  This paper focuses on online occupancy mapping and real-time collision
checking onboard an autonomous robot navigating in a large unknown environment.
Commonly used voxel and octree map representations can be easily maintained in
a small environment but have increasing memory requirements as the environment
grows. We propose a fundamentally different approach for occupancy mapping, in
which the boundary between occupied and free space is viewed as the decision
boundary of a machine learning classifier. This work generalizes a kernel
perceptron model which maintains a very sparse set of support vectors to
represent the environment boundaries efficiently. We develop a probabilistic
formulation based on Relevance Vector Machines, allowing robustness to
measurement noise and probabilistic occupancy classification, supporting
autonomous navigation. We provide an online training algorithm, updating the
sparse Bayesian map incrementally from streaming range data, and an efficient
collision-checking method for general curves, representing potential robot
trajectories. The effectiveness of our mapping and collision checking
algorithms is evaluated in tasks requiring autonomous robot navigation and
active mapping in unknown environments.
