Full SLAM

Full SLAM Problem

At time t-1 , the robot will estimate the robot pose x _t-1 and map m , given the measurements **z _t-1 **and controls u _t-1 .
At time t , the robot will estimate the entire path x _t-1:t and map m , given all the measurements z _t-1:t and controls u _t-1:t .
At time t+1 , the robot will estimate the entire path x _t-1:t+1 and map m , given all the measurements z _t-1:t+1 and controls u _t-1:t+1 .

This problem can be modeled with the probability equation p(x _1:t , m | z _1:t u _1:t ) , where we solve the posterior represented by the robot's trajectory x _1:t and the map m given all the measurements z _1:t and controls u _1:t . Thus, with full SLAM problem we estimate all the variables that occur throughout the robot travel time.

How will the robot solve the Full SLAM problem from t-1 to t+2 ?

The robot will estimate the “x _t+2 ” pose and map “m” given the measurements “z _t+2 ” and controls “u _t+2 ”

The robot will estimate the robot's trajectory “x _t-1:t+2 ” and map “m” given the measurements “z _t-1:t+2 ” and controls “u _t-1:t+2 ”

The robot will estimate the robot's trajectory “x _t-1:t+1 ” and map “m” given the measurements “z _t-1:t+1 ” and controls “u _t-1:t+1 ”

The robot will estimate the “x _t+2 ” pose and map “m” given the measurements “z _t:t+2 ” and controls “u _t:t+2 ”

SOLUTION:

The robot will estimate the robot's trajectory “x _t-1:t+2 ” and map “m” given the measurements “z _t-1:t+2 ” and controls “u _t-1:t+2 ”