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Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science

2016 Impact Factor: 1.015 2016 Ranking: 91/130 in Engineering, Mechanical Source: 2016 Journal Citation Reports® (Clarivate Analytics, 2017)

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Editor J W Chew University of Surrey, UK Editor Emeritus Emeritus Professor Duncan Dowson University of Leeds, UK Share Associate Editors S Abrate Southern Illinois University, USA T Berruti Politecnico di Torino, Italy D Croccolo University of Bologna, Italy V Crupi University of Messina, Italy L Cui Curtin University, Australia J Dai King's College London, UK L Dala Northumbria University, UK R G Dominy Durham University, UK G Epasto University of Messina, Italy I C Gebeshuber Vienna University of Technology, Austria G Genta Politecnico di Torino, Italy S Heimbs Airbus, Germany M Ichchou École Centrale de Lyon, France S Leigh University of Warwick, UK P Liatsis The Petroleum Institute, UAE X Luo University of Strathclyde, UK G McShane University of Cambridge, UK M Paggi IMT Insitute For Advanced Studies Lucca, Italy F Romeo Sapienza University of Rome, Italy S de Rosa Universita Degli Studi Di Napoli, Italy D Symons University of Cambridge, UK J Szwedowicz Siemens, Switzerland D T Pham Cardiff University, UK S Theodossiades Loughborough University, UK G Wei University of Salford, UK Z Xu Tianjin University, China S Zucca Politecnico di Torino, Italy

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Engineering & Technology | Mechanical Engineering

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EDITORIAL BOARD

I I Blekhman IPME RAS, Russia

S Boedo Rochester Institute of Technology, USA

D Breslavsky National Technical University 'Kharkov Polytechnic Institute', Ukraine

M Cartmell University of Sheffield, UK

F Chu Tsinghua University, China

M De Agostinis

J Durodola Oxford Brookes University, UK

S D Fassois University of Patras, Greece

X Gao University of Akron, USA

P Goncalves Pontifical Catholic University, Brazil

S T Halliday Rolls-Royce, UK

D Hills University of Oxford, UK W Huang Tsinghua University, China

M Ishihama Kanagawa Institute of Technology, Japan

A Krivtsov St. Petersburg State Polytechnical University, Russia

L Li University of Manchester, UK

T Lim University of Cincinnati, USA

G Lock University of Bath, UK

M Lucas University of Glasgow, UK

Y Mikhlin National Technical University 'Kharkov Polytechnic Institute', Ukraine

G Mullineux University of Bath, UK

S A Neild University of Bristol, UK

A Neville University of Leeds, UK

Nguyen Dinh Duc Vietnam National University, Vietnam

G Niu Tongji University, China

W M Ostachowicz Polish Academy of Sciences, Poland

M Paul University of Glasgow, UK

Giuseppe Petrone University of Naples, Italy

C Putignano Politecnico di Bari, Italy

R Randall University of New South Wales, Australia

J Reese University of Edinburgh, UK

R Singh Ohio State University, USA

T Sun Tianjin University, China

F B Tian University of New South Wales, Australia

G R Tomlinson University of Sheffield, UK

K Vafai University of California, USA

J Warminski Lublin University of Technology, Poland

M Wiercigroch University of Aberdeen, UK

Z You University of Oxford, UK

L C Zhang University of New South Wales, Australia

Y Zhang Tsinghua University, China

Jing-Shan Zhao Tsinghua University, China

H Zhou Huazhong University of Science and Technology, China

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Table of Contents

Volume 228, Issue 13, September 2014

Materials, Stress Analysis, Structures

Evaluation of tribological properties on PEEK + CA30 sliding against 17-4PH for water hydraulic axial piston motor

Anqing Zhang, Songlin Nie, Lijie Yang

First Published December 31, 2013; pp. 2253–2265

Abstract  Preview

Shape-design optimization of hull structures considering thermal deformation

Myung-Jin Choi, Min-Geun Kim, Seonho Cho

First Published December 25, 2013; pp. 2266–2277

Abstract  Preview

Dynamics and Control

Collision avoidance control for a human-operated four-wheeled mobile robot

Naoki Uchiyama, Tresna Dewi, Shigenori Sano

First Published January 16, 2014; pp. 2278–2284

Abstract  Preview

Design of a novel adaptive fuzzy sliding mode controller and application for vibration control of magnetorheological mount

Do Xuan Phu, Nguyen Vien Quoc, Joon-Hee Park, Seung-Bok Choi

First Published February 20, 2014; pp. 2285–2302 Abstract  Preview

Modal decoupling control for a double gimbal magnetically suspended control moment gyroscope based on modal controller and feedback linearization method

Xiaocen Chen, Yuan Ren

First Published March 13, 2014; pp. 2303–2313

Abstract  Preview

Numerical solution for dynamic analysis of semicircular curved beams acted upon by moving loads

Ali Nikkhoo, Hassan Kananipour

First Published January 7, 2014; pp. 2314–2322

Abstract  Preview

Theoretical investigation into balancing high-speed flexible shafts, by the use of a novel compensating balancing sleeve

Grahame Knowles, Antony Kirk, Jill Stewart, Ron Bickerton, Chris Bingham

First Published December 31, 2013; pp. 2323–2336

Abstract  Preview

Thermodynamics and Heat Transfer

Essential reformulations for optimization of highly conductive inserts embedded into a rectangular chip exposed to a uniform heat flux

MR Hajmohammadi, M Moulod, O Joneydi Shariatzadeh, SS Nourazar

First Published December 31, 2013; pp. 2337–2346

Abstract  Preview Design and Manufacture

Physical modeling and numerical simulation of V-die forging ingot with central void

Peter Christiansen, Jesper H Hattel, Niels Bay, Paulo AF Martins

First Published January 16, 2014; pp. 2347–2356

Abstract  Preview

Structural analysis and characterisation technique applied to a CNC vertical machining centre

DG Ford, MHN Widiyarto, A Myers, AP Longstaff, S Fletcher

First Published January 7, 2014; pp. 2357–2371

Abstract  Preview

Mechanisms and Machines

Compact system without moving parts for retrieving residuals from storage tanks

Cong Xu, Hui Yu

First Published January 7, 2014; pp. 2372–2382

Abstract  Preview

Dynamic analysis of closed high-speed precision press: Modeling, simulation and experiments

Fang Jia, Fengyu Xu

First Published December 18, 2013; pp. 2383–2401

Abstract  Preview

Mathematical modeling and simulation of high-speed cam mechanisms to minimize residual vibrations

Halit Kaplan

First Published January 9, 2014; pp. 2402–2415 Abstract  Preview

Modeling and analysis of a novel conical magnetic bearing for vernier-gimballing magnetically suspended flywheel

Jiancheng Fang, Chune Wang, Jiqiang Tang

First Published December 25, 2013; pp. 2416–2425

Abstract  Preview

Micro- and Nano- Mechanical Systems

Nonlinear analysis of carbon nanotube-based nanoelectronics devices

Mir Masoud Seyyed Fakhrabadi, Abbas Rastgoo, Mohammad Taghi Ahmadian

First Published January 7, 2014; pp. 2426–2439

Abstract  Preview

Structural and instrumentation design of a microelectromechanical systems biaxial accelerometer

Ting Zou, Jorge Angeles

First Published January 7, 2014; pp. 2440–2455

Abstract  Preview

Corrigendum

Corrigendum First Published July 24, 2014; pp. 2456–2456

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Copyright © 2018 by Institution of Mechanical Engineers Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science http://pic.sagepub.com/

Collision avoidance control for a human-operated four-wheeled mobile robot Naoki Uchiyama, Tresna Dewi and Shigenori Sano Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 2014 228: 2278 originally published online 16 January 2014 DOI: 10.1177/0954406213518523

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Proc IMechE Part C: J Mechanical Engineering Science 2014, Vol. 228(13) 2278–2284 Collision avoidance control for a ! IMechE 2014 Reprints and permissions: human-operated four-wheeled sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0954406213518523 mobile robot pic.sagepub.com

Naoki Uchiyama, Tresna Dewi and Shigenori Sano

Abstract Because the collision avoidance function is indispensable for providing safe and easy operation of human-operated robotic systems, this paper deals with the collision avoidance control for a human-operated mobile robot in unknown environments. A typical four-wheeled mobile robot with infrared distance sensors for detecting obstacles is considered. The robot cannot move in an arbitrary direction owing to a nonholonomic constraint. Therefore, we propose a simple control approach in which a human operator’s control input is modified in real time to satisfy the nonholonomic constraint and avoid collision with obstacles. The proposed controller has steering- and brake-like functions that are adjusted according to the distance sensor information. The stability of the proposed control system is analyzed with a linear model. The effectiveness of the proposed method is confirmed by experiments in which several operators control the robot in an environment with obstacles.

Keywords Four-wheeled mobile robot, collision avoidance, human-operated mobile robot

Date received: 10 June 2013; accepted: 26 November 2013

Introduction method based on the idea of imaginary forces acting on a robot is one of the most popular approaches to Fully automated robots are desirable to support obstacle avoidance. This approach has been extended household chores, nursing and welfare work, and by many studies. Because the four-wheeled robot is a industrial tasks performed by skilled workers. nonholonomic system, the obstacle avoidance func- However, from the viewpoint of cost efficiency, it is tion must consider this dynamic property. The robot impractical to produce such robots using the currently manipulator dynamics is considered and decoupled in available technology. Human-operated robotic sys- the implementation of the obstacle avoidance func- tems are a suitable solution, and hence, widely stu- tion presented in Ref. 7; however, this decoupling died. The objectives of human-operated robots approach cannot be applied to the nonholonomic include extending human mechanical power,1,2 pro- four-wheeled mobile robot. The dynamic window viding precise and smooth operations in difficult phys- approach is one of the most efficient approaches ical tasks,3,4 and executing missions in remote or that consider the nonholonomic constraint and can hazardous environments.5,6 In human-operated be applied to unknown environments.12,13 In this robotic systems, controllers are required to incorpor- approach, the mobile robot destination is given and ate the human operator commands and compensate the robot motion is generally determined by for operator’s mistakes without hampering the ease of operation. Collision avoidance functions are neces- sary for easy and safe operation of a robot operated Department of Mechanical Engineering, Toyohashi University of by an elderly or disabled person. We consider a colli- Technology, Toyohashi, Aichi, Japan sion avoidance control for human-operated four wheeled mobile robots that are widely used in Corresponding author: Naoki Uchiyama, Department of Mechanical Engineering, Toyohashi common vehicle systems. University of Technology, 1-1 Hibarigaoka, Tempaku, Toyohashi, Aichi Much research has been conducted on obstacle 441-8580, Japan. 7–11 avoidance for mobile robots. The potential field Email: [email protected]

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optimizing a certain cost function such as the distance walls F, and attractive force from the objects of inter- to the destination. est F In the field of autonomous vehicle control, 14 Reichardt and Schick proposed the concept of risk F ¼ F þ F þ F ð2Þ map to achieve human-like behavior. A risk map is an egocentric map of potentials reflecting the risk at a Helbing and Molnar18 conducted computer simula- certain position in the environment. Gerdes and tions of interacting pedestrians and showed that the Rossetter15 and Rossetter et al.16 proposed an social force model can describe the pedestrian behav- approach based on the concept of artificial potential ior including obstacle avoidance. The following sec- fields, which ensures safe motion in the absence of tion applies this concept to the robot vehicle control. driver inputs. Wolf and Burdick17 presented a set of potential function components to assist automated Dynamics and control of the four-wheeled and semiautomated vehicles. However, these mobile robot approaches require computational effort and expen- sive sensors to construct and employ the risk map and Figure 1 shows a schematic of the four-wheeled artificial potential fields. This paper aims to present a mobile robot. The dynamics of the four-wheeled simple approach that employs inexpensive distance mobile robot is represented as follows15 sensors. The social force model, which has been used to mu_x ¼ fxr þ fxf cos fyf sin þ m!uy ð3Þ explain pedestrian motion,18–20 considers the dynam- ics of a pedestrian and the imaginary social forces mu_y ¼ fyr þ fxf sin þ fyf cos m!ux ð4Þ acting on him/her in order to avoid collisions with other people or walls. Based on this concept, we pro- I!_ ¼afxf sin þ afyf cos bfyr pose a control approach for collision avoidance in d þ ff f þðf f Þ cos gð5Þ which the control input signal is modified according 2 xrr xlr xrf xlf to the distance sensor information. The proposed con- trol system is an extension of that in Ref. 21 to a four- fxf ¼ fxrf þ fxlf, fxr ¼ fxrr þ fxlr, wheeled robot. A stability analysis is performed to fyf ¼ fyrf þ fylf, fyr ¼ fyrr þ fylr validate the proposed approach. The effectiveness of the proposed approach is demonstrated by experi- where ux is the vehicle velocity in front–rear direction; mental results obtained when several unskilled oper- uy, vehicle velocity in the lateral direction; !, vehicle ators control the four-wheeled robot in a corridor-like angular velocity; fijk, force acting on each wheel [i: environment. force direction (x or y), j: right(r) or left(l) wheel, k: front(f) or real(r) wheel]; , steering angle; m, vehicle mass; a, b, distance between the center of gravity and Controller design for collision avoidance the rear or front wheel; d, distance between rear Social force model wheels (front wheels); and ( ) is the time derivative. We assume that fxr and are inputs provided by an 18 Helbing and Molnar first introduced the social force operator, fxrr ¼ fxlr, fxrf and fxlf are zero (i.e. rear- model to explain pedestrian motion. The social forces wheel drive), and vehicle parameters m, I, a, b, and are considered to act on a pedestrian in order to avoid d are known and constant. The forces fyf and fyr are collisions with other people or walls and to enable approximated as follows15 motion in a specific direction at a given speed. The social forces for collision avoidance are modeled as 1 uy þ !a fyf ’cff ¼cf tan ð6Þ repulsion forces from obstacles such as other people ux or walls. Follow-up studies on this concept have been conducted.19,20 This subsection briefly explains the concept of the social force model. The social force b a γ f model is defined as follows f f ylr ylf δ γ r ω f dw f xlf ¼ F þ F ð1Þ xlr u dt l y d

ux where w is the pedestrian velocity vector, F is the f yrr f f xrr yrf social force vector, and Fl is the fluctuation vector. f xrf The social force vector F defined in equation (2) con- sists of the attractive force from the desired position F, the repulsive force from other pedestrians and Figure 1. Four-wheeled robot model.

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1 uy !b where d and fd are the steering angle and driving force fyr ’crr ¼cr tan ð7Þ ux designated by an operator, respectively, and fd corres- ponds to the accelerating or braking force of a typical where cf and cr are the cornering stiffness and f and vehicle. The virtual steering angles gri and gli are r are the sliding angles of the front and rear wheels. assumed to be proportional to the distance measure- From equations (3) to (7), we have the following ment at each sensor location as follows dynamics gki ¼pidki þ qi, k ¼ l, r ð13Þ 1 uy þ !a mu_x ¼ fxr þ cf tan sin þ m!uy ux where the subscript l or r denote that the correspond- ð8Þ ing sensor is located on the left or right side of the robot body, i the sensor number, and p and q are i i positive constants. In this study, gri and gli are 1 uy !b mu_y ¼cr tan assumed to be positive. Equation (11) indicates that ux the controller steers to the left when the distance to 1 uy þ !a cf tan cos m!ux ð9Þ the obstacle measured by the sensor located at the ux right-hand side of the robot becomes small and vice versa. 1 uy þ !a I!_ ¼acf tan cos Because we cannot directly apply the social force to ux the dynamics in equations (3) to (5), we propose to 1 uy !b include the similar effect in the steering angle and þ bcr tan ð10Þ ux driving force, as given in equations (11) and (12), which are common control variables in four-wheeled This study assumes that several distance sensors are vehicle systems. This controller design has not been located on the robot. Figure 2 shows an example of a presented as far as the author’s knowledge. sensor location for the rectangular shaped robot. For simplicity, the virtual forces hri and hli in equa- Because the distance information to obstacles is avail- tion (12) are assumed to be proportional to the dis- able, we include this information in steering angles tance measurement at each sensor location as follows and driving force generated by rear wheels for colli- sion avoidance as follows hki ¼p^idki þ q^i, k ¼ l, r ð14Þ

Xm Xm where p^i and q^i are positive constants. From equation ¼ d þ gri gli ð11Þ (12), it can be seen that the smaller the distance, the i¼1 i¼1 larger the braking force provided by the controller. Xm Xm The effect of gki and hki can be interpreted as in the fxr ¼ fd hri hli ð12Þ social force model, in which the social force is mod- i¼1 i¼1 eled as a virtual repulsive force to avoid collisions with obstacles.

Stability analysis

Y Using the test case presented in Figure 2, we consider Distance the validity of the proposed method for realizing the φ d sensors r 2 collision avoidance function in the human-operated d robot. Namely, this subsection is devoted for analyz- r1 ing the validity of the control in equations (11) and d l 2 l l l 2 1 (12), and the measurement of rotational deviation and 2 d forward speed as well as actual parameter values is l1 l 1 not required for the control and the analysis in this subsection. Although the vehicle system has nonlinear B Robot x dynamics in equations (3) to (5), we apply a linear analysis at a certain operating point that is generally Wall L effective to predict the fundamental property of the control system. Experiments were conducted to fur- ther verify the effectiveness, and their results are X shown in ‘‘Experiments’’ section. For simplicity, the robot is assumed to have a rectangular shape. It is further assumed that the human operator intends to Figure 2. Robot moving between walls. move the robot along the centerline between two

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P parallel walls. Because of operational mistakes, the c þ c 2c N p l x€ ¼ r f x_ f i¼1 i i x robot deviates from the centerline as shown in mu m x0 P Figure 2. The lateral and rotational deviations are N bc ac 2c p l denoted by x and , respectively. The position in the þ u r f _ þ f i¼1 i i ð25Þ x0 mu m vertical direction is denoted by y. In addition, we x0 assume that all distance sensors are located symmet- rically with respect to the centerline and only above P ac bc 2ac N p l the robot’s center of gravity, as shown in the figure. € ¼ f r x_ f i¼1 i i x Iu I The number of sensors located at the left or right half x0 P 2 2 N side of the robot is denoted by N. a cf þ b cr 2acf pili _ i¼1 ð26Þ The distance between each sensor and the walls is Iux0 I given as follows where we assume the desired steering angle d ¼ 0. The L x breaking force effect appears as in equation (24), and dri ¼ þ li tan B ð15Þ cos it is obvious that the motion is decelerated when fxr is negative. Because the control objective is to reduce the L þ x d ¼ l tan B ð16Þ deviation in the x and directions, we only consider li cos i equations (25) and (26) for the stability analysis. It should be noted that owing to the nonholonomic con- where L is the half distance between the walls and B is straint, the robot cannot move instantaneously in the the half width of the robot. li is the distance from the x direction. Hence, we only consider the dynamics robot’s center of gravity to the ith distance sensor in equation (26) for the stability analysis. along the robot’s center line. To validate the proposed method, we simply con- From Figure 2, we obtain the following relations sider the case that the vehicle’s front and rear sides and the cornering stiffness satisfy a ’ b and cf ’ cr, x_ ¼ux sin uy cos ð17Þ respectively. Then, we can rewrite equation (26) as follows y_ ¼ ux cos uy sin ð18Þ € þ c _ þ c ¼ c x ð27Þ _ ¼ ! ð19Þ 1 2 3

Assuming that the robot moves with approximately where c1 c3 are positive constants. Equation (27) the constant speed (operating point) is a stable system with respect to . In addition, ðux, uy, !Þ¼ðux0,0,0Þ as follows the positive value of x provides a positive steady- state value for , which makes the robot turn left ux ¼ ux0 þ uxs, uy ¼ uys, ! ¼ !s ð20Þ and reduces the magnitude of x. Similarly, when x has a negative value, the negative steady-state value where ðuxs, uys, !sÞ is the deviation from the operat- for causes the robot to turn right and reduces ing point and the steering angle is small. Linearizing the magnitude of x. Hence, this approach is expected equations (8) to (10), we obtain the following linear- to provide the appropriate collision avoidance ized dynamics function.

mu_ ¼ f ð21Þ xs xr Experiments

uys b!s uys þ a!s Figure 3 shows the experimental robot equipped mu_ys ¼cr cf þ cf m!sux0 ux0 ux0 with distance sensors and the controller for human ð22Þ operators. The measurable range of the distance sensor is 10–80 cm. Rotary encoders (500 PPR) uys þ a!s uys b!s attached to the motors are used for measuring the I!_ s ¼acf þ acf þ bcr ð23Þ ux0 ux0 robot position and orientation by assuming that the wheel slip is negligible. The proposed controller Furthermore, assuming that the angle is small and design is verified in the environment shown in substituting equations (17) to (19) after linearization, Figure 4, where the robot controlled by six operators controller equations (11) and (12), and distance equa- is expected to move from the start position to the tions (15) and (16) into equations (21) to (23) yields destination. the following dynamics In order to achieve the effective collision avoid- ance, it is reasonable to employ a function that pro- f y€ ¼ xr ð24Þ vides a larger steering angle and breaking force near m obstacles compared with equations (13) and (14).

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(a) Steering wheel αi n = n 1 dij 3 n = 2 Accelerator

Distance n = 5 sensors 0 0.8 dij

° d (b) 22.5 l1 ° Figure 5. Function profile used for collision avoidance. 45 d Distance l 2 sensors ° 45 Table 1. Experimental parameters.

d Parameter Value Parameter Value 45° r2 2 3 1=3 ° m 1.33 (kgm ) 2.0 10 (radm ) 22.5 d 1 r1 2 3 1=3 I 0.02 (kgm ) 2 4.6 10 (radm ) 1=3 a 0.09 (m) 1 0.4 (Nm ) 1=3 Figure 3. Experimental robot system. b 0.07 (m) 2 0.5 (Nm )

Cf 15.0 (N/rad) n 3

Cr 15.0 (N/rad) (a) 900 27° Goal 10 Start 600 Table 2. Number of collisions occurred for each operator. 17 Operator No. Manual Proposed 1200 500 130 (b) 220 310 430 510 620

operating point in ‘‘Stability analysis’’ section is still valid for linearized equations of (28) and (29). Table 1 lists the parameters used in the experiment. Each operator operates the robot under the following conditions: Figure 4. Experimental environment. 1. Without the collision avoidance function (if the We consider the following nonlinear functions instead robot collides with the wall, the operator operates of equations (13) and (14) the robot from the start position again). 2. With the collision avoidance function. g ¼ pffiffiffiffiffiffii k ¼ l r ð Þ ki n , , 28 dki In case 2, we consider the worst case that the operator h ¼ pffiffiffiffiffiffii k ¼ l r ð Þ can control only on/off of the translational motion, ki n , , 29 dki and the breaking and the steering are controlled automatically. Figure 5 shows the profile of these functions in which Table 2 presents the number of collisions for each the parameters are set as i ¼ 0.5 and n ¼ 1, 2, 5. operator. No collisions occurred while operating the Regarding to the stability analysis, linearizing equa- robot with the collision avoidance function. tions (28) and (29) leads to equations (13) and (14), Figure 6 compares the time required for each oper- and hence the linear analysis assuming a certain ator to reach the goal. Because the robot collided the

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20 (a) 5 Accelerator Proposed control 15 Voltage [V] 10 Steering 5 Manual control Required time [s] 0 Time [s] 10 0 123456 Operator’s No. (b) 0.6 y Figure 6. Comparison of required time to reach the goal. [m] 0

-0.6 0 0.8 1.6 x [m] (a) 5

Accelerator (c) 1 Voltage [V] Steering

[rad] 0 Time [s] 10 –1 0 Time [s] 10 (b) 0.6

y Figure 8. Manual control results. (a) Commanded control 0 input voltage, (b) robot position, and (c) robot orientation. [m]

-0.6 0 0.8 1.6 x [m] fd ¼ 0:23 ðVf V0Þ½Nð31Þ

(c) 1 where V and Vf are control input voltages com- manded by the human operators and V0 ¼ 2.65 V. In [rad] Figure 7, although the operator does not steer the robot, it successfully moves to the goal by automatic- –1 ally adjusting the steering angle . In Figure 8, the 0 Time [s] 10 operator frequently adjusts both the steering wheel and accelerator. However, a collision occurs at Figure 7. Proposed control results. (a) Commanded control approximately x ¼ 1.8 m in Figure 8(b). These results input voltage, (b) robot position, and (c) robot orientation. confirm the effectiveness of the proposed controller design using inexpensive distance sensors and simple control input calculations. wall during the trial of all operators, they performed Experimental results show that the proposed con- several trials and the required time was reduced in the trol in equations (11) and (12) can provide successful last trial. The figure shows the required time recorded collision avoidance for the worst case that the oper- in the last trial of the manual control case. On an ator can control only on/off of the translational average, there is no significant difference in the motion. For the case that the operator can control required time to reach the goal with and without the the speed and the steering, the effect of functions gki proposed method. The average times were 9.42 s for and hki in equations (11) and (12) may be tuned by the manual control case and 10.12 s for the proposed changing the values i and n in Figure 5. If the oper- method. ator is skillful, the effect should be reduced, otherwise, Figures 7 and 8 compare the operator control with it should be increased. Hence, the proposed control and without the proposed method. Figures 7(a) and may be useful for any level of operators in collision 8(a) show the control input voltage commanded by avoidance. the operator. The control input voltage has the fol- lowing relation to the steering angle d and acceler- Conclusions ation force fd in equations (11) and (12), respectively This paper presents a new approach to collision avoidance for four-wheeled human-operated mobile d ¼ f16:2 ðV V0Þg ½radð30Þ 180 robots using inexpensive infrared distance sensors.

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