R5. Manipulator dynamics
Table of Contents
1 Info
The assignment presents properties of stationary robot dynamics.
The points marked with (*) are optional (not obligatory).
2 Preparation
Before the classes recall from the lecture
- the structure, elements and properties of robot dynamics equation.
- Euler-Lagrange method of calculation of dynamic equations
- definition and properties of pseudo-inertia matrix
- inertia parameters of basic figures, Steiner's (parallel axis) theorem
3 Tasks
Task 1: Euler-Lagrange approach to double pendulum dynamics
- Define the variables of vertical double pendulum model with link lengths l1 and l2 with point masses placed at the end of each link, m1 and m2, respectively
- Define the Lagrangian
- Use Euler-Lagrange formula to define the dynamics
- To report:
- What are kinetic and potential energy of the manipulator?
- Write the Lagrangian.
- What are the dynamics of the manipulator?
- Include inertia matrix, Coriolis and centrifugal matrix and gravitational vector.
Task 2: Double pendulum motion
- Assume some (numerical) values of lengths and masses
- Use Matlab ODE function to simulate motion of the model (begin with no control inputs, just modify initial conditions)
- Modify the masses and lengths and observe the changes
- To report:
- Include at least two selected sets of parameters and the results of simulation (plots of state variables wrt. time and a trajectory).
- Summarize observations of changes.
Task 3: (*) Moving the masses in the pendulum
- Determine the model (a change) of the double pendulum if the masses are placed in the center of the link instead of the ends
- Use two approaches: Steiner's theorem and pseudoinertia matrix
Task 4: (*) Computed torque control
- Determine control formula for computed torque method
- Choose a trajectory in joint coordinates (periodical)
- Substitute the control and check the error dynamics
- Choose Kd and Kp parameters
- Observe the trajectory tracking error
- Modify Kd and Kp parameters, observe the changes
- To report:
- Note formula of the control
- Include two examples for various parameter value
- Comment the obtained results
4 Summary
- The report should include the result of the tasks and answers to the questions.
- Please do not forget to indicate the author of the report!
- The report in PDF format should be submitted before the beginning of next classes using a method defined by the instructor.