Walking Support and Power Assistance of a Wheelchair Typed Omnidirectional Mobile Robot with Admittance Control

Walking ability is essential for the elderly/the disabled’s self-supported daily life. Currently the development of various robotic aids or devices for helping the elderly’s walking has attracted many researcher’s attentions. Guidecane ((Ulrich & Borenstein, 2001)), PAM-AID ((Lacey & Dawson-Howe, 1998)), Care-O-bot ((Graf et al., 2004)), PAMM ((S. Dubowsky, 2000)), and etc, are developed for intelligent walking support and other tasks for the elderly or the disabled. Mainly for the elderly’s walking support, a robotic power-assisted walking support system is developed (Nemoto & M. Fujie, 1998). The system is to support the elderly needing help in standing up from the bed, walking around, sitting down for rehabilitation. Meanwhile, a number of intelligent wheelchair-type aids are being designed for people who cannot walk and have extremely poor dexterity ((Yanco, 1998)-(Dicianno et al., 2007)). These devices are well suited for people who have little or no mobility, but they are not appropriate for the elderly with significant cognitive problems. Consequently, the facilities are generally reluctant to permit the elderly residents to use powered wheelchairs. Hence, the better solution is that the facility staff (the caregiver) pushes the wheelchair to move. Some technologies for the caregiver’s power assistance are proposed ((Kakimoto et al., 1997)-(Miyata et al., 2008)). Further, since the omnidirectional mobility is necessary to truly yield the user’s (here refer to the elderly/disabled, or the caregiver) intentions of walking speed and direction, omnidirectional mobility is investigated in order to obtain a smooth motion and high payload capability, not with the special tires but with the conventional rubber or pneumatic tires. An omnidirectional and holonomic vehicle with two offset steered driving wheels and two Walking Support and Power Assistance of a Wheelchair Typed Omnidirectional Mobile Robot with Admittance Control 5


Introduction
Walking ability is essential for the elderly/the disabled's self-supported daily life. Currently the development of various robotic aids or devices for helping the elderly's walking has attracted many researcher's attentions. Guidecane ( (Ulrich & Borenstein, 2001)), PAM-AID ( (Lacey & Dawson-Howe, 1998)), Care-O-bot ( (Graf et al., 2004)), PAMM ((S. Dubowsky, 2000)), and etc, are developed for intelligent walking support and other tasks for the elderly or the disabled. Mainly for the elderly's walking support, a robotic power-assisted walking support system is developed (Nemoto & M. Fujie, 1998). The system is to support the elderly needing help in standing up from the bed, walking around, sitting down for rehabilitation. Meanwhile, a number of intelligent wheelchair-type aids are being designed for people who cannot walk and have extremely poor dexterity ( (Yanco, 1998)- (Dicianno et al., 2007)). These devices are well suited for people who have little or no mobility, but they are not appropriate for the elderly with significant cognitive problems. Consequently, the facilities are generally reluctant to permit the elderly residents to use powered wheelchairs. Hence, the better solution is that the facility staff (the caregiver) pushes the wheelchair to move. Some technologies for the caregiver's power assistance are proposed ( (Kakimoto et al., 1997)- (Miyata et al., 2008)). Further, since the omnidirectional mobility is necessary to truly yield the user's (here refer to the elderly/disabled, or the caregiver) intentions of walking speed and direction, omnidirectional mobility is investigated in order to obtain a smooth motion and high payload capability, not with the special tires but with the conventional rubber or pneumatic tires. An omnidirectional and holonomic vehicle with two offset steered driving wheels and two Walking Support and Power Assistance of a Wheelchair Typed Omnidirectional Mobile Robot with Admittance Control 5 free casters is proposed (Wada & Mori, 1996). An omnidirectional mobile robot platform using active dual-wheel caster mechanisms is developed (Han et al., 2000), in which, the kinematic model of the active dual-wheel caster mechanism is derived and a holonomic and omnidirectional motion of the mobile robot using two such assembly mechanisms is realized. An omnidirectional platform and vehicle design using active split offset casters (ASOC) is also developed (Yu et al., 2004). Its structure is very similar to (Han et al., 2000), but particular attention is paid to the system performance on uneven floors. However, up to now, the wheelchair typed robot that can be used either for the elderly's walking support, or the disabled's walking rehabilitation, or the caregiver's power assistance has not been reported yet. In this study, we develop such kind of wheelchair typed omnidirectional robot that not only can support the elderly or the disabled's walking, but also can lessen the caregivers' burden, or saying, give the caregivers power assistance.

Overview of the developed robot
The developed new type of omnidirectional mobile robot for the elderly's walking support, the disabled's rehabilitation, and the caregiver's power assistance, is shown in Fig. 1. Its structure is illustrated in Fig. 2.

The robot objective and functions
Different from the other intelligent aids, the robot has a handle and a seat. The user holds the handle with his/her hands during walking. Usually, the elderly's walking ability (the capable walking distance), can be greatly enhanced with the help of the intelligent walking support devices. However, because of the muscle weakness, the knee and waist of the elderly will be painful after walking some distances. At that time, the elderly hopes to have a seat for a rest.
To meet such a very actual requirement, we embed a seat in the robot so that the elderly or the disabled can take a seat for rest when necessary. On the other hand, when the elderly or the disabled is sitting in the seat of the wheelchair type aids and wants to go to somewhere, the caregiver will have to push the wheelchair. Hence, the power assistance of the health caregivers is also necessary. Consequently, the main the objectives of the robot are To meet the above two main objectives, the functions the robot should have: 1. omnidirectional mobility.
2. few load feeling when the user (the elderly/disabled /caregiver) holding the handle during walking or pushing the robot.
3. guidance to destinations and obstacle avoidance via sensors and pre-determined maps.
4. adaptation to the different motion abilities of the different users.

Robot structure
The robot shown in Fig.1, 2 is considered to be used either indoor or outdoor. It includes two active dual-wheel modules and two free casters that provides the robot omnidirectional mobility. It will be discussed in section 3 in detail. A 6-axis force/torque sensor, mounted on the shaft of the handle, detects the forces and torques the user applies to the handle. With these force/torque signals, the embedded computer estimates the user's intention of walking velocity and walking direction, and the robot is controlled to yield the user's intention so that the user will feel few loads to fulfill the walking support and power assistance. The detail will be explained in section 4. The 2D laser ranger/area finder is employed to detect the obstacles.  the door, corner, elevator are used to identify the robot position and orientation. They are used for the destination guidance and obstacle avoidance. The problems of such obstacle avoidance and navigation are not discussed in this chapter. The control system of the robot as shown in Fig. 3 consists of a board computer running RTLinux operation system, an multi-functional interface board, two motor drivers in which each motor driver can drive two motors.

Omnidirectional mobility
The wheels of the robot consists of two active dual-wheel modules and two free casters. The two active dual-wheel modules enable the robot omnidirectional mobility and the two free casters keep the robot balance. First we analyze the kinematics of one dual-wheel module, than investigate the omnidirectional mobility of the robot realized by two dual-wheel modules.

Kinematics of one dual-wheel module
As shown in Fig. 4, an active dual-wheel module consists of two independently driven coaxial wheels, which are separated at a distance 2d and connected via an offset link s to the robot at the joint O i . The coordinate systems, valuables, and parameters are defined as follows.
x wi ,ẏ wi : velocities of the joint O i respectively in the X w , Y w axes. φ i : orientation of the module i with respect to the world frame. u i , u wi : velocity vectors of the joint O i respectively with respect to the frame where J i is the Jacobian matrix of the module in the moving frame O i X i Y i . On the other hand, the velocity of the joint O i expressed in the world system is given by Therefore, the kinematics of the module between the velocity of the joint O i and the two wheel rotation velocities is expressed as: where J wi is the Jacobian matrix of the module in the world frame O w X w Y w , and it is given as: The above expressions indicate that the velocity of the module is determined by the parameters s, d, r, and ω ri , ω li . But since s, d, r are structurally determined for a robot, the only controllable values are angular velocities ω ri , ω li of the two driving wheels. The determinant of J wi is : This means that the module has no singularity as long as the distance s is not zero. This fact implies that arbitrary and unique velocities at the joint point O i can be achieved by appropriately controlling the rotational velocities of the two wheels. Note that one such a module only has 2DOF. In other words, omnidirectional mobility (3DOF) cannot be achieved. Consequently, at least two modules are necessary to realize omnidirectional mobility. In this study, two modules are used to achieve the omnidirectional mobility.

Omnidirectional mobility with two modules
As shown in Fig.5, two active dual-wheel modules consists of a basic part of the mobile robot that enable the robot to have omnidirectional mobility. In Fig. 5, point O is the center of the robot platform. Its coordinates and velocities in the T is the velocity vector of the robot. The distance between the two joint points of two modules is L. ω = [ω r1 , ω l1 , ω r2 , ω l2 ] T is the angular velocity vector of the four driving wheels of the robot.
To obtain the rotational velocityφ of the robot, it it convenient to transformẋ wi ,ẏ wi in the world frame to the robot frame OX R Y R . The relationship is given by Therefore,φ of the robot can be expressed aṡ Hence, the velocity vector V can be expressed as: From (3), the velocity vector [ẋ w1 ,ẏ w1 ,ẋ w2 ,ẏ w2 ] T in the above expression is given by ⎡ where Furthermore, the robot possessing omnidirectional mobility realized by two active dual-wheel modules has three degrees of freedom with a total of four actuators. There should be a constraint for this redundancy. The physically constant distance between the two joint points O 1 and O 2 is used to eliminate the redundancy. It leads the following velocity constraint: From (6) it means 0 =ẋ w1 sin φ −ẏ w1 cos φ −ẋ w2 sin φ +ẏ w2 cos φ By combining Eqs. (9), (10) and (13), we can get the following homogeneous forward kinematics of the robot: Hence, the inverse kinematics of the robot, i.e., with the given desired velocity vector V d of the robot, the necessary driving velocity vector ω d of the four wheels is given by where, Now by rewriting B −1 as: We can get the following inverse kinematic equation of the robot: As discussed in section 4, the V d , the desired velocity of the robot, is obtained from the introduced admittance controller, and the ω d , each wheel's speed command, is used for velocity control.

Admittance based interaction control for power assistance
Admittance of a mechanical system is defined as (Newman (1992)) where, V is the velocity and F is the contact or applied force, both at the point of interaction. A large admittance corresponds to a rapid motion induced by applied forces; while a small admittance represents a slow reaction to act forces.
Here, admittance controller is introduced in order to fulfill the power assistance when the elderly/disabled holding the handle to walk or the caregiver holding the handle to push the robot while the elderly or the disabled sitting in the seat. Since user's (the elderly, the disabled, or the caregiver) walking speed doesn't change a lot, a large admittance implies relatively small forces needed to exert to the robot. This is the basic principle of power assistance. Note that almost similar approaches had been already used for the elderly's walking support (Nemoto & M. Fujie (1998); Yu et al. (2003)), since our robot can be used both by the elderly/disabled and the caregiver, the approach is extended to the caregiver's power assistance.
In this study, the admittance of the human-robot system can be defined as a transfer function with the user's applied forces and torques, F (s), as input and the robot's velocities, V (s), as the output. The time response V d (t) of the admittance model is used as the desired velocity of the robot. Then, the desired driving speed ω d of each wheel is calculated from V d (t) by the inverse kinematics equation (20), and the ω d , as each wheel's speed command, is used for velocity control. The admittance based control process is shown in Fig.6, in which a digital LF (low-pass filter) cuts off the high frequency noises in the force/torque signals from the 6-axis force/torque sensor. In the forward direction (X R direction in Fig.5), the admittance can be expressed as where, M x and D x are respectively the virtual mass and virtual damping of the system in forward (X R ) direction.

Force sesnor
Admittance model The time response V xd (t) for a step input F x of the above transfer function is: where, τ x is the time constant defined by τ x = M x /D x . The steady state velocity of the system is V xs = F x /D x . This means that the forces to the robot exerted by the user determines the velocities of the system (user and machine). In other words, when the user's steady forward walking velocity is V xs (this velocity usually doesn't change a lot for a user), then the necessary pushing force F xs , or saying, the burden the user feels reacted from the robot, should be Thus, by adjusting the virtual damping coefficient D x , the user will have different burden feeling. And further by altering virtual mass coefficient M x (therefore τ x is changed), we can get the different dynamic corresponds of human-machine system. Our experiments will verify this.

Experiments and remarks
The omnidirectional mobility of the robot is experimentally implemented in (Zhu et al., 2010).
Here, the developed admittance based interaction control is tested. The sampling and control period is 1 [kHz]. As shown in Fig. 7, a user is holding the robot handle to move the robot forward, or lateral, or tuning on the spot while a 65[kg] person sitting in the seat.

Forward experiment without power assistance
First, we turn off the motor drivers and do the experiment without power assistance. In this case, the motors are in free state and the robot is just like a traditional manual-operated wheelchair. From the the result shown in Fig. 8 (24). The purpose of power assistance for the caregiver is achieved. In addition, Fig. 9 indicates that a slow and big pushing force occurs at the start to move the robot, while there is no such phenomenon in Fig. 10. This can be explained as follows. The parameter M x , the virtual mass coefficient, is set to be 15.4[kg] in Fig.9 and M x is 7.0[kg] in Fig.10. Since mass is a metric of inertia, the more the inertia of an object is, the slower the object starts to move. But a too small M x will make the system too sensitive to the exerted force. This will lead to the user fearful to use the robot. user's burden) is well controlled by the admittance based controller. In Fig. 10 there occurs a comparatively big force for starting to move the robot. As aforementioned, this is caused by a relatively big mass coefficient M x . How to optimally select the two parameters is one of our future tasks.

Lateral experiments without power assistance
We turn off the motor drivers and do the experiment without power assistance. In this case, the motors are in free state. From the the result shown in Fig. 13

Turning-on-the-spot experiment without power assistance
We switch off the motor drivers and do the experiment without power assistance. In this case, the motors are in free state. From the the result shown in Fig. 15 Fig. 16. Turning-on-the-spot experimental result with assistance (as D z = 6 and τ z = 0.5)

Conclusions
In this research, we developed a new type of omnidirectional mobile robot that not only can fulfill the walking support or walking rehabilitation as the elderly or the disabled walks while holding the robot handle, but also can realize the power assistance for a caregiver when he/she pushes the robot to move while the elderly or the disabled is sitting in the seat. The omnidirectional mobility of the robot is analyzed, and an admittance based human-machine interaction controller is introduced for power assistance. The experimental results show that the pushing force is reduced and well controlled as we planned and the purpose of walking support and power assistance is achieved.