EE6221-ROBOTICS AND INTELLIGENT SENSORS
SEMESTER 2 EXAMINATION 2021-2022
1. A robotic manipulator with six joints is shown in Figure 1.
Figure 1
(a) Obtain the link coordinate diagram by using the Denavit-Hartenberg (D-H)algorithm. (12 Marks)
(b) Derive the kinematic parameters of the robot based on the coordinate diagram obtained in part (a). (8 Marks)
2. The dynamic equations of a Cartesian robot which is in contact with a frictionless surfacedare given as follows:
where x1 x2, x3 represent the position of the end effector in Cartesian coordinates, fiand f2 are the contact forces, u1, u2, u3 are the control inputs. The contact forces exertedon the environment are given by
The system possesses unmodelled resonances at 8 rad/s, 16 rad/s and 24 rad/s.
(a) Design a hybrid position and force controller for the robot. The system should be critically damped and does not excite all the unmodelled resonances. (12 Marks)
(b) The controller designed in part (a) is now implemented on the robot but a constant steady state position error is found on x3. Explain the possible effects and derive the error equations. Design a controller so that the steady state error can be eliminated and the same performance in part (a) is achieved. (8 Marks)
3. (a) A three-wheeled mobile robot with two castor wheels and one steered standard wheel is shown in Figure 2 on page 3. A local reference frame. (xn yr) and a steered angle ß are assigned to the mobile robot as shown in Figure 2. The radius of each wheel is 5 cm. If the rotational velocities of the steered standard wheel and the two castor wheels are denoted by ss, e1, and e2, respectively, derive the rolling and sliding constraints of the mobile robot. (10 Marks)
Note: all lengths are in centimeters.
Figure 2
(b) A robot manipulator with four joint variables q1, 92. 93, q4 are mounted on amobile robot. The link-coordinate homogeneous transformation matrix from thebase coordinate to the tool coordinate of the robotic manipulator is given as:
where s = sin (q1), s3 = sin(q3), s4= sin(q4), G1 = cos (q1), c3 = cos (93), C4 = cos(q4).
(i) Solve the inverse kinematic problem using an analytic method to express (q1, q2, 93)T in terms of the position of the end effector (x, y, z)T. (Note: orientation is not required).
(ii) Find the first column of the tool-configuration Jacobian matrix of this robot.(Note: only first column is required). (10 Marks)