Pose-Graph SLAM: Loop-Closure Optimization

Simultaneous Localization and Mapping (SLAM) has to solve a problem odometry alone can't: every wheel-encoder or IMU measurement carries a little noise, and that noise compounds step after step into a trajectory that drifts steadily away from the truth. This simulator drives a robot around a closed loop while integrating noisy relative-pose measurements into a dead-reckoning estimate, then adds the one thing pure odometry lacks — a loop-closure constraint from recognizing a previously visited place — and runs a real pose-graph relaxation over the resulting graph of nodes and relative-pose edges. Watch the raw odometry trajectory drift away from ground truth, then watch loop-closure optimization redistribute that error across the whole loop until the pose-graph estimate collapses back onto a globally consistent trajectory, exactly the back-end step that runs inside every modern SLAM stack.