Many robot tasks impose constraints on the workspace. For example, a robot may need to move a container without spilling its contents or open a door following the doorknob’s arc. Such constraints may induce narrow volumes in the configuration space, traditionally a challenge for sampling-based methods, and further cause infeasibility. We extend sample-driven connectivity learning (SDCL), a robust approach for planning with narrow passages, to develop a sampling ensemble for workspace constraints. In particular, the ensemble combines SDCL, projection via dual quaternion optimization, and random sampling. These complementary sampling approaches support efficient and robust planning under workspace constraints. Further, this framework offers the ability to determine infeasibility under workspace constraints, which is unaddressed by previous constrained planning methods.

Failure of any component in a robotic system during operation is a critical concern, and it is essential to address such incidents promptly. This work investigates a novel technique to recover from failures or changes in the configuration space while avoiding expensive re-computation or re-planning. We propose the Minimal Path Violation (MPV) concept to find the best feasible path with minimal re-configurations. The algorithm ranks pathways based on visibility, expansiveness, and cost. We perform experiments with articulated 3 DOF to 28 DOF robots ranging from serial linkage robots, Kuka YouBots, and PR2 robots. Our results show that our method outperforms existing optimal planners in computation time, total nodes, and path cost while preserving path feasibility in changed configuration space.

Intrinsically disordered proteins (IDPs) play vital regulatory roles in biology, emphasizing the significance of understanding their conformational behavior and interaction mechanisms during protein-ligand or protein-protein interactions. However, IDP analysis becomes difficult due to the lack of a stable structure. In this work, we investigate the binding behavior of an IDP using the surface information of the interacting protein complex. Our algorithm extracts the protein surface model’s topological and geometric features and predicts a geometrically favorable binding pose for an IDP around it. A transition path is planned to the predicted bound position to help evaluate the RMSD deviation in the IDP conformation structure. In our results, we use the Zernike descriptor metric to examine the structural homology of the binding pose and analyze the molar Gibbs free energy (binding affinity) of experimental conformation.

We present an incremental topology-based motion planner that, while planning paths in the configuration space, performs metric gluing on the constructed Vietoris-Rips simplicial complex of each sub-space (voxel). By incrementally capturing topological and geometric information in batches of voxel graphs, our algorithm avoids the time overhead of analyzing the properties of the entire configuration space. We theoretically prove in this paper that the simplices of all voxel graphs joined together are homotopy-equivalent to the union of the simplices in the configuration space. Experiments were carried out in seven different environments using various robots, including the articulated linkage robot, the Kuka YouBot, and the PR2 robot. In all environments, the results show that our algorithm achieves better convergence for path cost and computation time with a memory-efficient roadmap than state-of-the-art methods.

Geometric features of protein surfaces play an important role in the identification of biomolecular structures, functions, and interactions. These features have been crucial in predicting binding sites for protein-ligand or protein-protein interactions. This paper introduces simplicial complexes and discrete Morse theory to extract important geometric information on the protein surface. Using the extracted geometric information, we provide possible intermediate conformations around the protein surface as the ligand travels to the binding site. We compare the efficiency of our method with the state-of-art-method in terms of computation time and total complexes needed to generate the topological structure of the protein surface. We also show comparable relevance of the binding affinity of our method in relation to the known native protein binding site.

We present a topological method for finding coarsely diverse pathways. The use of pre-computed paths for online planning in a dynamic context reduces the overhead of re-planning alternate routes. Our algorithm applied the notion of discrete Morse theory to identify critical points incident on the obstacles and used this information to identify and return a diverse set of coarse paths. Three sampling-based planning approaches are converted to topology-aware planners and compared to another that employs the SPARS2 path planning algorithm. We report on the number of coarse pathways found, computation time, and average path length and show that our approach outperformed previously published path diversity algorithms.

We present a new way of constructing sparse roadmaps using point clouds that approximates and measures the underlying topology of the Cfreespace. The main advantage of the constructed roadmap is its homotopy equivalence to the η-offset of the Cfreespace. Though only used to plan paths as a regular roadmap in this work, because the roadmap preserves the topology of the underlying sampled space, the information can be used to plan paths beyond the simple connection of graph vertices. To construct the roadmap, we first sample the configuration space so that the resulting graph is a n-skeleton graph that constructs a Vietoris-Rips (VR) complex. Then, we perform a series of topological collapses to remove vertices from the graph while still preserving its topological properties. The resulting roadmaps are used to plan paths for different robots and the experimental results show that the proposed topological approach is faster and more feasible in complex high-dimensional spaces.