Related papers: New perspective on sampling-based motion planning …
An approximate formulation of a robust geometric program (RGP) as a convex program is proposed. Interest in using geometric programs (GPs) to model complex engineering systems has been growing, and this has motivated explicitly modeling the…
We present a theoretical analysis of a recent whole body motion planning method, the Randomized Possibility Graph, which uses a high-level decomposition of the feasibility constraint manifold in order to rapidly find routes that may lead to…
Recent progress in randomized motion planners has led to the development of a new class of sampling-based algorithms that provide asymptotic optimality guarantees, notably the RRT* and the PRM* algorithms. Careful analysis reveals that the…
Sampling-based motion planning algorithms have been continuously developed for more than two decades. Apart from mobile robots, they are also widely used in manipulator motion planning. Hence, these methods play a key role in collaborative…
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…
Random geometric graphs (RGG) can be formalized as hidden-variables models where the hidden variables are the coordinates of the nodes. Here we develop a general approach to extract the typical configurations of a generic hidden-variables…
RRT* is one of the most widely used sampling-based algorithms for asymptotically-optimal motion planning. This algorithm laid the foundations for optimality in motion planning as a whole, and inspired the development of numerous new…
We describe a general probabilistic framework to address a variety of Frechet-distance optimization problems. Specifically, we are interested in finding minimal bottleneck-paths in $d$-dimensional Euclidean space between given start and…
Sampling-based algorithms, such as Rapidly Exploring Random Trees (RRT) and its variants, have been used extensively for motion planning. Control barrier functions (CBFs) have been recently proposed to synthesize controllers for…
We present a novel framework based on optimal transport for the challenging problem of comparing graphs. Specifically, we exploit the probabilistic distribution of smooth graph signals defined with respect to the graph topology. This allows…
Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…
Sampling-based motion planners rely on incremental densification to discover progressively shorter paths. After computing feasible path $\xi$ between start $x_s$ and goal $x_t$, the Informed Set (IS) prunes the configuration space…
Sparse model selection is ubiquitous from linear regression to graphical models where regularization paths, as a family of estimators upon the regularization parameter varying, are computed when the regularization parameter is unknown or…
Graph kernels are widely used for measuring the similarity between graphs. Many existing graph kernels, which focus on local patterns within graphs rather than their global properties, suffer from significant structure information loss when…
It is not until recently that graph neural networks (GNNs) are adopted to perform graph representation learning, among which, those based on the aggregation of features within the neighborhood of a node achieved great success. However,…
Probabilistic graphical models (PGMs) are powerful tools for representing statistical dependencies through graphs in high-dimensional systems. However, they are limited to pairwise interactions. In this work, we propose the simplicial…
Spatial generalized linear mixed models (SGLMMs) are popular and flexible models for non-Gaussian spatial data. They are useful for spatial interpolations as well as for fitting regression models that account for spatial dependence, and are…
Hidden Markov models (HMMs) and partially observable Markov decision processes (POMDPs) form a useful tool for modeling dynamical systems. They are particularly useful for representing environments such as road networks and office…
We study the effectiveness of metrics for Multi-Robot Motion-Planning (MRMP) when using RRT-style sampling-based planners. These metrics play the crucial role of determining the nearest neighbors of configurations and in that they regulate…
Many exciting robotic applications require multiple robots with many degrees of freedom, such as manipulators, to coordinate their motion in a shared workspace. Discovering high-quality paths in such scenarios can be achieved, in principle,…