fig.5 Power spectrum Experimental Method

to these actuators is the input to system. The actual input to each actuator is calculated as follows :

+ dv

(32)

Vo - dv

(33)

IV

40U.O

Frcqucncy (117.)

(31)

Vo

(J.B

,.

The proposed control algorithm uses the impulse response of the system. We first got the impulse response of the system. Based on the impulse response, we constructed the matrix L of eq .(2), solved the Riccati equation, and gain matrix K.

here Vo is the offset vol tage to the con troller. Experimen tal were carried ou t as follows: 1) we put the manipulator arm at the its initial position, 2) . the manipulator was controlled by the input signal calculated by the learning control algorithm until the collision was detected , 3) the input to the system at the next trial was calculated using eq.(21), 4) we put the manipulator at its initial position again and go to the step 2 to repeat the learning process. Experimental Results The desired impact sound is shown in Fig .5. The experimental results in v'= 1.0 are shown in Figs.7, 8 and 9, the results with v'=O .Ol are shown in Fig. 10 and 11, and the results with v'=O.OOOl are shown in Fig .12 and 13. Fig.l4 shows the meansquares error of the output for each experiment.

FigA Experimental setup filtering of impact sound The sound, which is emitted by the collision phenomenon and record ed by a microphone, contains

As shown in Fig.l4, the output error decreases as the number of trials increase. The results il-

392

lustrate the effectiveness of the proposed control algorithm.

1.0

:E:

CONCLUSIONS

C1J

bfl

0.0

~

"0

:>

We proposed a learning control algorithm for the control of collisions between the manipulator and its environment. The proposed control algorithm reproduces the desired impact phenomena using sound information. The control algorithm is based on the learning control using weighted leastsquares method. The algorithm is designed based and does on the impulse response of the system , not require the details description of the model. The algorithm was experimentally applied to the planar manipulator with one degree of freedom driven by a pneumatic actuator . Experimental results illustrated the effectiveness of the proposed algorithm. The proposed control method can be applied to a series of impact phenomena without modification.

0.125 -1.0

Time (s)

Fig.S Experimental results in v'= l.O(k=2)

1.0

:E: C1J

CIl

0.0

~

"0

:>

0.125 -1.0

Timc (s)

Fig.9 Experimental results in v'= l.O(k=6)

1.0 _ 1.0

C1J

-1.0

ncn

0.125

0.0

o

Tillle (s)

:>

0.125 -1.0

Tillle (s)

Fig.6 Desired impact sound Fig.lO Experimental results in v'=O .Ol(k=2)

1.0 1.0

..-.. >

'-"

..-..

C1J

en

~

~

0.0

C1J

0.125

"0

:>

en £1 0.0

"0

-1.0

:>

0.125

Time (s)

-1.0 Timc (s)

Fig.7 Experimental results in v'= l.O(k=O)

Fig.ll Experimental results in v'=O .Ol(k=6)

393

workshop on Intelligent Robots and Systems (IROS'91), pp.179-184 .

1.0

Kahng .J. and Anirouche .F .M.L. (1988). Impact Force Analysis in Mechanical Hand Design - Part I, International Journal of Robotics and Automation, 3-3, pp.158-164 .

CL>

Oil

.El 0.0 "0 ;>

-1.0

Tilllc (s)

Khatib .O. and Burdick.J. (1986). Motion and Force Control of Robotic Manipulators, Proc . of the IEEE International Conference on Robotics and Automation, pp.1381-1386 .

Fig.12 Experimental results in v'=0 .0001(k=2)

Mills.J .K. (1990) . Manipulator Transition To and From Contact Tasks : A Discontinuous Control Approach, Proc. of the IEEE International Conference on Robotics and Automation, pp.440-446 .

1.0

CL>

....~Il

0.0

"0 ;>

0.125 -1.0

Shoji .Y., Inaba.M. and Fukuda.T. (1991). Impact Control of Grasping, IEEE transaction on industrial electronics, 38-3, pp .187193.

Tilllc (s)

Fig.13 Experimental results in v'=0.0001(k=6)

Walker .I.D. (1990). The Use of Kinematic Redundancy in Reducing Impact and Contact Effects in Manipulation, Proc. of the IEEE Int.ernational Conference on Robot.ics and Automation, pp.434-439 .

-{)- .'= 0.0001 20.0

Wang.Y. and Mason.M.T. (1987). Modeling Impact Dynamics for Robotic Operations, Proc. of the IEEE International Conference on Robotics and Automation, pp .678-685 .

10.0

Watanabe .K., Fukuda.T. and Tzafestas.S.G . Iterative Learning (1991). An Control Scheme Using the Weighted LeastSquares Methods, Journal of Intelligent and Robotics Systems, 4-3, pp.267-284 .

0.0

o

2

Trial k

4

6

(Times)

Fig.14 Mean-squared errors with respect to various weights

Yousef-Toumi.K. and Gutz .D.A . (1989) . Impact and Force Control, Proc . of the IEEE International Conference on Robotics and Automation, pp.410-416.

REFERENCES

Fukuda.T., Shoji .Y. and Inaba.M. (1990). Stable Position and Force Control of Robotic Manipulator with Collision Phenomena, Proc . of the 11th IFAC World Congress, Automatic Control in the Service of Mankind, ~, pp.262-267.

Zheng.Y.F. and Hemami .H. (1985). Mathematical Modeling of a Robot Collision with its Environment, Journal of Robotic Systems, 2-3, pp.289-307 . Zheng.Y.F . (1987). Two Robot Arms in Assembly by Impulsive Information, Journal of Robotic Systems, 4-5,pp.585-603 .

Gertz .M.W., kim .J .0. and Khosla.P.K. (1991). Exploiting Redundancy to Reducing Impact Force, Proc . of the IEEE International

394