What is meant by configuration space?

What is meant by configuration space?

In mathematics, a configuration space is a construction closely related to state spaces or phase spaces in physics. In physics, these are used to describe the state of a whole system as a single point in a high-dimensional space.

What is configuration space in quantum mechanics?

In the quantum mechanics the domain space of the wave functions is the classical configuration space . In classical field theory, the configuration space of the field is an infinite-dimensional space. The single point denoted in this space is represented by the set of functions where and. represents an index set.

What is the difference between configuration space and phase space?

Point in configuration space represents configuration of the system, i.e. positions of the constituent particles. Point in phase space represents state of the system, i.e. positions and velocities of the constituent particles together.

What is joint space and task space?

Task space (or Cartesian space) is defined by the position and orientation of the end-effector of a robot. Joint space is defined by a vector whose components are the translational and angular displacements of each joint of a robotic link.

Is the configuration space of a robot the same as joint space?

For the robotic manipulator in the picture it can be assumed that its configuration is completely determined by its joint parameters. It can be said that Configuration space and Joint space are equivalent for this robot (give or take few mathematical definitions of equivalent).

How are joint parameters used to define configurations?

The joint parameters of the robot are used as generalized coordinates to define configurations. The set of joint parameter values is called the joint space. A robot’s forward and inverse kinematics equations define maps between configurations and end-effector positions, or between joint space and configuration space.

Which is space does joint configuration q belong to?

So, joint configuration Q is a vector of length N and the elements of that vector are either an angle or a length. The joint angle vector belongs to a space, the space C.

Is the configuration space the same as the task space?

The next important consideration then is the dimensions of these different spaces, the task space, the space in which we describe the pose of the end effector, and the configuration space in which we describe the joint coordinates of the robot.