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:
    1. What are kinetic and potential energy of the manipulator?
    2. Write the Lagrangian.
    3. What are the dynamics of the manipulator?
    4. 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:
    1. Include at least two selected sets of parameters and the results of simulation (plots of state variables wrt. time and a trajectory).
    2. 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:
    1. Note formula of the control
    2. Include two examples for various parameter value
    3. 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.

Author: Janusz Jakubiak

Created: 2018-05-22 wto 16:53

Emacs 24.4.1 (Org mode 8.2.10)

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