ROBOTICS 9/2/2015 Last and First Name Matricola PART 1 - QUIZ (8 marks) 1. The geometric specification of the robot working space - considers the last 3 degrees of freedom of a manipulator T F - is only used to exactly compute whether a point is in the working space T F - is used to select the best robot structure for a given task T F FFT 2. The 4 parameters in the DH notation - depend on the choice of the reference systems on the robot chain T F - are unique for any given robot T F - do not depend on the limits of the joint ranges T F TFT 3. The accuracy of a robot manipulator - is very important for high repetitive tasks T F - can be easily measured T F - does depend on the inverse kinematics solution T F FFT 4. The insertion operation accomplished by a robot arm - always requires to use two manipulators together T F - can be easily done if a Remote Center of Compliance device is used T F - cannot be done by pneumatic arms T F FTF 5. The ideal wheel used in kinematics - is a 3D real object T F - has one degree of freedom T F - can only roll T F FTT 6. An autonomous robot - is only tele-controlled by the user T F - needs some ways to detect the external environment T F - does not need internal sensors T F FTF 7. Paths and trajectories - paths are only for mobile robots, trajectories for manipulators T F - can be defined in Cspace T F - do always require a map to be available T F FTF 8. The distance transform algorithm - connects given obstacle points T F - directly constructs the path from the obstacles map T F - is a possible way to construct the shortest path for a mobile robot T F FFF 9. The robot vision system - can be installed on the robot itself T F - is a necessary part of the sensors system when using artificial potential methods T F - cannot be used to detect obstacles T F TFF 10. The gait of a legged robot - is regular on a plane T F
- for some gaits, it may require high velocities to be feasible T F - does consider the time of foot moving, not the forces necessary to move T F TTT
PARTE 2- OPEN QUESTIONS - (10 marks) 1. Illustrate the main schemata for controlling a manipulator robot. control in position and velocity in Cartesian space - in joint space 2. Discuss about the degrees of freedom and the degrees of mobility of industrial manipulators, wheeled mobile robots, and humanoid robots.
3. Define the inverse kinematics problem of wheeled mobile robots and indicate how to solve it. 4. Illustrate how, when, and for which purposes it is possible to obtain data about the forces acting on the robot.
PART 3- EXERCISES - (15 marks) Consider the 3 dof robot as in figure. Define the Denavit-Hartenberg representation, the working space, and discuss about its direct and inverse kinematics. A i-1 i-1,i Cθi Sθi = 0 Cα Sθ 0 i Cα Cθ i SαiSθi Sα Cθ 0 aicθi aisθi d 1 i i i i 0 Sαi Cαi i z2, z3 z1 x1 link theta alpha d a 1 --- 90 D1 0 2 --- 90 0 A2 3 0 0 --- 0 given the z axes as indicated, with the parking position with the last link in horizontal plane. Derive the 3 A matrices, and from T derive the equations to solve the IK (given the x, y and z coordinates of the point to reach).
2. Consider a wheeled robot that has to move in this room. Develop a grid map and use the distance transform to generate a path from the door to the last window. Illustrate all the steps and the intermediate results. For a big robot the passages between the chairs are not usable, so there are two big obstacles. For a small robot, like a roomba, the only obstacles are the steps the trash bins the legs of the chairs In a map of the obstacles we have this kind of situation (simplified, with a large number of small obstacles).we can use a grid size about the radius of the roomba (20 cm) and obtain this situation. The initial point is the door, the final point is near the last windows, as indicated. The goal square receives 0, all the other squares a large value. After the application of the algorithm we expect to have increasing values from the windows in any other direction.
3. Write a AL program for the following problem: A robot with one arm has to move a small object from an initial position to a final position and depose it upside down. Define the positions, the world model, the instructions. pos2 pos1 define 2 references pos1 (vertex on the table oriented as in station) and pos2 (vertex on to oriented down) on the cube on the vertices we want to exchange in the initial and final positions, and a grasping point on the side of the object. To be sure that the object is moved in the air define a via point. begin scalar lunghezza, larghezza, altezza; rot r1, r2, r3, r4; frame pos1, via_alto, pos2, grasp; lunghezza = 3; larghezza = 2; altezza = 2; r1 = ROT (XHAT, 90); r2 = ROT (ZHAT, 90); r3 = ROT (YHAT, 180); pos1 = FRAME (NILROT, VECTOR (20, 20, 0); via_alto = FRAME (NILROT, VECTOR (20, 20, 20); grasp = pos1*frame(r1*r2, VECTOR (larghezza/2, lunghezza/2, altezza/2 )); AFFIX grasp TO pos1 RIGIDLY; pos2 = FRAME (r3, VECTOR (20, 20, altezza));. MOVE barm TO grasp; CENTER barm; AFFIX grasp TO barm RIGIDLY; MOVE pos1 TO pos2 VIA via_alto; OPEN bhand TO 3; UNFIX grasp FROM barm; end