text: Sampling-based Motion Planners (SMPs) have become increasingly popular as they provide collision-free path solutions regardless of obstacle geometry in a given environment. However, their computational complexity increases significantly with the dimensionality of the motion planning problem. Adaptive sampling is one of the ways to speed up SMPs by sampling a particular region of a configuration space that is more likely to contain an optimal path solution. Although there are a wide variety of algorithms for adaptive sampling, they rely on hand-crafted heuristics; furthermore, their performance decreases significantly in high-dimensional spaces. In this paper, we present a neural network-based adaptive sampler for motion planning called Deep Sampling-based Motion Planner (DeepSMP). DeepSMP generates samples for SMPs and enhances their overall speed significantly while exhibiting efficient scalability to higher-dimensional problems. DeepSMP's neural architecture comprises of a Contractive AutoEncoder which encodes given workspaces directly from a raw point cloud data, and a Dropout-based stochastic deep feedforward neural network which takes the workspace encoding, start and goal configuration, and iteratively generates feasible samples for SMPs to compute end-to-end collision-free optimal paths. DeepSMP is not only consistently computationally efficient in all tested environments but has also shown remarkable generalization to completely unseen environments. We evaluate DeepSMP on multiple planning problems including planning of a point-mass robot, rigid-body, 6-link robotic manipulator in various 2D and 3D environments. The results show that on average our method is at least 7 times faster in point-mass and rigid-body case and about 28 times faster in 6-link robot case than the existing state-of-the-art.
  @cite_16: In this paper, we present Batch Informed Trees (BIT*), a planning algorithm based on unifying graph- and sampling-based planning techniques. By recognizing that a set of samples describes an implicit random geometric graph (RGG), we are able to combine the efficient ordered nature of graph-based techniques, such as A*, with the anytime scalability of sampling-based algorithms, such as Rapidly-exploring Random Trees (RRT).
  @cite_3: Rapidly-exploring random trees (RRTs) are pop- ular in motion planning because they find solutions efficiently to single-query problems. Optimal RRTs (RRT*s) extend RRTs to the problem of finding the optimal solution, but in doing so asymptotically find the optimal path from the initial state to every state in the planning domain. This behaviour is not only inefficient but also inconsistent with their single-query nature. For problems seeking to minimize path length, the subset of states that can improve a solution can be described by a prolate hyperspheroid. We show that unless this subset is sam- pled directly, the probability of improving a solution becomes arbitrarily small in large worlds or high state dimensions. In this paper, we present an exact method to focus the search by directly sampling this subset. The advantages of the presented sampling technique are demonstrated with a new algorithm, Informed RRT*. This method retains the same probabilistic guarantees on complete- ness and optimality as RRT* while improving the convergence rate and final solution quality. We present the algorithm as a simple modification to RRT* that could be further extended by more advanced path-planning algorithms. We show exper- imentally that it outperforms RRT* in rate of convergence, final solution cost, and ability to find difficult passages while demonstrating less dependence on the state dimension and range of the planning problem.
summary: @cite_3 proposed the Informed-RRT* algorithm which takes an initial solution from RRT* algorithm to define an ellipsoidal region from which new samples are drawn to minimize the initial solution for a given cost function. Although Informed-RRT* demonstrated enhanced convergence towards an optimal solution, this method suffers in situations where finding an initial path solution takes most of the computation time. To address this limitation, proposed Batch Informed Trees (BIT*) @cite_16 . BIT* is an incremental graph search technique where an ellipsoidal subset, containing configurations to update the graph, is incrementally enlarged. BIT* is shown empirically to outperform prior methods such as RRT* and Informed-RRT*. However, confining a graph search to ellipsoidal region slows down the performance of an algorithm in maze-like scenarios especially where the start and goal configurations are very close to each other, but the path among them traverses a complicated maze stretching waypoints far away from the goal. Furthermore, such a method would not translate to non-stationary environments or unseen environments.