  In the context of autonomous robots, one of the most important tasks is to
prevent potential damage to the robot during navigation. For this purpose, it
is often assumed that one must deal with known probabilistic obstacles, then
compute the probability of collision with each obstacle. However, in complex
scenarios or unstructured environments, it might be difficult to detect such
obstacles. In these cases, 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 suited for computing risk
assessments for continuous paths due to its discrete nature. Hence, we
introduce a novel type of map called the Lambda Field, which is specially
designed for risk assessment. We first propose a way to compute such a map and
the expectation of a generic risk over a path. Then, we demonstrate the
benefits of our generic formulation with a use case defining the risk as the
expected collision force 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, such as tall grass. Where
standard environment representations would always generate trajectories going
around such obstacles, our framework allows the robot to go through the grass
while being aware of the risk taken.
