Stochastic functional gradient for motion planning in continuous occupancy maps

Abstract

Abstract-Safe path planning is a crucial component in autonomous robotics. The many approaches to find a collision free path can be categorically divided into trajectory optimisers and sampling-based methods. When planning using occupancy maps, the sampling-based approach is the prevalent method. The main drawback of such techniques is that the reasoning about the expected cost of a plan is limited to the search heuristic used by each method. We introduce a novel planning method based on trajectory optimisation to plan safe and efficient paths in continuous occupancy maps. We extend the expressiveness of the state-of-the-art functional gradient optimisation methods by devising a stochastic gradient update rule to optimise a path represented as a Gaussian process. This approach avoids the need to commit to a specific resolution of the path representation, whether spatial or parametric. We utilise a continuous occupancy map representation in order to define our optimisation objective, which enables fast computation of occupancy gradients. We show that this approach is essential in order to ensure convergence to the optimal path, and present results and comparisons to other planning methods in both simulation and with real laser data. The experiments demonstrate the benefits of using this technique when planning for safe and efficient paths in continuous occupancy maps.

Functional Path Optimisation for Exploration in Continuous Occupancy Maps

“…This is a major difference from existing methods that typically depend on a finite path parametrisation, such as finite sets of time steps or waypoints, or employ simple representations such as quadratic or cubic splines. Instead, our method can utilise a highly expressive path representation; such as non-parametric [17] or approximate kernel paths [18]. As our method uses continuous occupancy maps, the MI utility can be derived directly from the map model in closed form, which simplifies computations.…”

“…It has been successfully applied to motion planning problem in recent years with the main objective of producing safe, collision-free paths. It was recently suggested as an alternative approach to samplingbased methods for path planning using occupancy maps [17]. In this section, the general method is discussed, before the extension for autonomous exploration is described in section IV.…”

“…Other methods optimise an information-based objective over the entire path, however, these are highly dependent on the path parameterisation. Formulating exploration as a variational problem and solving it using functional gradient descent, provides a general optimisation framework which is invariant to the choice of path parameterisation and can even take a non-parametric form as shown in [17].…”

“…However, in all methods the objective is sampled via a deterministic schedule. Such approaches have proved unsatisfactory for planning using occupancy maps [17]. To ensure convergence to a safe solution, the path is stochastically sampled in the entire t ∈ [0, 1] domain and any uninformative gradient updates, such as those coming from unsafe parts of the map, are rejected.…”

Fast Stochastic Functional Path Planning in Occupancy Maps

“…2) Employing Stochastic Gradient Descent (SGD) [6] in the path planning paradigm to ensure convergence to an optimal solution under the guarantees of SGD. SGD exploits kernel approximation methods in order to keep the model tractable, unlike the non-parametric approach taken in [3]. The remainder of this paper is organised as follows.…”