A quantitative method for comparing trajectories of mobile robots using point distribution models

In the field of mobile robotics, trajectory details are seldom taken into account to qualify robot performance. Most metrics rely mainly on global results such as the total time needed or distance traveled to accomplish a given navigational task. Indeed, usually mobile roboticists assume that, by using appropriate navigation techniques, they can design controllers so that the error between the actual and the ideal trajectory can be maintained within prescribed bounds. This assumption indirectly implies that there is no interesting information to be extracted by comparing trajectories if their variation is essentially resulting from uncontrolled noisy factors. In this paper, we will instead show that analyzing and comparing resulting trajectories is useful for a number of reasons, including model design, system optimization, system performance, and repeatability. In particular, we will describe a trajectory analysis method based on point distribution models (PDMs). The applicability of this method is demonstrated on the trajectories of a real differential- drive robot, endowed with two different controllers leading to different patterns of motion. Results demonstrate that in the space of the PDM, the difference between the two controllers is easily quantifiable. This method appears also to be extremely useful for comparing real trajectories with simulated ones for the same set-up since it affords an assessment of the simulation faithfulness before and after appropriate tuning of simulation features.