Problem 44837. Composing relative poses in 2D: problem 1

We consider a world reference frame denoted by {0} which has its x-axis pointing east and its y-axis pointing north.

There is a playing field with a reference frame denoted by {F}. The rigid-body displacement from {O} to {F} is given by the homogenous transformation TF .

There are two robots (robot 1 and robot 2) on the playing field, with attached body-fixed coordinate frame {B} and {C} respectively with their origins at the centre of the robot. The x-axis of each robot's frame points in the robot's forward direction.

The rigid-body displacement of robot 1 with respect to the world frame is estimated by GPS to be the homogenous transformation TB . The displacement of robot 2 with respect to robot 1 is estimated by a novel radar sensor and is given by the homogenous transformation TBC .

Where is robot 2 with respect to the field?