Stochastic Functional Gradient Path Planning in Occupancy Maps

Planning safe paths is a major building block in robot autonomy. It has been an active field of research for several decades, with a plethora of planning methods. Planners can be generally categorised as either trajectory optimisers or sampling-based planners. The latter is the predominat planning paradigm for occupancy maps. Trajectory optimisation entails major algorithmic changes to tackle contextual information gaps caused by incomplete sensor coverage of the map. However, the benefits are substantial, as trajectory optimisers can reason on the trade-off between path safety and efficiency. In this work, we improve our previous work on stochastic functional gradient planners. We introduce a novel expressive path representation based on kernel approximation, that allows cost effective model updates based on stochastic samples. The main drawback of the previous stochastic functional gradient planner was the cubic cost, stemming from its nonparametric path representation. Our novel approximate kernel based model, on the other hand, has a fixed linear cost that depends solely on the number of features used to represent the path. We show that the stochasticity of the samples is crucial for the planner and present comparisons to other stateof-the-art planning methods in both simulation and with real occupancy data. The experiments demonstrate the advantages of the stochastic approximate kernel method for path planning in occupancy maps.