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AuthorsPo-Er Hsu (2013-01-28); recommended: Yeh-Liang Hsu (2013-02-10).
Note: This article is the Chapter 4 of Po-Er Hsu’s doctoral thesis “Development of an intelligent robotic wheelchair as the center of mobility, health care, and daily living of older adults.”

Chapter 4. Seat adjustment design of the intelligent robotic wheelchair based on the Stewart platform

This chapter presents the multiple-degrees-of-freedom (DOF) seat adjustment mechanism of the iRW. The seat adjustment mechanism of the iRW is achieved by a four-axis Stewart platform [1965], which is a parallel structure robot that has greater stiffness, positioning accuracy, and payload-to-weight ratio than do serial structure robots.

The multiple-DOF seat adjustment mechanism developed in this research is capable of the motions of heaving, pitching, and swaying to provide a comfortable sitting posture, seat elevation adjustment function, and transfer activities assist. Special consideration is paid to arranging the actuators to reduce the control complexity of the parallel mechanism, so that the wheelchair user can make the seat adjustment by simply pressing a button. Equipped with soft pressure-sensing units, the seat also provides pressure management by adjusting the seat mechanism when continuous, concentrated pressure is detected.

4.1      Design concept of the multiple-degrees-of-freedom seat adjustment mechanism

The literature review in Chapter 1.2 indicated that a wheelchair seat adjustment mechanism should meet the following design requirements:

(1)     Tilt-in-space

Tilt-in-space is important for pressure management and comfortable sitting posture. Aissaoui et al. [2001] found that an effective weight shift could be achieved when tilt-in-space angle was at least 15°. Sonenblum et al. [2006] evaluated 10 participants and found that none required an angle of tilt-in-space function as great as 20°. Ding et al. [2008] concluded from a survey that the most often-used ranges of tilt-in-space angles were 2.5° to 10°, followed by 10° to 20°, and their frequency and time were 6.6 ± 4.9 times for 272.7 ± 228.7 minutes and 7.3 ± 6.6 times for 157.3 ± 171.8 minutes a day. Based on the literature above, the range of tilt-in-space angle of the iRW was set to be 20°.

(2)     Seat elevation / Sideways movement

The capabilities of adjusting seat elevation and sideways movement by the wheelchair user enhance transfer activities assist. Seat elevation adjustment is used to reduce the height difference when performing transfer activities. To accommodate the height of facilities in the living environment where transfer activities often occur, e.g., a range in height of a toilet from 279 to 432 mm and of a bed from 430 to 485 mm [Americans with Disabilities Act Accessibility Guidelines (ADAAG) for buildings and facilities, 2002], the seat elevation adjustment of the iRW ranges from 370 to 490 mm. The seat can move sideways a maximum of 150 mm, which is believed sufficient to cover the gap when crossing between wheelchair and target surface.

(3)     Practical considerations

Besides the functional requirements, the size, weight, and control complexity of the adjustment mechanism were considered. The specifications for 16 models of electric wheelchairs commercially available in Taiwan were examined, and their average size was 910×640 mm (L×W). These dimensions were taken as the upper limit for the iRW. Moreover, the wheelchair user should be able to make the seat adjustment in all DOFs by simply pressing a button, and stop the seat movement by releasing the button.

The seat adjustment mechanism of the iRW is based on the Stewart platform. The seat adjustment mechanism has three DOFs: heave, sway, and pitch. These facilitate tilt-in-space, seat elevation, and moving sideways.

The Stewart platform has been used in flight simulators [Advani et al., 2002], machine tools [Ting et al., 2004], a biped locomotion system [Sugahara et al., 2005] and surgery manipulators [Wapler et al., 2003; Tsai et al., 2007]. The Stewart platform, illustrated in Figure 4-1, is composed of a fixed base, a movable platform, and six linear actuators connecting the fixed base to the movable platform. This is a six-DOF universal-prismatic-spherical mechanism, which supports heave, surge, sway, yaw, pitch, and roll. No additional structural members are needed in the Stewart platform because the actuators also function as structural members. One drawback of the Stewart platform is the small workspace. Another is complexity in control, which is due to the need to control six linear actuators simultaneously in a nonlinear manner and to the existence of singular positions.

Figure 4-1. Schematic diagram and degrees of freedom of Stewart platform

In this research, the Stewart Platform is converted into a multiple-DOF seat adjustment mechanism, as shown in Figure 4-2. The seat acts as the movable platform of the Stewart platform, and the h-shape structure of the omni-directional moving vehicle of the iRW acts as the fixed base of the Stewart platform. The number of linear actuators is reduced from six to four because only three DOFs (heave, pitch, and sway) of seat adjustments are required. The seat and actuators are connected with universal joints, and the omni-directional moving vehicle and actuators are coupled with two revolute joints and two universal joints.

Figure 4-2. The multiple-DOF seat adjustment mechanism of the iRW

Figure 4-3 depicts the multiple-DOF seat adjustment mechanism of the iRW. Actuators 1 and 2 are fixed at an incline of 20° from the y-z plane. Actuators 1 and 2 extend or retract at the same constant speed to provide a smooth adjustment. An offset angle (7.4°) between Actuators 1 and 2 and the z-axis provides a horizontal force component when swaying sideways (i.e., in the +y direction). Actuators 3 and 4 are fixed at an incline of 20° from the y-z plane. The offset angle (7.4°) and direction (+y direction) of Actuator 4 are the same as for Actuators 1 and 2. To constrain the DOFs, the offset angle between Actuator 3 and the z-axis, 10.6°, differs from that of the other actuators.

Table 4-1 shows the coordinated actions of actuators when the seat is adjusted. For example, when raising the seat, Actuators 1 and 2 retract, and Actuators 3 and 4 extend. When adjusting the seat to the right, Actuators 1, 2, and 4 extend, and Actuator 3 retracts. In this setup, the initial height of the seat is 414 mm. The range of height adjustment is from 370 mm to 488 mm, limited by the stroke of the actuators. The range of tilt-in-space angle is from -15° to 22°. The -15° tilt-in-space can be used in sit-to-stand assist. The range of moving sideways varies with the height of the seat. At the initial height of 414 mm, the range of moving sideways is 140 mm. Table 4-2 shows the fundamental specifications of the linear actuators and the iRW.

Figure 4-3. The multiple-DOF seat adjustment mechanism in front and side view

Table 4-1. Coordinated actions of actuators

Adjustment

Direction

Actuator 1

Actuator 2

Actuator 3

Actuator 4

Heave

Retract

Retract

Extend

Extend

Extend

Extend

Retract

Retract

Pitch

Extend

Extend

Extend

Extend

Retract

Retract

Retract

Retract

Sway

Extend

Extend

Retract

Extend

Retract

Retract

Extend

Retract

Table 4-2. Specifications of the linear actuator and the iRW

Device

Characteristic

Value

Actuator (HIWIN LAS3-1)

Tensile / Thrust / Self-locking force

1200 / 1200 / 800 (Max, N)

Stroke

150 mm

Speed (maximum / minimum load)

8 / 12 mm/s

Optical sensor accuracy

0.3175 mm/pulse

Voltage / Current

24 V / 2.5 (A, Max)

iRW

L×W×H

800×610×870 mm

Initial height of the seat

414 mm

Range of the seat elevation

370 ~ 488 mm

Range of the tilt-in-space

22° (clockwise) / -15° (counterclockwise)

Range of the transfer activities assist

Varies with height of the seat, 140 mm at the initial height

4.2      Simulation of the multiple-degrees-of-freedom seat adjustment mechanism

As shown in Figure 4-4, Actuators 1, 2, and 4 are designed to extend or retract at the same constant speed when the wheelchair user pushes a button to perform tilt-in-space, change elevation, or move sideways. Actuator 3 is the only actuator that has to be controlled in a nonlinear manner to maintain the seat in a horizontal orientation when adjusting elevation or moving sideways.

This section presents the results of using SimWise 4D ver. 8.0.2 to examine how the motion of the seat was affected by the length of each actuator. This simulation also confirmed the ranges of the seat adjustment described in Table 4-2.

Figure 4-4 shows the simulation result of adjusting seat elevation from 370 mm to 488 mm in 10 seconds. The origin represents the center of the seat. Figure 4-4(a) shows that the motion of all actuators appears to be linear. In particular, the lengths of Actuators 1 and 2 remained equal throughout, and the change in their length was inversed to the change in length of Actuator 4. Figure 4-4(b) shows that the seat slightly moved forward or backward (i.e., along the x-axis) when the height of the seat was changed. The range of this moving distance along the x-axis was 43 mm.

Figure 4-4. Simulation of seat elevation

Figure 4-5 shows the simulation result of the tilt-in-space at the initial height, from -15° (counterclockwise) to 22° (clockwise) in 10 seconds. Figure 4-5(a) indicates that the change in length of all actuators appears to be linear. In particular, the lengths of Actuators 1, 2, and 4 remain equal. Figure 4-5(b) shows that the seat maintains a constant horizontal orientation within the y- and z-axes while undergoing tilt-in-space along the x-axis.

Figure 4-5. Simulation of tilt-in-space

Figure 4-6 shows the simulation result of the seat moving sideways 140 mm from its initial position. Figure 4-6(a) indicates that the lengths of Actuators 1, 2, and 4 remain equal throughout, while the length of Actuator 3 varies nonlinearly. Figure 4-6(b) shows that the seat itself maintains a constant horizontal orientation (z- and x-axes) while moving sideways in the +y direction.

Figure 4-6. Simulation of sideways movement

In all three simulations, the absolute values of the speeds of Actuators 1, 2, and 4 remained constant. This simplifies the design of the control scheme, which is discussed in the next section.

4.3      Control scheme for the multiple-degrees-of-freedom seat adjustment mechanism

On the iRW, the user would adjust the seat by pushing one of three buttons located on the armrest, which correspond to tilt-in-space, seat elevation adjustment, or moving sideways. Actuator 1, 2, and 4 extend / retract at a preset constant speed at all time. The extend / retract speed of Actuator 3 would be calculated by an Arduino microcontroller.

Figure 4-7 shows how the speed of Actuator 3 would be derived when the seat moves sideways. The coordinates of the joints of the four actuators on the fixed base and the position of the movable platform (the seat) are known. There is an optical sensor in each actuator that detects its current stroke, i.e., the amount of extension of the actuator. As shown in Figure 4-7, the current coordinates of the joint of Actuator 3 at the movable platform J3, expressed as (x3, y3, z3), can then be calculated. When the wheelchair user pushes a button to move the seat sideways, Actuators 1, 2, and 4 start to extend at the same constant speed. After a small interval of time t, the coordinate of J3 would need to become (x3, y3 + y, z3), which is calculated from the expected changes of the strokes of Actuator 1, 2, and 4 after this time interval. In the program in the Arduino microprocessor, t = 0.04 second (25Hz). The expected change of the stroke of Actuator 3 can then be easily calculated and expressed as a “speed ratio” of Actuator 3 to Actuators 1, 2 or 4. This “speed ratio” is then implemented in the pulse-width modulation (PWM) control of the Arduino microcontroller, in which the motor speed control is digitized on a scale of 0~255. The movement stops when the wheelchair user releases the button, or when one of the actuators reaches its limit.

Figure 4-7. Derive the speed of Actuator 3 when the seat moves sideways

The seat control scheme was implemented in a prototype. A test was performed to confirm that the seat maintains a constant orientation when it is being adjusted. A tri-axial accelerometer module (KXPA4-2050, Kionix) set up at the center of the seat was used to detect its orientation.

The accelerometer module has a built-in low-pass filter at the cutoff frequency of 50 Hz. The module’s sensing range along each axis is ±2 g, and its output varies with acceleration at the rate of 660 mV/g. If there is no acceleration applied along an axis, the output voltage Voff equals half Vdd (3.3 V). If acceleration A exists toward the positive direction, the output voltage increases (Vout > Voff) and vice versa. Equation (1) shows the relation:

                                                                 (1)

Tilt / inclination sensing is a common application for low-g accelerometers. Figure 4-8 indicates the tilt angles (pitch and roll) of the seat, where φ, ρ, and θ represent the tilt angles with respect to the x-, y-, and z-axes relative to ground. Equation (2) identifies the relation between the tilt angles and accelerations along each axis. Note that in pitch, θ + φ = 90°, while in roll, θ + ρ = 90°.

                                                                                                  (2)

Figure 4-8. Pitch and roll represented as changes in angle along the coordinate axes

In the initial setup, the height of the seat is 414 mm, and the angle φ is + 5°. As shown in Figure 4-9, two conditions were considered: the seat was empty (continuous lines) and the seat was loaded with a 70 kg mass (short dash lines).

Figure 4-9. Resulting values of the tilt angles for each type of seat movement

Figure 4-9(a) shows the values of the tilt angles while the seat elevation was raised from 370 mm to 488 mm in about 8 seconds. When no mass was loaded on the seat, the angle φ obtained from the accelerometer module maintained at 4.73° ± 0.43° to ground, while angle θ maintained at 85.21° ± 0.44° to ground during the elevation process. When the seat was loaded with the mass, the angle φ obtained was 4.26° ± 1.70° to ground.

Figure 4-9(b) shows the values of the tilt angles while the seat’s tilt-in-space changed from -15° to 22° in about 8 seconds. Note that when θ exceeds 90°, the arctan function in Equation (2) will generate a θ value less than 90°. Therefore both the arctan value and the true angle θ are displayed in Figure 4-9(b).

Figure 4-9(c) shows the values of the tilt angles while the seat, which was maintained at the initial height of 414 mm, was adjusted sideways from 0 mm to 140 mm in about 8 seconds. The angle φ maintained at 6.14° ± 0.24° when there was no mass loaded on the seat. When the seat was loaded, the angle φ maintained at 5.61° ± 1.84°. The results depicted in Figure 4-9 indicate that the orientation of the seat remained stable when using the proposed control scheme, though the 70 kg mass has some effect to the stability.

Figure 4-10 depicts the flow chart for processing a user’s pressing a button to move the seat. To avoid different functions’ disrupting each other and to foster safety, there are three basic rules in the control flow:

(1)     Only one function can be performed at a time. If two buttons are pressed at the same time by the wheelchair user, neither function will operate.

(2)     To start seat elevation adjustment or the tilt-in-space function, the distance of sideways movement has to be zero. If this distance is not zero, the seat will automatically move back to the center vertical axis, after which the requested movement will be carried out.

(3)     To start sideways movement, the angle of tilt-in-space has to be zero. If this angle is not zero, the seat automatically will move back to the horizontal plane while maintaining its height, after which the requested movement will be carried out.

The seat also provides pressure management function by automatically adjusting the tilt-in-space when continuous, concentrated pressure is detected by the soft pressure-sensing units. As shown in the flowchart in Figure 4-10, when no buttons are pressed, if the pressure distribution is not changed in 30 minutes, the tilt-in-space function will start to increase (or decrease) five degrees of seat angle in 60 seconds automatically. The pressure management function will be interrupted if the wheelchair user pushes any button during the 60 seconds.

Figure 4-10. Flow chart for processing a user’s pressing a button to move the seat

References

Aissaoui R., Lacoste M., Dansereau J., 2001. “Analysis of sliding and pressure distribution during a repositioning of persons in a simulator chair,” IEEE Trans Neural Syst Rehabil Eng., v. 9, pp. 215-224. [PMID: 11474974]

Advani S., Giovannetti D., Blu M., 2002. “Design of a Hexapod Motion Cueing System for the NASA Ames Vertical Motion Simulator,” AIAA Modeling and Simulation Technologies Conference.

Americans with Disabilities Act Accessibility Guidelines (ADAAG) for buildings and facilities, 2003. Accessible elements and spaces: scope and technical requirements.

Ding D., Leister E., Cooper R. A., Cooper R., Kelleher A., Fitzgerald S. G., Boninger M. L., 2008. “Usage of tilt-in-space, recline, and elevation seating functions in natural environment of wheelchair users,” J Rehabil Res Dev., v. 45, pp. 973-983.

Sonenblum S. E., Sprigle S., Maurer C., 2006. “Monitoring power upright and tilt-in-space wheelchair use,” the Rehabilitation Engineering and Assistive Technology Society of North America (RESNA) Conference.

Stewart D., 1965. “A platform with six degrees of freedom,” Proc. Inst. Mech. Engrs., part 1, p 371-386.

Sugahara Y., Ohta A., Hashimoto K., Sunazuka H., Kawase M., Tanaka C., Lim H. O., Takanishi A., 2005. “Walking Up and Down Stairs Carrying a Human by a Biped Locomotor with Parallel Mechanism,” Intelligent Robots and Systems, pp. 3425-3430.

Ting Y., Chen Y. S., Jar, H. C., 2004. “Modeling and control for a Gough-Stewart platform CNC machine,” Journal of Robotic Systems 21, v. 11, pp. 609-623.

Tsai T. C., Hsu Y. L., 2007. “Development of a parallel surgical robot with automatic bone drilling carriage for stereotactic neurosurgery,” Biomedical Engineering: Applications, Basis and Communications, v. 19, pp. 269-277.

Wapler M., Urban V., Weisener T., Stallkamp J., Durr M., Hiller A., 2003. “A Stewart platform for precision surgery,” Transactions of the Institute of Measurement and Control 25, v. 4, pp. 329-334.