RoboticsLesson 2 of 2 in the course Motion planning

Configuration Space, Robot Kinematics, and Classical and Quantum States

5 flashcards · 5 quiz questions · 5 match pairs · 5 fill-in sentences · English

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Summary

A physical system’s configuration describes how its parts are arranged at a particular moment, without specifying how they are moving. The collection of all possible configurations forms its configuration space. This idea lets us represent the possible states of a system geometrically and provides a foundation for studying motion.

A system’s generalized coordinates are parameters that specify its configuration. For a single particle in ordinary three-dimensional space, the Cartesian coordinates q=(x,y,z)q=(x,y,z) are one possible choice. More generally, the symbol qq commonly denotes a point representing a configuration, while q˙=dq/dt\dot{q}=dq/dt denotes its velocity.

All flashcards

Configuration space
The set of all possible configurations of a system, represented using generalized coordinates.
Generalized coordinates
Parameters that specify a system’s configuration, such as particle coordinates or joint angles.
Free rigid body in three dimensions
Its configuration space is R3×SO(3)\mathbb{R}^3\times\mathrm{SO}(3), describing position and orientation.
Classical phase space
The cotangent bundle T∗QT^*Q, collecting configurations and their associated momentum covectors.
Joint space
The set of possible values of a robot’s joint parameters.

Quiz questions

  1. What is the unrestricted configuration space of nn independent particles in three dimensions?Answer: R3n\mathbb{R}^{3n}
  2. In robotics, what does forward kinematics calculate from joint values?Answer: The end-effector’s position and orientation.
  3. What does inverse kinematics determine for a specified end-effector pose?Answer: Joint values that can produce the specified pose.
  4. At a configuration q∈Qq\in Q, what does the tangent space TqQT_qQ represent?Answer: Possible instantaneous velocities at that configuration.
  5. Which space represents pure states of a two-state quantum system in the projective description?Answer: CP1\mathbb{C}\mathbf{P}^1

Based on the Wikipedia article Configuration space (physics), licensed CC BY-SA 4.0. Adapted into a summary, flashcards and quizzes.

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