On the Power of Manifold Samples in Exploring Configuration Spaces and the Dimensionality of Narrow Passages

We extend our study of Motion Planning via Manifold Samples (MMS), a general algorithmic framework that combines geometric methods for the exact and complete analysis of low-dimensional configuration spaces with sampling-based approaches that are appropriate for higher dimensions. The framework explores the configuration space by taking samples that are entire low-dimensional manifolds of the configuration space capturing its connectivity much better than isolated point samples. The contributions of this paper are as follows: (i) We present a recursive application of MMS in a six-dimensional configuration space, enabling the coordination of two polygonal robots translating and rotating amidst polygonal obstacles. In the adduced experiments for the more demanding test cases MMS clearly outperforms PRM, with over 20-fold speedup in a coordination-tight setting. (ii) A probabilistic completeness proof for the most prevalent case, namely MMS with samples that are affine subspaces. (iii) A closer examination of the test cases reveals that MMS has, in comparison to standard sampling-based algorithms, a significant advantage in scenarios containing high-dimensional narrow passages. This provokes a novel characterization of narrow passages which attempts to capture their dimensionality, an attribute that had been (to a large extent) unattended in previous definitions.Comment: 20 page

Kinematic Flexibility Analysis: Hydrogen Bonding Patterns Impart a Spatial Hierarchy of Protein Motion

Elastic network models (ENM) and constraint-based, topological rigidity analysis are two distinct, coarse-grained approaches to study conformational flexibility of macromolecules. In the two decades since their introduction, both have contributed significantly to insights into protein molecular mechanisms and function. However, despite a shared purpose of these approaches, the topological nature of rigidity analysis, and thereby the absence of motion modes, has impeded a direct comparison. Here, we present an alternative, kinematic approach to rigidity analysis, which circumvents these drawbacks. We introduce a novel protein hydrogen bond network spectral decomposition, which provides an orthonormal basis for collective motions modulated by non-covalent interactions, analogous to the eigenspectrum of normal modes, and decomposes proteins into rigid clusters identical to those from topological rigidity. Our kinematic flexibility analysis bridges topological rigidity theory and ENM, and enables a detailed analysis of motion modes obtained from both approaches. Our analysis reveals that collectivity of protein motions, reported by the Shannon entropy, is significantly lower for rigidity theory versus normal mode approaches. Strikingly, kinematic flexibility analysis suggests that the hydrogen bonding network encodes a protein-fold specific, spatial hierarchy of motions, which goes nearly undetected in ENM. This hierarchy reveals distinct motion regimes that rationalize protein stiffness changes observed from experiment and molecular dynamics simulations. A formal expression for changes in free energy derived from the spectral decomposition indicates that motions across nearly 40% of modes obey enthalpy-entropy compensation. Taken together, our analysis suggests that hydrogen bond networks have evolved to modulate protein structure and dynamics

On Providing Efficient Real-Time Solutions to Motion Planning Problems of High Complexity

The holy grail of robotics is producing robotic systems capable of efficiently executing all the tasks that are hard, or even impossible, for humans. Humans, undoubtedly, from both a hardware and software perspective, are extremely complex systems capable of executing many complicated tasks. Thus, the complexity of many state-of-the-art robotic systems is also expected to progressively increase, with the goal to match or even surpass human abilities. Recent developments have emphasized mostly hardware, providing highly complex robots with exceptional capabilities. On the other hand, they have illustrated that one important bottleneck of realizing such systems as a common reality is real-time motion planning. This thesis aims to assist the development of complex robotic systems from a computational perspective. The primary focus is developing novel methodologies to address real-time motion planning that enables the robots to accomplish their goals safely and provide the building blocks for developing robust advanced robot behavior in the future. The proposed methods utilize and enhance state-of-the-art approaches to overcome three different types of complexity: 1. Motion planning for high-dimensional systems. RRT+, a new family of general sampling-based planners, was introduced to accelerate solving the motion planning problem for robotic systems with many degrees of freedom by iteratively searching in lowerdimensional subspaces of increasing dimension. RRT+ variants computed solutions orders of magnitude faster compared to state-of-the-art planners. Experiments in simulation of kinematic chains up to 50 degrees of freedom, and the Baxter humanoid robot validate the effectiveness of the proposed technique. 2. Underwater navigation for robots in cluttered environments. AquaNav, a real-time navigation pipeline for robots moving efficiently in challenging, unknown, and unstructured environments, was developed for Aqua2, a hexapod swimming robot with complex, yet to be fully discovered, dynamics. AquaNav was tested offline in known maps, and online in unknown maps utilizing vision-based SLAM. Rigorous testing in simulation, inpool, and open-water trials show the robustness of the method on providing efficient and safe performance, enabling the robot to navigate by avoiding static and dynamic obstacles in open-water settings with turbidity and surge. 3. Active perception of areas of interest during underwater operation. AquaVis, an extension of AquaNav, is a real-time navigation technique enabling robots, with arbitrary multi-sensor configurations, to safely reach their target, while at the same time observing multiple areas of interest from a desired proximity. Extensive simulations show safe behavior, and strong potential for improving underwater state estimation, monitoring, tracking, inspection, and mapping of objects of interest in the underwater domain, such as coral reefs, shipwrecks, marine life, and human infrastructure

Multilevel Motion Planning: A Fiber Bundle Formulation

Motion planning problems involving high-dimensional state spaces can often be solved significantly faster by using multilevel abstractions. While there are various ways to formally capture multilevel abstractions, we formulate them in terms of fiber bundles, which allows us to concisely describe and derive novel algorithms in terms of bundle restrictions and bundle sections. Fiber bundles essentially describe lower-dimensional projections of the state space using local product spaces. Given such a structure and a corresponding admissible constraint function, we can develop highly efficient and optimal search-based motion planning methods for high-dimensional state spaces. Our contributions are the following: We first introduce the terminology of fiber bundles, in particular the notion of restrictions and sections. Second, we use the notion of restrictions and sections to develop novel multilevel motion planning algorithms, which we call QRRT* and QMP*. We show these algorithms to be probabilistically complete and almost-surely asymptotically optimal. Third, we develop a novel recursive path section method based on an L1 interpolation over path restrictions, which we use to quickly find feasible path sections. And fourth, we evaluate all novel algorithms against all available OMPL algorithms on benchmarks of eight challenging environments ranging from 21 to 100 degrees of freedom, including multiple robots and nonholonomic constraints. Our findings support the efficiency of our novel algorithms and the benefit of exploiting multilevel abstractions using the terminology of fiber bundles.Comment: Submitted to IJR

Probabilistic motion planning for non-Euclidean and multi-vehicle problems

Trajectory planning tasks for non-holonomic or collaborative systems are naturally modeled by state spaces with non-Euclidean metrics. However, existing proofs of convergence for sample-based motion planners only consider the setting of Euclidean state spaces. We resolve this issue by formulating a flexible framework and set of assumptions for which the widely-used PRM*, RRT, and RRT* algorithms remain asymptotically optimal in the non-Euclidean setting. The framework is compatible with collaborative trajectory planning: given a fleet of robotic systems that individually satisfy our assumptions, we show that the corresponding collaborative system again satisfies the assumptions and therefore has guaranteed convergence for the trajectory-finding methods. Our joint state space construction builds in a coupling parameter $1\leq p\leq \infty$, which interpolates between a preference for minimizing total energy at one extreme and a preference for minimizing the travel time at the opposite extreme. We illustrate our theory with trajectory planning for simple coupled systems, fleets of Reeds-Shepp vehicles, and a highly non-Euclidean fractal space.Comment: 12 pages, 8 figures. Substantial revision

Computational approaches to shed light on molecular mechanisms in biological processes

Computational approaches based on Molecular Dynamics simulations, Quantum Mechanical methods and 3D Quantitative Structure-Activity Relationships were employed by computational chemistry groups at the University of Milano-Bicocca to study biological processes at the molecular level. The paper reports the methodologies adopted and the results obtained on Aryl hydrocarbon Receptor and homologous PAS proteins mechanisms, the properties of prion protein peptides, the reaction pathway of hydrogenase and peroxidase enzymes and the defibrillogenic activity of tetracyclines. © Springer-Verlag 2007

Grasp plannind under task-specific contact constraints

Several aspects have to be addressed before realizing the dream of a robotic hand-arm system with human-like capabilities, ranging from the consolidation of a proper mechatronic design, to the development of precise, lightweight sensors and actuators, to the efficient planning and control of the articular forces and motions required for interaction with the environment. This thesis provides solution algorithms for a main problem within the latter aspect, known as the {\em grasp planning} problem: Given a robotic system formed by a multifinger hand attached to an arm, and an object to be grasped, both with a known geometry and location in 3-space, determine how the hand-arm system should be moved without colliding with itself or with the environment, in order to firmly grasp the object in a suitable way. Central to our algorithms is the explicit consideration of a given set of hand-object contact constraints to be satisfied in the final grasp configuration, imposed by the particular manipulation task to be performed with the object. This is a distinguishing feature from other grasp planning algorithms given in the literature, where a means of ensuring precise hand-object contact locations in the resulting grasp is usually not provided. These conventional algorithms are fast, and nicely suited for planning grasps for pick-an-place operations with the object, but not for planning grasps required for a specific manipulation of the object, like those necessary for holding a pen, a pair of scissors, or a jeweler's screwdriver, for instance, when writing, cutting a paper, or turning a screw, respectively. To be able to generate such highly-selective grasps, we assume that a number of surface regions on the hand are to be placed in contact with a number of corresponding regions on the object, and enforce the fulfilment of such constraints on the obtained solutions from the very beginning, in addition to the usual constraints of grasp restrainability, manipulability and collision avoidance. The proposed algorithms can be applied to robotic hands of arbitrary structure, possibly considering compliance in the joints and the contacts if desired, and they can accommodate general patch-patch contact constraints, instead of more restrictive contact types occasionally considered in the literature. It is worth noting, also, that while common force-closure or manipulability indices are used to asses the quality of grasps, no particular assumption is made on the mathematical properties of the quality index to be used, so that any quality criterion can be accommodated in principle. The algorithms have been tested and validated on numerous situations involving real mechanical hands and typical objects, and find applications in classical or emerging contexts like service robotics, telemedicine, space exploration, prosthetics, manipulation in hazardous environments, or human-robot interaction in general

Optimal anticipatory control as a theory of motor preparation

Supported by a decade of primate electrophysiological experiments, the prevailing theory of neural motor control holds that movement generation is accomplished by a preparatory process that progressively steers the state of the motor cortex into a movement-specific optimal subspace prior to movement onset. The state of the cortex then evolves from these optimal subspaces, producing patterns of neural activity that serve as control inputs to the musculature. This theory, however, does not address the following questions: what characterizes the optimal subspace and what are the neural mechanisms that underlie the preparatory process? We address these questions with a circuit model of movement preparation and control. Specifically, we propose that preparation can be achieved by optimal feedback control (OFC) of the cortical state via a thalamo-cortical loop. Under OFC, the state of the cortex is selectively controlled along state-space directions that have future motor consequences, and not in other inconsequential ones. We show that OFC enables fast movement preparation and explains the observed orthogonality between preparatory and movement-related monkey motor cortex activity. This illustrates the importance of constraining new theories of neural function with experimental data. However, as recording technologies continue to improve, a key challenge is to extract meaningful insights from increasingly large-scale neural recordings. Latent variable models (LVMs) are powerful tools for addressing this challenge due to their ability to identify the low-dimensional latent variables that best explain these large data sets. One shortcoming of most LVMs, however, is that they assume a Euclidean latent space, while many kinematic variables, such as head rotations and the configuration of an arm, are naturally described by variables that live on non-Euclidean latent spaces (e.g., SO(3) and tori). To address this shortcoming, we propose the Manifold Gaussian Process Latent Variable Model, a method for simultaneously inferring nonparametric tuning curves and latent variables on non-Euclidean latent spaces. We show that our method is able to correctly infer the latent ring topology of the fly and mouse head direction circuits.This work was supported by a Trinity-Henry Barlow scholarship and a scholarship from the Ministry of Education, ROC Taiwan