EE6221 - ROBOTICS AND INTELLIGENT SENSORS
SEMESTER 1 EXAMINATION 2024-2025
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)
Note: Question No. 1 continues on page 2.
(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 robot when it is in contact with a workpiece are given as follows:
where u, u2, u3 are the control inputs, q1,92.93 are the joint variables, d1,d2, d3 are the unknown disturbances and f=22(q3-0.2) is the contact force. The system possesses unmodelled resonances at 5 rad/s, 10 rad/s and 15 rad/s.
(a). If di, d2, d3 are zero, design a hybrid position and force controller for the robot to track the desired trajectories q92 and the desired force fa. The motion control subspace should be overdamped with a damping ratio of 1.05, and the force control subspace should be critically damped. The control system should not excite all the unmodelled resonances. (14 Marks)
(b). If d,dz, d3 are not zero, derive the error equations of the system based on the hybrid position and force controller designed in part (a). (6 Marks)
3. (a) A mobile platform. is shown in Figure 2 The platform. has one steered standard wheel and two standard wheels. A local reference frame. (xr, yr) is assigned as shown in the figure. The radius of each standard wheel is 10 cm. If the rotational velocities of the steered standard wheel and the two standard wheels are denoted by ss, s1, s2 respectively, derive the rolling and sliding constraints of the mobile platform.
Figure 2
(b). A robot manipulator with four ioint variables is mounted on a mobile platform. The transformation matrix from tool tip to base coordinate of the robot is given as:
where q1,q2,q3 are the joint variables for the major axes, q4 is the tool roll angle, Ck = cos qk and S = sin qk.
(i) Derive the tool configuration Jacobian matrix of the manipulator.
(ii) Given that x= 0.2, y=0.2, z=0, solve the inverse kinematic problem to obtain q1, 92, 93. (Note: orientation is not required).
(iii) Determine the approach vector of the robot at this joint configuration. (12 Marks)