Independent traction control for uneven terrain using stick-slip phenomenon: application to a stair climbing robot

Transcription

1 DOI /s x Independent traction control for uneven terrain using stick-slip phenomenon: application to a stair climbing robot Hyun Do Choi Chun Kyu Woo Soohyun Kim Yoon Keun Kwak Sukjune Yoon Received: 20 August 2006 / Accepted: 7 March 2007 Springer Science+Business Media, LLC 2007 Abstract Mobile robots are being developed for building inspection and security, military reconnaissance, and planetary exploration. In such applications, the robot is expected to encounter rough terrain. In rough terrain, it is important for mobile robots to maintain adequate traction as excessive wheel slip causes the robot to lose mobility or even be trapped. This paper proposes a traction control algorithm that can be independently implemented to each wheel without requiring extra sensors and devices compared with standard velocity control methods. The algorithm estimates the stick-slip of the wheels based on estimation of angular acceleration. Thus, the traction force induced by torque of wheel converses between the maximum static friction and kinetic friction. Simulations and experiments are performed to validate the algorithm. The proposed traction control algorithm yielded a 40.5% reduction of total slip distance and 25.6% reduction of power consumption compared with the standard velocity control method. Furthermore, the algorithm H.D. Choi C.K. Woo S. Kim Y.K. Kwak ( ) Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 373-1, Guseong-dong, Yuseong-gu, Deajeon, , Republic of Korea ykkwak@kaist.ac.kr H.D. Choi chlguseh80@kaist.ac.kr C.K. Woo zedai@kaist.ac.kr S. Kim soohyun@kaist.ac.kr S. Yoon Mechatronics and Manufacturing Technology Center Samsung Electronics, 416, Maetan-3Dong, Yeongtong-gu, Suwon, Gyeonggi-do, Republic of Korea sukjune.yoon@samsung.com does not require a complex wheel-soil interaction model or optimization of robot kinematics. Keywords Traction control Mobile robot Uneven terrain 1 Introduction and background Mobile robots have been developed in various application fields, including building inspection and security, military reconnaissance, and planetary exploration. The NASA Jet Propulsion Laboratory (JPL) rovers are examples of successful robots developed for planetary missions (Golombek 1998; Schenker et al. 2003; Hayati et al. 1997). Other examples of traversing rough terrain can be found in the mining industries and hazardous material handling applications as well as in building inspection (Siegwart et al. 2002; Dalvand and Moghadam 2006; Lee et al. 2003; Cho et al. 2005; Maurette 2003). The common requirements of these mobile robots are long-term operation and high mobility in rough terrain to perform difficult tasks. For rough terrain, it is important for mobile robots to maintain adequate wheel traction. Excessive wheel slip could cause an increase in the amount of dissipated energy at the contact point between the wheel and ground or, even more seriously, the robot could lose all mobility and become trapped. Traction control has been applied to flat surfaces to improve the mobility and energy efficiency of vehicles (Lee and Tomizuka 1996; Tan and Chin 1992). Such works have been developed for the car industry, however, and are not appropriate for rough terrain mobile robots as the required wheel velocity to maintain the rolling state of each wheel is different. The different kinematics of mobile robots should be considered to apply traction control technology for overcoming rough terrain. In this regard, more recent work has

2 considered the kinematics and dynamics of mobile robots in developing slip-based traction control (Yoshida and Hamano 2002). However, online calculation of kinematics and dynamics would be unavoidable in addition to analysis of these aspects in order to apply this method to a newly developed robot (Sarkar and Yun 1998). Although measurement via an inclinometer or potentiometer is quite simple and inexpensive, continuous calculation of kinematics and dynamics could inflict a burden on the main controller which has many tasks to perform in accomplishing a given mission. Another approach to minimize the slip is physics-based traction control, which optimizes individual wheel torque based on terrain information. A key element of the method is inclusion of estimates of wheel-terrain contact angles (Iagnemma and Dubowsky 2004; Iagnemma et al. 2004; Lamon et al. 2004). Another estimation method to control actively articulated suspensions so as to enhance rover tipover stability was developed (Iagnemma et al. 2003). Poor estimation is obtained when the mobile robot is still and terrain profiles slowly change. Furthermore, bad wheel-ground contact angle estimation result in unadapted motor torque and the wheel slip induces the wrong contact angles. Thus, a more recent study has focused on direct measurement of the contact angle between the wheel and ground (Lamon and Siegwart 2005). The present paper proposes a traction control algorithm that can be independently implemented to each wheel, and the proposed algorithm does not require real-time calculation of kinematics and dynamics compared to other traction control algorithm. The algorithm estimates the stick-slip of wheels based on observation of angular acceleration, and commands linear increases or decreases of the torque. The proposed algorithm does not need real-time calculation of kinematics and dynamics compared to other traction control algorithms. The calculations of kinematics and dynamics are only required in the controller design phase. Thus, eliminating the need to calculate the kinematics and dynamics will be helpful for the mobile robot to traverse rough terrain or perform missions because of the reduced control burden, especially in areas where the robot operates in conjunction with another task. Integrated modeling including the dynamics of robot and controller is performed to verify the proposed traction control algorithm and related assumptions. The algorithm is tested with a mobile robot developed for climbing stairs. It is shown that the traction control algorithm increases robot mobility and reduces power consumption as compared to the conventional velocity control system. Torque comparison results show that the integrated modeling is reliable. Experiment results for stair climbing show that the proposed control algorithm decreases the net work performed at the wheel. 2 Test bed: ROHBAZ-6WHEEL The test bed developed at KAIST, named ROBHAZ- 6WHEEL (Robot for Hazardous Environment), is designed based upon passivity and adaptability to uneven terrain. Figure 1 shows ROBHAZ-6WHEEL. The linkage parameters can be optimized for the robot to overcome target stairs. It has 6 motorized wheels connected by a passive 4-bar linkage mechanism, which allows extensive adaptability to rough terrain. ROBHAZ-6WHEEL has eight DOFs: six DOFs for the robot body and two DOFs for the right and left sides of the passive linkage mechanism (Yoon et al. 2004). The dimension and mass parameters are defined in Fig. 2, and Table 1 shows the design parameters of test bed. The robot can be divided into three main parts: the driving wheel assembly, the passive linkage mechanism, and the robot body. A 50 Watt Maxon EC flat motor, 500 pulse USDigital optical encoders, and 80:1 HarmonicDrive harmonic gears are assesmbled inside the wheel to afford a compact driving unit. The passive mechanism is composed of a four bar linkage and a limited pin joint. The pin joint confines the working range of the four bar linkage mechanism so as to avoid overturning. The parameters of the linkage mechanism are optimized for adaptation to the shape of the target stairs. An electrical subsystem in the main body consists of a single board computer (SBC), a controller area network (CAN) module, a wireless LAN, a motor controller, and batteries. The robot has a symmetrical structure. The configuration of the right and left sides of the proposed linkage mechanism is independently determined according to the environment. By using the linkage mechanism, the wheelbases between the wheels and the positions of the wheel axes relative to the gravity center of the robot body can be altered. 3 Independent traction control algorithm In this section, we describe the proposed traction control algorithm, which can be independently implemented to each Fig. 1 Test bed ROBHAZ-6WHEEL

3 Fig. 2 Definition of system parameters Table 1 The system parameter of ROBHAZ-6WHEEL Parameters Values Dimensions (mm) L L L 3 74 L L 5 93 L L L 8 48 L 9 48 L 10 8 L L R 60.0 Mass (kg) Robot Body 10 Wheels and Linkage 20 Batterie 3 Total 33 wheel without any extra sensors and devices. First, principle of the stick-slip phenomenon is presented to show it is applied to the proposed traction control algorithm. 3.1 Stick-slip phenomenon Whenever the coefficient of kinetic friction is less than the coefficient of static friction, there will exist a tendency for the motion to be intermittent rather than smooth. The two contact surfaces will stick until the sliding force reaches the value of the maximum static friction. The two surfaces will Fig. 3 Simple model for stick-slip then slide against each other with a small value of kinetic friction until they stick again. This friction mechanism can be explained with a simple spring-mass model (see Fig. 3). m is the mass of moving body, N is the normal force, T is the traction force, F is the applied external force, and k is the stiffness of spring. We assume that y moves with constant velocity. When the spring is pulled with sufficient force to overcome the static force, the block begins to move. The block moves at a velocity faster than the spring because kinetic friction is far less than the static friction, rapidly restoring the spring until the velocity of the block becomes zero. The block will again remain at rest until the tension exceeds the maximum static friction, causing the block to move forward another unit of distance. With a constant velocity of y, the block continuously repeats stick-slip. 3.2 Proposed traction control algorithm The proposed traction algorithm is analogous to the stickslip friction mechanism. Figure 4 shows the qualitative time history of the proposed traction control algorithm. Upper curve is the maximum friction force; lower curve is the kinetic friction force. Time history of these curves is determined by the robot kinematics and surface conditions. Based on the acceleration of wheels, the state of torque is switched

4 Fig. 5 Forceactingonasingle wheel Auton Robot Fig. 4 Qualitative time history of the proposed traction control algorithm. Excessive slip of wheels so as to avoid excessive slip. The maximum traction force a terrain can bear increases with increasing normal force (Bekker 1969; Wong 2001). μ s and μ k are the maximum friction coefficient and kinetic friction coefficient, k i is the increase slope of torque, k d is the decrease slope of torque, and τ(t) is the applied wheel torque. The key concept of the method is to set the wheel torque at a level similar to the spring force explained in the previous subsection. The wheel torque linearly increases until the controller observes specific angular acceleration, which indicates that the applied torque is higher than the torque induced by the maximum friction force. The torque then linearly decreases until the applied torque is less than the torque induced by the kinetic friction force, and the specific deceleration is then detected. Therefore, the traction force induced by torque of the wheel will converse to the interval between the maximum static friction and the kinetic friction, asshowninfig.4. Each wheel could also be accelerated so as to maintain the stick condition while traversing rough terrain, because of kinematic incompatibility of a mobile robot. Therefore, the observed angular acceleration is influenced by not only wheel slip but also kinematic incompatibility. A robot traversing with rapid movements accelerates and decelerates very rapidly. Thus, wheels inevitably slip on the terrain since the commanded velocity must be high in order to maintain fast movements and the traction force applied to the wheels is limited by the product of the normal force and the maximum static friction coefficients. Under these conditions, the dissipated energy on the contact point drastically increases or, even more seriously, the robot could lose all mobility and become trapped and thus fail to perform its mission or be shocked to the structure. For these reason, the slow speed of an autonomous rover is recommended in rough terrain. The dynamic contributions can be neglected with slow motion; the acceleration by kinematic incompatibility could be neglected because of its small amount rela- tive to the acceleration by the torque of the wheel. Moreover, we discriminate between these two causes of acceleration by selecting a higher value of specific angular acceleration relative to the acceleration level induced by kinematic incompatibility. The rapid change of angular velocity could indicate whether the applied wheel torque is higher than the torque induced by the maximum friction force or lower than that induced by kinetic friction force. Because the only information required in the proposed algorithm is the angular velocity of each wheel, the algorithm is easily implemented to mobile robots. In order to determine the parameters of the traction controller, the dynamics of a single wheel model is analyzed. Although natural outdoor terrain is rarely rigid, there are equivalent normal forces and equivalent friction forces. Moreover, the proposed traction controller can work in practice without accurate estimation of the normal force and friction coefficient. Figure 5 shows the forces acting on the single wheel of a mobile robot. P x and P y are external wheel force, N is the normal force, T is the traction force, τ is the torque applied to the wheel, and θ is the angular velocity of wheel. The dynamic equation of the single wheel can be written as follows: J θ = τ B θ rt, T < μ s N (1) where J is the moment of inertia of wheel, B is the internal damping coefficient of wheel modules, r is the radius of the wheel, and μ s is the maximum friction coefficient. When τ<b θ + rμ s N, the traction force can be calculated from rt = τ B θ. Under this condition, torque applied to wheel is not sufficient to overcome the force of static friction and consequently the wheel does not accelerate. If we assume the torque linearly increases and set τ = k i t, (1) can be rewritten as J θ = k i t B θ rt. (2) And there exists a moment t 1 when the torque balances with the maximum static friction force. kt 1 = B θ 1 + rμ s N. (3) After t 1, the wheel acceleration causes wheel slip and T = μ k N, where μ k is the kinetic friction coefficient. We define

5 t = t t 1. Then, θ can be a function of t. Thus, if we substitute these relations into (1), (4) can be obtained. J θ(t ) + B θ(t ) = k i t + B θ 1 + r(μ s μ k )N. (4) Equation (4) is a linear 1st order differential equation. Assumption of a constant normal force is possible because switching of the torque state repeats in an infinitesimal time interval compared to the change of environment. Multiplying both sides integrating factor, a general solution of the differential equation can be obtained as follows (Grossman and Derrick 1988) θ(t ) = k i B t + θe B J t + 1 ( r(μ s μ k )N + B θ 1 k ) ij B B (1 e B J t ). (5) Differentiating (5) byt, the wheel acceleration can be obtained as follows θ(t ) = k i B + 1 ( r(μ s μ k )N k ) ij e B J t. (6) J B Equation (6) provides a guideline for determining the parameters of the proposed controller. We define α max as the permissible maximum angular acceleration of the wheel, which indicates the applied wheel torque is higher than the torque induced by maximum friction force. Hence, when α max observed, the applied wheel torque will decrease. In order to obtain the control parameters, we assume the friction coefficients are constant. Though knowledge of the static and dynamic friction coefficients is required in mathematical derivation, this information does not necessarily have to be known in practice. Part of the sufficient condition for the proposed approach is that the wheels should accelerate with increasing torque so as to detect the wheel slip. The traction increases with increasing torque in the adhesion region, while the traction remains relatively unchanged in the slip region as the wheel accelerates. More important than estimation of the static and dynamic friction coefficients is ensuring that the increase of acceleration is more strongly affected by the increase of torque than by variation of the friction coefficient. Thus, we attempted to design the proposed traction controller so as to be robust to variation of the friction coefficients. This robustness can be possible by increasing k i and k d (slope of torque). However, the sampling frequency and resolution of the encoder should be enhanced with increasing k i and k d, because the wheel accelerates very rapidly. In the first step to determine the parameters of controller, we assume that the kinematic incompatibility of the mobile robot influences angular acceleration of the wheel. Traversing a mobile robot over rough terrain in a simulation, we find the angular acceleration level of the wheel is indeed influenced by kinematic incompatibility. In order to discriminate the two sources of acceleration, the following relationship should be satisfied α max > max{α j (t)}+ε, 0 <t<t f (7) j where α j (t) represents the angular acceleration of wheel j induced by kinematic incompatibility while traversing the terrain. Then, as shown in (8), α max can be selected as the minimum value of angular acceleration of each wheel to cause the torque states (increasing or decreasing) to be switched within t = t r α max = min j { θ j (k i,t r,n j, μ j )}, (8) μ j is the difference between static friction and kinetic friction coefficients, where μ μ s μ k. α max increases with increasing k i and t r in (8). t r, which denotes the response time of the algorithm after a wheel meets the maximum static friction, should be selected under consideration of the roughness of the environment and the speed of the mobile robot (10 ms in this case). Finally, k i is determined to satisfy (7), because α max increases with increasing k i. Now the torque state is switched and it linearly decreases until the applied torque is less than the torque induced by the kinetic friction force. The specific deceleration is then detected. Setting τ = τ max k d t,(1) can be rewritten as J θ = τ B θ rμ k N. (9) And there exists a moment t 2 when the torque balances with the kinetic friction force, as shown in the following τ 2 = B θ 2 + rμ k N (10) where τ 2 = τ(t 2 ), θ 2 = θ(t 2 ), and t = t t 2. After t 2, the equation of motion for a single wheel can be written as J θ(t ) + B θ(t ) = k d t + B θ. (11) The general solution of the equation can be obtained with the assumption of constant normal force, as follows θ(t ) = k d B t + θe B J t + 1 ( B θ s k ) dj (1 e B J t ). (12) B B Differentiating (12) byt, we obtain the wheel deceleration θ(t ) = k d B + k d B e B J t. (13)

6 Here, we define α min as the permissible minimum angular acceleration of the wheel, This parameter indicates that the applied wheel torque is lower than the torque induced by kinetic friction force. When α min is observed, the torque states are switched and the applied wheel torque will increase. α min and k d are determined in the same manner as in the previous analysis of wheel acceleration. For the simulations and experiments, the proposed traction control algorithm is implemented in the discrete-time domain. We define the state vector, X k =[ω k ω k 1 ˆα k st k τ k ] T, where ω k is the angular velocity of the wheel, ˆα k is the estimated angular acceleration of the wheel, st k is a flag indicating the torque state, and τ k is the output torque in k step. Initial condition X k =[ω k ω k 1 ˆα k st k τ k ] T =[00030] T. (14) Update step ω k+1 = ω k+1, ω k = ω k, 2, if ˆα k >α max, st k+1 = 3, else if ˆα k <α min, st k, otherwise, 1 ˆα k+1 = 1 + σ t ( ˆα k + σ(ω k+1 ω k )), { τk k τ k+1 = d t, if st k = 2, τ k + k i t, if st k = 3. Output (15) Y k = τ k. (16) Equations (14), (15), and (16) represent the initial condition, update equation, and output equation, respectively. σ is the cutoff frequency of acceleration, and t is the sampling time of controller. 4 Simulation Simulations have been performed in order to verify the proposed algorithm and assumptions. The intention of the simulation is not to obtain the optimal control parameters but to verify the potential of the algorithm and compare it with the conventional velocity control method. 4.1 Preliminary simulation Each wheel is independently controlled in order to satisfy the condition that the traction force has to converse to the interval between the maximum static friction and kinetic friction force. Since the maximum friction force is exerted on Fig. 6 Coefficient of friction varying with slip velocity every wheel, the robot overcomes the obstacles or rough terrain with the maximum applicable force from the terrain. The necessary condition that is considered in this chain of reasoning is that the traction force should be tracking the maximum friction force, which varies according to the normal force and friction coefficients. We performed preliminary simulations in order to investigate whether the proposed algorithm has this important feature or not. The model of single wheel described in (1) is used for this simulation. we adopted velocity-based friction model in order to calculate the traction force on the contacts. Figure 6 shows the coefficient of friction varying with slip velocity. The following parameters were used: static friction coefficient μ s = 0.7; kinetic friction coefficient μ k = 0.5; static transition velocity v s = 6mm/s; kinetic transition v k = 20 mm/s; radius of wheel r = 60 mm; moment of inertia J = kg m 2 ; damping coefficient of wheel B = 0.01 N m s. And the normal force variation is N(t)= sin(2πf t) N, where f = 0.2 Hz. Though the difference between maximum and minimum value of normal force is 100 N, real traction force tracks the variation of the maximum friction force as shown in Fig. 7. We observed the slip distance of wheel in order to investigate the sensitivity of the proposed method to uncertain estimates of μ s and μ k, and assumed the normal force of 100 N. Figure 8 shows that the sensitivity of the friction coefficients is low enough to neglect the effect of the estimating friction coefficients on the slip distance. This is true if the proposed traction method could maintain the maximum traction force. The slip distance has nothing special significance at the area, where the kinetic friction coefficients are larger than the static friction coefficient, as a result of the inability of the proposed traction method. These results show that the proposed traction control is robust to the variation of normal force and friction coefficient.

7 Fig. 7 Slip velocity and traction varying with normal force variation Fig. 8 Sensitivity of μ s and μ k to the proposed method 4.2 Dynamic model of ROBHAZ-6WHEEL and controller Simulations have been performed with ADAMS and MAT- LAB toolbox. The dynamic simulation parameters have been set as close as possible to correspond with a real mobile robot. All the geometric dimensions, mass, and inertia parameters are imported from a 3-D CAD program. Thus, these parameters can be accurately calculated from the geometry and density information of the 3-D CAD program, including the battery, single board computer, DC-DC converter, etc. Internal damping torque of the wheel proportional to the angular velocity has been implemented from a parameter identification process. The impact and friction between interfacing surfaces are modeled as follows (Goldsmith 1960; Lankarani and Nikravesh 1994): N = k c g n + c dg for g 0, (17) dt T = μn (18) where k c is the stiffness of contacts, g represents the penetration of geometry into another, n is a real positive value Fig. 9 Integrated simulation environment denoting the force exponent, c is a damping coefficient of contacts, dg dt is the penetration velocity at the contact points, and μ is the friction coefficient defined in Sect The following parameters were used: the stiffness of contact k c = 150 N/mm; the force exponent n = 2.1; damping coefficient c = 20 N s/mm. Figure 9 shows the integrated simulation environment. The proposed traction control algorithm is modeled and implemented in MATLAB simulink including S-function. For-

8 Fig. 10 Schematic of the traction control algorithm Fig. 11 Acceleration caused by kinematic incompatibility Fig. 12 Snapshots of a simulation Table 2 Parameters of traction control algorithm Parameters k i k d Value 4Nm/s 4Nm/s α max 1rad/s 2 α min 0.7 rad/s 2 σ 100 rad/s 2 Sampling time of controller Sampling time of dynamic simulation 10 ms 1 ms ward dynamics of the mobile robot is solved by ADAMS. The traction control algorithm is implemented in S-function. Figure 10 shows a schematic of the traction control algorithm. τ v is the velocity adjust torque. While the traction is maximized by traction control loop, the velocity of robot can be controlled by τ v of which increase induces the increase of average velocity of the robot. In simulation and experiments, we assumed that it is a constant. With nonslip condition to three wheels, the angular velocity of two wheels can be a function of the other wheel s angular velocity. This means that if the rover traverses 2-D environments and three motorized wheels are controlled so as to rotate with constant angular velocity, two wheels should

9 Fig. 13 Simulation results (a) Slip speed of wheels (b) Slip distance of wheels

10 Fig. 13 (Continued) (c) Dissipated power (d) Dissipated work

11 Table 3 Simulation results Velocity control Traction control Slip distance (mm) Wheel Wheel Wheel Total Dissipated work (Nm) Wheel Wheel Wheel Total Arrival time (s) Commanded total traverse (mm) slip. Thus, the traction control algorithm is applied to the middle and rear wheels while the front wheel is operated with conventional PID velocity control. The front wheel is wheel 1, the middle wheel is wheel 2, and the rear wheel is wheel 3. The S-function achieves the control law described from (14)to(16) in discrete time domains. ADAMS model is imported as a plant in order to incorporate the control model into the mechanical model of the mobile robot; the inputs and outputs defined for the model analysis are the torque and angular velocity of the wheels, respectively. The exported ADAMS plant is linked to MATLAB simulink. Using these programs, we performed an integrated simulation that allows us to test and compare the traction control algorithm with high accuracy. 4.3 Simulation results In this subsection, we compare the proposed algorithm and the conventional velocity control method. Parameters of the proposed algorithm are determined as shown in Table 2 based on the procedure described in Sect. 3. Analysis of acceleration by kinematic incompatibility should be performed prior to determining the control parameters, since the observed angular acceleration is influenced by not only wheel slip but also kinematic incompatibility. Wheel 1 moves with constant velocity of 60 mm/s, while wheel 2 and wheel 3 are forced to maintain the non-slip condition on the contact points. Figure 11 shows that the magnitude of acceleration caused by kinematic incompatibility is below 1 rad/s 2 in most of areas. When the robot meets the condition that the velocity kinematic become singular, the required velocity of wheel 2 and wheel 3 for non-slip condition should be infinite or zero while the angular velocity of wheel 1 is bounded. Thus, we do not consider the acceleration with singular point, since the wheels inevitably slip. Finally, the traction controller Fig. 14 Experimental setup for stair climbing perceives that the wheel slips if the detected angular acceleration is higher than 1 rad/s 2. Stairs are selected as a test environment because they are the most challenging obstacles in rough terrain. Wheel slip caused by kinematic incompatibility of the mobile robot occurs with the velocity control system upon confronting stairs. It is verified that the effect of kinematic incompatibility on wheel slip is efficiently compensated by the proposed traction control algorithm. Figure 12 shows snapshots that are captured during the simulation, and total commanded traverse is 1074 mm. Using both the velocity control system and the traction control system, the mobile robot successfully traversed the stairs as it has wide-ranging adaptability to uneven terrain. However, better performance in terms of total slip and dissipated work was observed with the proposed traction control algorithm. Figures 13(a) and (b) describe the slip velocity and slip distance of each wheel. The total slip distance induced by the traction control system is 432 mm, compared to 726 mm using the velocity control system, as shown in Ta-

12 Fig. 15 Applied torque of wheel while the mobile robot climbs the stairs Auton Robot Fig. 16 Snapshots of ROBHAZ-6WHEEL climbing stairs in experiments ble 3. The improvement is 40.5%. As noted in the previous section, slip occurs in two wheels with the velocity control algorithm. For a specific wheel, slip can be locally higher with traction control than with velocity control. However, the slip distance is always smaller with traction control for all time domains. Figures 13(c) and (d) show the dissipated power and dissipated work on the contact point of the wheel. The reduc-

13 Fig. 17 Experiment results during stair climb (a) Applied torque of wheels (b) Power consuption of wheels

14 Fig. 17 (Continued) Auton Robot (c) Work done by wheels tion of total dissipated work on the contact points is 48.4%, and is attributed to reduced slip velocity of the wheels. 5 Experiment results Two experiments are performed in order to validate the simulation model and the proposed algorithm. Experiments are prepared as shown in Fig. 14. Via a CAN (Controllable Area Network) communication system, the control torque is sent to a motor driver and the angular velocity is obtained. The first experiment is performed to validate the simulation model implemented in Sect. 4. With the same conditions as employed in the simulation, the applied wheel torque is measured while the mobile robot traverses the stairs with constant wheel velocity. Figure 15 shows the experiment results agree well with those of the simulation, and thus it is concluded that the integrated simulation model in ADAMS and MATLAB toolbox accurately describes the real system. An exact simulation model can guarantee reduced slip in the simulation results. Periodic jitter motion observed in the experiment is due to a misaligned harmonic gear in the wheel modules. In the second experiment, the mobile robot was commanded to traverse stairs having the same dimensions as in the previous experiment. Figure 16 shows the mobile robot climbing the stairs with the proposed traction control algorithm. The total distance traveled along the surface of the stairs is roughly 1.3 m. In order to test the performance of the traction control algorithm, we measured and compared the angular velocity and applied torque of the wheel. Figure 17 shows the power consumption and work done by the wheels during stair climbing. The total energy consumed using the traction control algorithm is 87.2 J compared to J when the velocity control algorithm is employed. Although the total works done by wheel 1 with the traction control algorithm is almost the same as that with velocity control, the total work done with the traction control algorithm is 25.6% smaller than that with velocity control. Notably, the proposed traction control algorithm saves energy and increases the mobility of the mobile robot by reducing wheel slip without using extra sensors or devices. We compared work done by the wheels, because reduced work means dissipated work on the contact points is reduced. Reduction of dissipated energy can be caused by reduced torque or reduction of slip speed. Reduction of wheel slip mainly causes a reduction in dissipated energy, since the torque required to traverse the stairs is of a similar level of magnitude. Therefore, slip with the proposed traction control is less than that of velocity control.

15 6 Conclusion In this paper, a traction control algorithm to improve wheel traction and reduce power consumption has been presented. This algorithm can be implemented in each wheel with only angular velocity information. The algorithm is developed based on the stick-slip phenomenon; it linearly increases or decreases the torque applied to the wheels in order for the traction to converse to the interval between the maximum static friction and kinetic friction. An integrated model including the dynamics of the mobile robot and the controller is established for simulations. Simulation results for traversing stairs demonstrated that the proposed algorithm leads to higher mobility and less power consumption than the conventional velocity control algorithm by reducing wheel slip. It is verified in experiments that the integrated model used in the simulation phase is reliable. 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Motion dynamics of a rover with slip-based traction model. In Proceedings of the 2002 IEEE international conference on robotics & automation. Hyun Do Choi graduated with BS in Department of Mechanical Engineering from Pusan National University, Korea in He received the MS degree from KAIST in He is currently a PhD candidate in Mechanical Engineering in the same school. His research interest includes mechanism design, traction control of mobile robot, and piezoelectric motor. Chun Kyu Woo graduated with BS in Department of Mechanical Engineering from Pusan National University, Korea in He received the MS degree from KAIST in He is currently a PhD candidate in Mechanical Engineering in the same school. His research interest includes mechanism design of mobile robot and embedded system.

16 Soohyun Kim graduated with his B.S. degree in Mechanical Engineering from Seoul National University in 1978 and went to KAIST, where obtained got the M.S. degree in Mechanical Engineering in He got his Ph.D. degree from the Imperial College of Science and Technology, University of London in He is now a Professor wish KAIST. He has authored many articles/papers published in archival international journals and conference proceedings. His research interests are micro-actuation, miniature mechanisms, precision mechanisms, and optical methods for micro/nano motion sensing and control. Sukjune Yoon received his B.Sc., M.Sc. and Ph.D. in Mechanical Engineering from Korea Advanced Institute of Science and Technology in 1999, 2001, 2005, respectively. His research is concerned with field and service robots, especially vision-based localization and map building. He is currently a senior engineer at the Samsung Electronics CO. LTD. Yoon Keun Kwak graduated with the B.S. degree in Mechanical Engineering from Seoul National University, Korea in He received the M.S. degree in Engineering Design and Economic Evaluation from the University of Colorado, Boulder, USA in 1974 and the Ph.D. degree in Mechanical Engineering from the University of Texas, Austin, USA in He is now a Professor of Mechanical Engineering with KAIST. His research interests are the design, control and application of an emotional robot system and an offroad mobile robot system.