2.4: Exercises
- Page ID
- 14777
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)
Take-home lessons
- In order to do planning for a robot, you need to understand how its control parameters map to actions in the physical world.
- The kinematics of a robot are fully defined by the position and orientation of its wheels, joints and links no matter whether it swims, flies, crawls or drives.
- Many robotic systems cannot be fully understood by considering kinematics alone, but require you to model their dynamics as well. This book will be limited to modeling kinematics, which is sufficient for low-speed, mobile robots and arms.
Exercises
- What are the degrees of freedom of a lawnmower with four standard wheels? Why are you still able to mow your entire lawn?
- Is a car statically or dynamically stable? What about a Segway?
- What are the degrees of freedom of an office chair with all caster-wheels?
- What are the maximum degrees of freedom for objects driving on the plane?
- What are the maximum degrees of freedom for objects that can freely move in the world?
- Calculate the degrees of freedom of a differential wheels robot with a front caster wheel. What happens when you add a second caster wheel?
- Calculate the degrees of freedom of a standard car. How can you still reach every point on the plane?
- A steering wheel allows you to change the yaw of your car. Can you also change its pitch and its roll?