ECE 470: Introduction to Robotics
Homework #1

Due: Thursday, Sept. 14, 2017.

Rigid Body Motions

Rotations and homogeneous transformations are examples of rigid body motions, i.e., motions that preserve distance and angles. The first questions explore this topic.
  • Solve problems 2-1, 2-2 and 2-3. These problems demonstrate a few properties of rigid body transformations.

Properties of Rotation Matrices

These problems will explore in a bit more depth some properties of rotation matrices
  • Solve problems 2-4 and 2-5. These problems investigate properties of the Special Orthogonal group of matrices. You may restrict your attention to SO(3) for these problems (if that makes things simpler to express).
  • Solve problem 2-6. This problem merely demonstrates the intuitive fact that successive rotations about a single access can be expressed in terms of the sum of the two angular rotations.
  • Solve problem 2-7. This problem establishes that SO(n) is a group.

Homogeneous Transformations

  • Solve problems 2-38, 2-39, 2-40 and 2-41. These problems illustrate the assignment of coordinate frames in 3D, and the use of homogeneous transformations.