Assignment 3. Position of the center +/- 0.1 inches Orientation +/- 1 degree. Decal, marker Stereo, matching algorithms Pose estimation

Transcription

1 Assignment 3 1. You are required to analyze the feasibility of designing a vision system for the robot gas station attendant. Assume that the driver parks the car so that the flap and the cap are in a predetermined workspace of 36 in (length) 24 in (height) 24 in (depth). Recall that the two main functions of the vision system are: to locate the gas flap, and (possibly) the hinge, so that the robot arm with an end effector equipped with suction cups can open the flap; and to locate the gas cap so that the robot arm with another suitable end effector unscrews the gas cap. a) Develop specifications for the performance of the vision system for each of the two tasks. In other words, identify the specific parameters (e.g., position of the target, orientation of the target, shape of the target, size of the target) that will have to be returned to the robot control system in order for the robot to perform its task. Also try to estimate the allowable errors in these parameters for the task. b) For each task, determine the sequence of operations (algorithms) and hardware that are required for the vision system. Examples of algorithms include edge detection, contrast operator, and pose estimation. Examples of the hardware set up include one CCD camera, two CCD cameras, or one camera with structured light. Discussion in class. Locate the gas tank flap Specifications Position of the center +/- 0.5 inches Shape of the flap Flap open or not Possible cues about the hinge Algorithms Edge detection Contouring, chaining, linking Shape recognition, pattern matching Estimation of the center Locate the cap to the gas tank Position of the center +/- 0.1 inches Orientation +/- 1 degree Decal, marker Stereo, matching algorithms Pose estimation Hardware required 2 cameras with adequate field of view stereo pair Alt. Hardware Structured lighting system stereo pair -1-

2 2. Explore the ability of any one of the edge operators (others optional) using the ideal image shown in the figure and compare them to each other and the Roberts operator. See Excel spreadsheet. Visionoperators.xls in the same directory. 3. Robot A and Robot B are both electric robots powered by dc servo motors with identical geometry. Robot A is equipped with high accuracy, low friction potentiometers at the joints and a 12 bit A/D (analog to digital) card. Robot B is equipped with 512 line encoders (with quadrature) at the motor shafts. Both robots have digital controllers. Therefore, the joint position information has to be fed back to the controller as a digital signal. Find the resolution for each robot at the joint? Which one has a superior resolution? Robot A has continuous sensors (potentiometers), but the analog to digital converter results in a discretization of 2 12 = 4096 counts per revolution. Robot B has a 512 line encoder and the quadrature allows 512x4=2048 counts per revolution. Clearly Robot A has superior (two times better) resolution. 4. A commercial robot has a regional structure (the first three joints) consisting of revolute joints. The first axis is vertical, the second intersects the first at 90 degrees and is horizontal, and the third is parallel to the second. See, for example, the first three joints of the Kawasaki JS series. The two link lengths (the distance between the second and third axes and the distance between the third axes and the tool center point) are 1 meter each. In other words, ), a 2 = a 3 = 1 meter. Each joint is driven by a dc servo motor with a peak continuous torque rating of 100 in lbs, a 70:1 harmonic drive reduction and a 512 line optical encoder with quadrature. Assignment 4-2- April 22, 2000

3 P a 3 a 2 Axis 3 Axis 2 Axis 1 (a) Estimate the resolution (control resolution) when the end point at the workspace (outer) boundary. Hint: Calculate the joint resolution at each joint. The joint resolution in radians multiplied by the distance to the tool end point gives the linear resolution at the end point. The inaccuracies of joints 2 and 3 will add because they are parallel. The worst case resolution is when the arm is completely outstretched. The worst case scenario (in terms of resolution) happens when the end point is at the workspace boundary as shown in the figure below: Assignment 4-3- April 22, 2000

4 a 2 a 3 Axis 2 Axis 3 z Axis 1 x The resolution in the z direction is dictated by the resolutions of joint 2 and joint 3. In fact, the errors at joint 2 and joint 3 will add. If a 2 = a 3 = a, z = a θ 3 + 2a θ 2 Since the joints are identical, the errors at the joints are also the same and therefore z = 3a θ 2 The angular resolution can be calculated as follows: 2 π rads/rev θ = counts/rev Thus resolution in the z direction is simply 1joint rev 70 motor shaft rev z = 3a θ = mm = rads/count Similarly, the resolution in the y direction is dictated by the resolution of joint 1. Note that the manipulator cannot move in the x direction (at least instantaneously). Since all the joints have the same angular resolution: Thus the spatial resolution at the end point is y = 2a θ 1 = 2a θ = mm y 2 + z 2 = y = 2a θ 1 = 2a θ = mm (b) The robot manufacturer claims an accuracy of inches. Do you believe this claim? Assignment 4-4- April 22, 2000

5 Since the accuracy is of the order of twice the spatial resolution, we can argue that is roughly inches. The claimed accuracy of inches seems somewhat high. Even if the robot uses a very stiff transmission with very little backlash, it is unlikely that the accuracy is better than inches. (c) If no force sensors are used, do you think this robot can be used (with a suitable end effector to grasp a cap) to screw on caps for bottles or jars typically found with such food products as jelly and peanut butter? Make appropriate assumptions on the accuracy with which the bottle or jar needs to be positioned. What kind of control strategy would you suggest? The caps for jars with food products are threaded with very coarse pitch screws. Generally, this is so that a person with the dexterity of a four year old or that of a seventy year old can open and close the jar easily. Thus a positioning error of as high as 1/16 inches ( inches) is likely to be acceptable. To be safe, one could design a workcell with a positioning accurcay of 1/64 inch and the proposed robot would be acceptable. Should a higher accuracy be desirable, the assembly area can be moved closer to the base of the robot where the control resolution and therefore the accuracy is superior. Note that the successful and accurate orientation of the cap is very critical and not considered in this problem. If the robot is used to assemble the cap (as opposed to using a special purpose end effector that can screw on the cap), the trajectory in the operation is important. The rotation of the cap and its translation need to be completely coordinated. Thus a contouring type control strategy needs to be employed. The main problem is likely to be with over tightening. Specifying the number of turns required may not be practical since it is difficult to know when the threads catch. Note that the =7000 inch lbs of torque at the joint shaft is more than adequate in terms of payload. Assignment 4-5- April 22, 2000