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.
Sampling efficiency in a highly constrained environment has long been a major challenge for sampling-based planners. In this work, we propose Rapidly-exploring Random disjointed-Trees * (RRdT * ), an incremental optimal multi-query planner. RRdT * uses multiple disjointed-trees to exploit localconnectivity of spaces via Markov Chain random sampling, which utilises neighbourhood information derived from previous successful and failed samples. To balance local exploitation, RRdT * actively explore unseen global spaces when localconnectivity exploitation is unsuccessful. The active trade-off between local exploitation and global exploration is formulated as a multi-armed bandit problem. We argue that the active balancing of global exploration and local exploitation is the key to improving sample efficient in sampling-based motion planners. We provide rigorous proofs of completeness and optimal convergence for this novel approach. Furthermore, we demonstrate experimentally the effectiveness of RRdT * 's locally exploring trees in granting improved visibility for planning. Consequently, RRdT * outperforms existing state-of-the-art incremental planners, especially in highly constrained environments.
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. * Gilad Francis, Lionel Ott and Fabio Ramos are with The
Autonomous exploration is a complex task where the robot moves through an unknown environment with the goal of mapping it. The desired output of such a process is a sequence of paths that efficiently and safely minimise the uncertainty of the resulting map. However, optimising over the entire space of possible paths is computationally intractable. Therefore, most exploration methods relax the general problem by optimising a simpler one, for example finding the single next best view. In this work, we formulate exploration as a variational problem which allows us to directly optimise in the space of trajectories using functional gradient methods, searching for the Next Best Path (NBP). We take advantage of the recently introduced Hilbert maps to devise an informationbased functional that can be computed in closed-form. The resulting trajectories are continuous and maximise safety as well as mutual information. In experiments we verify the ability of the proposed method to find smooth and safe paths and compare these results with other exploration methods.
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