Lambda-Field: A Continuous Counterpart Of The Bayesian Occupancy Grid For Risk Assessment And Safe Navigation

In the context of autonomous robots, one of the most important tasks is to prevent potential damages on the robot during navigation. For this purpose, it is often assumed to deal with known probabilistic obstacles, then to compute the probability of collision to each obstacle. However, in complex scenarios or unstructured environments, it might be difficult to detect such obstacles. In this case, a metric map is used where each position stores the information of occupancy. The most common type of metric map is the bayesian occupancy map. However, this type of map is not well fitted to compute risk assessment for continuous paths due to its discrete nature. Hence, we introduce a novel type of map called Lambda-Field, specially designed for risk assessment. We first propose a way to compute such a map and the expectancy of a generic risk over a path. Then, we demonstrate the utility of our generic formulation with a use case defining the risk as the expected force of collision over a path. Using this risk definition and the Lambda-Field, we show that our framework is capable of doing classical path planning while having a physical-based metric. Furthermore, the Lambda-Field gives a natural way to deal with unstructured environments like tall grass. Where standard environment representations would generate trajectories going around such obstacles, our framework allows the robot to go through the grass while being aware of the risk taken.