代写TRC4800/MEC4456 Robotics PC 4: Trajectory Generation

Department of Mechanical and Aerospace Engineering

TRC4800/MEC4456 Robotics

PC 4: Trajectory Generation

Objective: To master trajectory generation using cubic splines or linear paths with parabolic blends.

Problem 1. How many individual cubics are computed when a six-jointed robot moves its end- effector along a cubic spline path through two separate points and stops at a goal point? How many coefficients are stored to describe these cubics?

Problem 2. A single-link robot with arevolute joint is motionless at θ1 = −5°. It is desired to move the joint in a smooth manner to θ1   = 80° in 4 seconds. Find the coefficients of a cubic that accomplishes this motion and brings the arm to rest at the goal.

Problem 3. Referring to the same single-link robot and its proposed angular positions in Problem 2, compute the corresponding parameters of linear trajectory with parabolic blends. Where, .

Problem 4. Frame {3} of the two-link manipulator shown in Figure 1 is projected to move to the following locations:

Based on the transformation matrices at each point, if L1 = L2 = 1, find the cubic functions that describe each joint angle as the end-effector moves from rest at its starting point at time t0, to the mid-point at t1, before coming to rest at its endpoint at t2 . Ensure the rate of change of the angles of joint 1 and 2 at t1 are continuous.

Figure 1: A two-link RR manipulator