Manifold Learning Methods for Sensor Model Discovery

A mobile robot typically has access to a high dimensional stream of multi-modal sensor information. Modern mobile robots navigate uncertain environments using complex mixtures of camera, laser, and sonar sensor data. Manual calibration of these sensors is a tedious process that involves determining sensor behavior and geometry through model specification. To automate the construction of sensor models requires mining the uninterpreted sensor stream for regularities in both known and unknown environments. One method of doing so involves using the interpoint distances between individual sense element sensor streams as a proxy for the interpoint distances between sense elements themselves. We can then apply dimensionality reduction to generate a low dimensional representation of sensor geometry. We present a series of initial comparisons of manifold learning methods for discovering sensor geometry on a mobile robot. 1 Bootstrap Learning We can view the problem of a robot situated in the world as a dynamical system xt = G(xt−1, μt−1) (1) st = H(xt) (2) νt = C(st) (3) μt = M(νt) (4) where G is a function representing the effect robot motion μ has on the state of the world x, H is a sensor model that determines the observable state s, C is the motor control law adopted by the robot, and M is the (possibly noisy) realization of motor commands ν as actual motions μ. We denote the composition M ◦ C ◦H by ψ. Then the state evolution of the complete robot-world system is given by: {G(xt, ψ(xt))}t∈T (5) A roboticist faces many challenges in trying to define control laws that result in desirable trajectories of system evolution. Accurate sensor, motor, and world models are a crucial component in the design of effective control laws. For robots undergoing autonomous development, these models must be generated from data since no external observer is available. We refer to the process of autonomously building sensor, motor, and world models from data as bootstrap learning.