Showing papers by "Nancy M. Amato published in 2003"

Using motion planning to map protein folding landscapes and analyze folding kinetics of known native structures.

Abstract: We investigate a novel approach for studying the kinetics of protein folding. Our framework has evolved from robotics motion planning techniques called probabilistic roadmap methods (PRMs) that have been applied in many diverse fields with great success. In our previous work, we presented our PRM-based technique and obtained encouraging results studying protein folding pathways for several small proteins. In this paper, we describe how our motion planning framework can be used to study protein folding kinetics. In particular, we present a refined version of our PRM-based framework and describe how it can be used to produce potential energy landscapes, free energy landscapes, and many folding pathways all from a single roadmap which is computed in a few hours on a desktop PC. Results are presented for 14 proteins. Our ability to produce large sets of unrelated folding pathways may potentially provide crucial insight into some aspects of folding kinetics, such as proteins that exhibit both two-state and three-state kinetics that are not captured by other theoretical techniques.

A general framework for sampling on the medial axis of the free space

Abstract: We propose a general framework for sampling the configuration space in which randomly generated configurations, free or not, are retracted onto the medial axis of the free space. Generalizing our previous work, this framework provides a template encompassing all possible retraction approaches. It also removes the requirement of exactly computing distance metrics thereby enabling application to more realistic high dimensional problems. In particular, our framework supports methods that retract a given configuration exactly or approximately onto the medial axis. As in our previous work, exact methods provide fast and accurate retraction in low (2 or 3) dimensional space. We also propose new approximate methods that can be applied to high dimensional problems, such as many DOF articulated robots. Theoretical and experimental results show improved performance on problems requiring traversal of narrow passages. We also study tradeoffs between accuracy and efficiency for different levels of approximation, and how the level of approximation effects the quality of the resulting roadmap.

Extracting optimal paths from roadmaps for motion planning

Abstract: We present methods for extracting optimal paths from motion planning roadmaps. Our system enables any combination of optimization criteria, such as collision detection, kinematic/dynamic constraints, or minimum clearance, and relaxed definitions of the goal state, to be used when selecting paths from roadmaps. Our algorithm is an augmented version of Dijkstra's shortest path algorithm which allows edge weights to be defined relative to the current path. We present simulation results maximizing minimum path clearance, minimizing localization effort, and enforcing kinematic/dynamic constraints.

A general framework for PRM motion planning

Abstract: An important property of PRM roadmaps is that they provide a good approximation of the connectivity of the free C-space. We present a general framework for building and querying probabilistic roadmaps that includes all previous PRM variants as special cases. In particular, it supports no, complete, or partial node and edge validation and various evaluation schedules for path validation, and it enables path customization for variable, adaptive query requirements. While each of the above features is present in some PRM variant, the general framework proposed here is the only one to include them all. Our framework enables users to choose the best approximation level for their problem. Our experimental evidence shows this can result in significant performance gains.

Improving the connectivity of PRM roadmaps

Abstract: In this paper we investigate how the coverage and connectedness of PRM roadmaps can be improved by adding a connected component (CC) connection step to the general PRM framework. We provide experimental results establishing that significant roadmap improvements can be obtained relatively efficiently by utilizing a suite of CC connection methods, which include variants of existing methods such as RRT and a new ray tracing based method. The coordinated application of these techniques is enabled by methods for selecting and scheduling pairs of nodes in different CCs for connection attempts. In addition to identifying important and/or promising regions of C-space for exploration, these methods also provide a mechanism for controlling the cost of the connection attempts. In our experiments, the time required by the improvement phase was on the same order as the time used to generate the initial roadmap.

A motion planning approach to protein folding

Abstract: Protein folding is considered to be one of the grand challenge problems in biology. Protein folding refers to how a protein's amino acid sequence, under certain physiological conditions, folds into a stable close-packed three-dimensional structure known as the native state. There are two major problems in protein folding. One, usually called protein structure prediction, is to predict the structure of the protein's native state given only the amino acid sequence. Another important and strongly related problem, often called protein folding, is to study how the amino acid sequence dynamically transitions from an unstructured state to the native state. In this dissertation, we concentrate on the second problem. There are several approaches that have been applied to the protein folding problem, including molecular dynamics, Monte Carlo methods, statistical mechanical models, and lattice models. However, most of these approaches suffer from either overly-detailed simulations, requiring impractical computation times, or overly-simplified models, resulting in unrealistic solutions. In this work, we present a novel motion planning based framework for studying protein folding. We describe how it can be used to approximately map a protein's energy landscape, and then discuss how to find approximate folding pathways and kinetics on this approximate energy landscape. In particular, our technique can produce potential energy landscapes, free energy landscapes, and many folding pathways all from a single roadmap. The roadmap can be computed in a few hours on a desktop PC using a coarse potential energy function. In addition, our motion planning based approach is the first simulation method that enables the study of protein folding kinetics at a level of detail that is appropriate (i.e., not too detailed or too coarse) for capturing possible 2-state and 3-state folding kinetics that may coexist in one protein. Indeed, the unique ability of our method to produce large sets of unrelated folding pathways may potentially provide crucial insight into some aspects of folding kinetics that are not available to other theoretical techniques.

Solving motion planning problems by iterative relaxation of constraints

Abstract: This dissertation presents a new approach to improve automated motion planners. Automatic motion planning has application in many areas such as robotics, virtual reality systems, and computer-aided design. Surprisingly, a single class of planners, called probabilistic roadmap methods (PRMs), have proven effective on problems from all these domains. Strengths of PRMs are simplicity and efficiency, even in high-dimensional configuration spaces. Nevertheless, PRMs are not as effective in environments where the solution path requires the robot to pass through a narrow passage. In this dissertation, we suggest a hierarchical strategy addressing this problem where we first simplify the problem by relaxing some feasibility constraints, solve the easier version of the problem, and then use that solution to help find a solution for the harder problem. We show how this strategy can be applied to (i) “virtual prototype” analysis, where the goal is to find a removal path for one part (the robot) from an assembly of other parts (obstacles), (ii) “ligand binding,” where we generate candidate binding sites for a ligand in a large protein molecule, and (iii) “deformable objects,” where the robot can deform itself to avoid collision while following a path.

Enveloping obstacles with hexagonal metamorphic robots

Abstract: The problem addressed is the distributed reconfiguration of the metamorphic robot system composed of any number of two dimensional robots (modules). The initial configuration we consider is a straight chain of modules, while the goal configuration satisfies a simple admissibility condition. Our reconfiguration strategy depends on finding a contiguous path of cells, called a substrate path that spans the goal configuration. Modules fill in this substrate path and then move along the path to fill in the remainder of the goal without collision or deadlock. In this paper, we address the problem of reconfiguration when a single obstacle is embedded in the goal environment. We introduce a classification for traversable surfaces, which allows for coherence in defining admissibility characteristics for various objects in the hexagonal grid. We present algorithms to 1) determine if an obstacle embedded in the goal fulfills a simple admissibility requirement, 2) include an admissible obstacle in a substrate path, and 3) accomplish distributed reconfiguration.

Feature-based localization using scannable visibility sectors

Abstract: This paper presents methods for navigating and localizing mobile robots in a known indoor environment. We introduce a restricted visibility concept called a scannable sector that can aid many existing navigation and localization algorithms. The scannable sectors are based on the physical characteristics of the environment and the limitations of the localization sensors used. We describe a complete navigation system that includes a scannable sector based localizer, sonar sensors, and a probabilistic roadmap path planner. Simulation and hardware results using a real robot with sonar sensors show the potential of our approach.