Waalbot - NanoRobotics Lab - Carnegie Mellon University

More documents

Recommendations

Info

MURPHY AND SITTI: WAALBOT: AN AGILE SMALL-SCALE WALL-CLIMBING ROBOT UTILIZING DRY ELASTOMER ADHESIVES 333 wall during climbing can be found by examining the case when only one foot per side is attached and the C g is at its furthest distance from the surface [(Fig. 5(b)]. The quasi-static equation for this case giving a maximum force that the adhesives must be able to provide is represented as F Rn = W L t ( Lycg(max) sin θ − (L t − L xcg )cosθ ) . (2) If this force exceeds the magnitude of F cr then, the robot will detach from the surface. Therefore, this equation gives the minimum adhesive performance needed to climb. Because of the consequences of a fall, a safety factor is used when choosing an adhesive and adhesive foot area. Graphing this function with the known design parameters of the robot, it is possible to find the maximum peeling force over all angles. For the prototype parameters the maximum peeling force occurs at a climbing angle of 160 ◦ . The corresponding minimum for the critical peeling force of the adhesive F cr is 0.43 N. This value must be supported by the adhesives for the robot to climb on surfaces of all slope angles, and represents one of the adhesive requirements. From (2), it is clear that in order to minimize the peeling force on the adhesive pad during climbing, the length of the tail should be increased, and the center of gravity should be moved close to the wall. Also, the weight of the robot should be minimized. This can be accomplished through fabricating the robot from lighter materials or through miniaturization. Miniaturization is advantageous to this robot design because mass is proportional to L 3 while the adhesion is proportional to area, i.e., L 2 , where L is the characteristic length. As the robot shrinks in size, the adhesion becomes less than the gravitational force, so we see an increase in the performance of the robot. Both (1) and (2) suggest that the tail should be long to increase the preload force and to minimize the peeling force. However, it is important to note that the weight of the robot is also increased with the tail length, so there is a coupling between W and L t . Furthermore, a longer tail increases the amount of room necessary for turning, as the tail may sweep out and contact obstacles causing the robot to lose adhesion and fall. So a longer tail limits the ability to climb in small areas. Therefore, for maximum performance without compromising agility, the tail length is chosen to be the longest length possible while remaining fully within the turning circle (described in Section IV). With these parameters fixed, it is necessary to examine the adhesive to determine whether these requirements can be met. B. Adhesive Requirements The values from Figs. 2 and 6 and (2) are used to create a set of requirements for the adhesive. For the <strong>Waalbot</strong> to have the ability to climb on vertical surfaces of θ =90 ◦ , the operating critical peeling force must be no less than 0.16 N (2) and the adhesive must hold with a minimum of two times as much force as it was preloaded with (Fig. 6) at this operating peeling force. To visualize such a requirement it is convenient to plot an adhesive–substrate performance curve with bounds, which represent the requirements as in Fig. 7. Using this representation Fig. 7. Performance curve plotted with ratio lines for various surface slope angles. For a surface slope of 90 ◦ , the adhesives converge to the steady-state operating preload and adhesion (s). L ∞ and F ∞ indicate the steady-state operating preload and adhesion pressure for this slope angle, respectively. F safe indicates a minimum safe adhesion pressure, and the difference between these values is the margin of safety M s . it is possible to determine if an adhesive is suitable, and if it is what the minimum footpad size must be. In Fig. 7, the performance curve is plotted along with lines of various slopes (m(θ)) called “ratio lines” for θ values of 160 ◦ , 90 ◦ , 60 ◦ , 0 ◦ , and 340 ◦ . These slopes are the inverse of the ratio of adhesion-to-preload (Fig. 6). The case when the robot is climbing on a surface oriented at 160 ◦ was found to be the most challenging [(2), Fig. 6], and appears here as the steepest ratio line while the slope of 340 ◦ was found to be the easiest, and has the ratio line with the lowest slope. Ratio lines for all other slope angles fall between these two extremes. In general, the equation of a ratio line is F = m(θ)L (3) where F is the adhesion pressure, L is the preload pressure, and m is the slope. The performance curve of the adhesive–surface combination [Fig. 2(b)] can be approximated by a power law function (which has similar rising curve and saturation behavior) with general form F = aL 1/n (4) where n>1 and a is a scaling coefficient. The preload value at the intersection of the two lines (L ∗ )isgivenby ( a n L ∗ n −1 = . (5) m) For each step the robot has an initial preload L i . The maximum peeling pressure F i is determined by the performance curve. This maximum adhesion pressure is transferred to the preload pressure for the next step with a force ratio of 1/m. To determine the steady-state operating adhesion and preload (the pressures at which the feet will press onto and adhere to the surface after many steps), we examine an iterative function where each iteration represents one forward step of the robot.
334 IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 12, NO. 3, JUNE 2007 It can be shown that the preload converges to the intersection preload (L ∗ ) through an iterative proof using the update rule ( a L i+1 = L m) ( 1 n ) i (6) which mathematically represents a single step, where L i is the preload for step number i. The steady-state operating preload (L ∞ ) is given by ( a ) A ( L ∞ = lim L 1 n ) n→∞ 0 (7) m A =1+ 1 ( 1+ 1 (1+ 1 )) n n n (...) = n n − 1 . (8) Therefore, ( a n n −1 L ∞ = = L m) ∗ . (9) The steady-state operating preload (L ∞ ) converges to the preload at the intersection of the two lines (L ∗ ) from (5). The steady-state operating adhesion (F ∞ ) is then equal to mL ∞ . These two values define a steady-state operating point, point S in Fig. 7. There is also a minimum safe adhesion value (F safe ), which is a function of the area of the footpads and the surface slope angle θ, and can be calculated from (2) and foot size. The steady state operating adhesion (F ∞ ) must be greater than the minimum safe adhesion value (F safe ) to prevent the robot from detaching from the climbing surface. The margin between the steady-state operating adhesion and the minimum safe adhesion is the margin of safety (M s ). Since the robot will not always have ideal force transfer on every step, it is important to have a large margin of safety so that the robot can recover from a problematic step, or continue to operate if the adhesives become contaminated and function with degraded performance. It is possible to increase the margin of safety by increasing the area of the adhesives (foot pad size), which lowers the minimum adhesion pressure requirement. However, there is a tradeoff because the motors then need to provide more torque to peel the larger feet. This causes an increased power requirement, which leads to larger batteries, and also necessitates a larger and heavier motor. C. Robot Fabrication A printed circuit board (PCB) acts as the chassis for the robot instead of using an additional body frame in order to keep the mass low. The leg and feet assemblies are fabricated via 3-D printing (Z-Corp. ZPrinter and 3-D Systems Invision HR). The heaviest components of the system are the leg assemblies, motors, and batteries. In order to move the center of gravity as close as possible to the surface and balanced around the motor axes, all these parts are located close to the shaft axes with the batteries beneath the PCB, nearly in contact with the climbing surface. The robot is controlled by a PIC microcontroller (PIC16F737), and is able to perform preprogrammed actions such as climbing and turning without instructions from the user. Gait is controlled with feedback from foot position sensors. Limit switches are triggered when the legs are aligned so that only one foot on each side is in contact with the surface. This Fig. 8. <strong>Waalbot</strong>’s small turning radius (R t ) and turning circle radius (R tc ) allow it to climb around obstacles, and operate in narrow corridors with sharp bends. information is used to keep the robot’s gait synchronized by pausing one of the motors until the opposing motor catches up, assuring that the assumptions of symmetry in (1) are valid. Foot position tracking is also important for safely putting the robot into steering mode. Infrared (IR) RC5 communication is used to teleoperate the robot to climb straight, stop, and turn. Commands can be sent for turning 180 ◦ , 90 ◦ , and in increments of 15 ◦ in either direction. Power is provided by two lithium ion polymer batteries which are placed in series beneath the body of the robot for 7.4 V. The two motors (Sanyo 12GA-N4s) have a torque output of approximately 400 mN.m each, which is sufficient to peel the rear feet from the surface. IV. AGILITY A. Steering When only one foot on a side is in contact with the surface, that foot can be used as a pivot point for the robot to rotate about. By advancing the opposite motor, the robot rotates around the passive revolute joint in the pivoting foot. If the robot attempted to turn while the two feet were attached on a side, the robot would shear itself off the surface, since the center of rotation would not be aligned with a joint. Since this can be a catastrophic failure for a climbing robot, foot position sensors are used to prevent this occurrence. In steering mode, the robot takes discrete steps around the pivoting foot. The turning radius is less than the width of the robot, which allows tight turns (Fig. 8). The ability to make tight turns is an important feature for climbing through small passageways or for avoiding closely spaced obstacles. Steering angle per step can be calculated from the turning radius R t and the stepping distance d step by examining the triangle between the pivot, front, and rear stepping feet as ( ) θ =cos −1 1 − d2 step 2Rt 2 (10)
Page 1 and 2: 330 IEEE/ASME TRANSACTIONS ON MECHA
Page 3: 332 IEEE/ASME TRANSACTIONS ON MECHA
Page 7 and 8: 336 IEEE/ASME TRANSACTIONS ON MECHA
Page 9: 338 IEEE/ASME TRANSACTIONS ON MECHA

Waalbot - NanoRobotics Lab - Carnegie Mellon University

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?