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In robotics, a twist is a 6x1 column vector of linear and angular velocities. In ROS, this is implemented as a Twist message, which you can see for yourself by entering the following in a terminal:

rosmsg show geometry_msgs/Twist

An interactive marker is another ROS tool to interface with robots through rviz. You can drag around this marker, and generally a robot will try to follow it. The server you mentioned publishes twists (velocity commands) to get to the interactive marker pose (position command).

Here is the source code, and here is a video I found of someone using it to drive their robot. Note that this server is configured to work with differential-wheeled (AKA tank-drive or skid-steer) robots.