Kevin C. Wolfe

The Banana Distribution is Gaussian: A Localization Study with Exponential Coordinates

Distributions in position and orientation are central to many problems in robot localization. To increase efficiency, a majority of algorithms for planar mobile robots use Gaussians defined on positional Cartesian coordinates and heading. However, the distribution of poses for a noisy two-wheeled robot moving in the plane has been observed by many to be a “bananashaped” distribution, which is clearly not Gaussian/normal in these coordinates. As uncertainty increases, many localization algorithms therefore become “inconsistent” due to the normality assumption breaking down. We observe that this is because the combination of Cartesian coordinates and heading is not the most appropriate set of coordinates to use, and that the banana distribution can be described in closed form as a Gaussian in an alternative set of coordinates via the so-called exponential map. With this formulation, we can derive closed-form expressions for propagating the mean and covariance of the Gaussian in these exponential coordinates for a differential-drive car moving along a trajectory constructed from sections of straight segments and arcs of constant curvature. In addition, we detail how to fuse two or more Gaussians in exponential coordinates together with given relative pose measurements between robots moving in formation. These propagation and fusion formulas utilized here reduce uncertainty in localization better than when using traditional methods. We demonstrate with numerical examples dramatic improvements in the estimated pose of three robots moving in formation when compared to classical Cartesiancoordinate-based Gaussian fusion methods.

M 3 Express: A low-cost independently-mobile reconfigurable modular robot

This paper presents M3Express (Modular-Mobile-Multirobot), a new design for a low-cost modular robot. The robot is self-mobile, with three independently driven wheels that also serve as connectors. The new connectors can be automatically operated, and are based on stationary magnets coupled to mechanically actuated ferromagnetic yoke pieces. Extensive use is made of plastic castings, laser cut plastic sheets, and low-cost motors and electronic components. Modules interface with a host PC via Bluetooth® radio. An off-board camera, along with a set of modules and a control PC form a convenient, low-cost system for rapidly developing and testing control algorithms for modular reconfigurable robots. Experimental results demonstrate mechanical docking, connector strength, and accuracy of dead reckoning locomotion.

Multiscale Modeling of Double-Helical DNA and RNA: A Unification through Lie Groups

Several different mechanical models of double-helical nucleic-acid structures that have been presented in the literature are reviewed here together with a new analysis method that provides a reconciliation between these disparate models. In all cases, terminology and basic results from the theory of Lie groups are used to describe rigid-body motions in a coordinate-free way, and when necessary, coordinates are introduced in a way in which simple equations result. We consider double-helical DNAs and RNAs which, in their unstressed referential state, have backbones that are either straight, slightly precurved, or bent by the action of a protein or other bound molecule. At the coarsest level, we consider worm-like chains with anisotropic bending stiffness. Then, we show how bi-rod models converge to this for sufficiently long filament lengths. At a finer level, we examine elastic networks of rigid bases and show how these relate to the coarser models. Finally, we show how results from molecular dynamics simulation at full atomic resolution (which is the finest scale considered here) and AFM experimental measurements (which is at the coarsest scale) relate to these models.

Approaches to robotic teleoperation in a disaster scenario: From supervised autonomy to direct control

The ability of robotic systems to effectively address disaster scenarios that are potentially dangerous for human operators is continuing to grow as a research and development field. This leverages research from areas such as bimanual manipulation, dexterous grasping, bipedal locomotion, computer vision, sensing, object segmentation, varying degrees of autonomy, and operator control/feedback. This paper describes the development of a semi-autonomous bimanual dexterous robotic system that comes to the aid of a mannequin simulating an injured victim by operating a fire extinguisher, affixing a cervical collar, cooperatively placing the victim on a spineboard with another bimanual robot, and relocating the victim. This system accomplishes these tasks through a series of control modalities that range from supervised autonomy to full teleoperation and allows the control model to be chosen and optimized for a specific subtask. We present a description of the hardware platform, the software control architecture, a human-in-the-loop computer vision algorithm, and an infrastructure to use a variety of user input devices in combination with autonomous control to compete several dexterous tasks. The effectiveness of the system was demonstrated in both laboratory and live outdoor demonstrations.

An architecture for universal construction via modular robotic components

Abstract A set of modular components is presented for use in reconfigurable robotic construction systems. The set includes passive and active components. The passive components can be formed into static structures and adaptable grids carrying electrical power and signals. Passive and active components can be combined into general purpose mobile manipulators which are able to augment and reconfigure the grid, construct new manipulators, and potentially perform general purpose fabrication tasks such as additive manufacturing. The components themselves are designed for low-cost, simple fabrication methods and could potentially be fabricated by constructors made of the same components. This work represents a step toward a Cyclic Fabrication System, a network of materials, tools, and manufacturing processes that can produce all of its constituent components. These and similar systems have been proposed for a wide range of far-term applications, including space-based manufacturing, construction of large-scale industrial facilities, and also for driving development of low-cost 3D printing machines.

Quantitative Comparison of Conformational Ensembles

A number of measures have been used in the structural biology literature to compare the shapes or conformations of biological macromolecules. However, the issue of how to compare two ensembles of conformations has received far less attention. Herein, the problem of how to quantitatively compare two such ensembles is addressed in several different ways using concepts from probability and information theory. Ultimately, such metrics could be used in the evaluation of structure-prediction algorithms and the analysis of how conformational mobility is inhibited by bound ligands.

Trajectory generation and steering optimization for self-assembly of a modular robotic system

A problem associated with motion planning for the assembly of individual modules in a new self-reconfigurable modular robotic system is presented. Modules of the system are independently mobile and can be driven on flat surfaces in a similar fashion to the classic kinematic cart. This problem differs from most nonholonomic steering problems because of an added constraint on one of the internal states. The constraint properly aligns the docking mechanism, allowing modules to connect with one another along wheel surfaces. This paper presents an initial method for generating trajectories and control inputs that allow module assembly. It also provides an iterative method for locally optimizing a nominal control function using weighted perturbation functions, while preserving the final pose and internal states.

A Craniomaxillofacial Surgical Assistance Workstation for Enhanced Single-Stage Reconstruction Using Patient-Specific Implants.

Background:Craniomaxillofacial reconstruction with patient-specific, customized craniofacial implants (CCIs) is ideal for skeletal defects involving areas of aesthetic concern—the non-weight-bearing facial skeleton, temporal skull, and/or frontal-forehead region. Results to date are superior to a variety of “off-the-shelf” materials, but require a protocol computed tomography scan and preexisting defect for computer-assisted design/computer-assisted manufacturing of the CCI. The authors developed a craniomaxillofacial surgical assistance workstation to address these challenges and intraoperatively guide CCI modification for an unknown defect size/shape. Methods:First, the surgeon designed an oversized CCI based on his/her surgical plan. Intraoperatively, the surgeon resected the bone and digitized the resection using a navigation pointer. Next, a projector displayed the limits of the craniofacial bone defect onto the prefabricated, oversized CCI for the size modification process; the surgeon followed the projected trace to modify the implant. A cadaveric study compared the standard technique (n = 1) to the experimental technique (n = 5) using surgical time and implant fit. Results:The technology reduced the time and effort needed to resize the oversized CCI by an order of magnitude as compared with the standard manual resizing process. Implant fit was consistently better for the computer-assisted case compared with the control by at least 30%, requiring only 5.17 minutes in the computer-assisted cases compared with 35 minutes for the control. Conclusion:This approach demonstrated improvement in surgical time and accuracy of CCI-based craniomaxillofacial reconstruction compared with previously reported methods. The craniomaxillofacial surgical assistance workstation will provide craniofacial surgeons a computer-assisted technology for effective and efficient single-stage reconstruction when exact craniofacial bone defect sizes are unknown.

Effects of tools inserted through snake-like surgical manipulators.

Snake-like manipulators with a large, open lumen can offer improved treatment alternatives for minimally-and less-invasive surgeries. In these procedures, surgeons use the manipulator to introduce and control flexible tools in the surgical environment. This paper describes a predictive algorithm for estimating manipulator configuration given tip position for nonconstant curvature, cable-driven manipulators using energy minimization. During experimental bending of the manipulator with and without a tool inserted in its lumen, images were recorded from an overhead camera in conjunction with actuation cable tension and length. To investigate the accuracy, the estimated manipulator configuration from the model and the ground-truth configuration measured from the image were compared. Additional analysis focused on the response differences for the manipulator with and without a tool inserted through the lumen. Results indicate that the energy minimization model predicts manipulator configuration with an error of 0.24 ± 0.22mm without tools in the lumen and 0.24 ± 0.19mm with tools in the lumen (no significant difference, p = 0.81). Moreover, tools did not introduce noticeable perturbations in the manipulator trajectory; however, there was an increase in requisite force required to reach a configuration. These results support the use of the proposed estimation method for calculating the shape of the manipulator with an tool inserted in its lumen when an accuracy range of at least 1mm is required.

Planar Uncertainty Propagation and a Probabilistic Algorithm for Interception

Many robotics applications involve motion planning with uncertainty. In this paper, we focus on path planning for planar systems by optimizing the probability of successfully arriving at a goal. We approach this problem with a modified version of the Path-of-Probability (POP) algorithm.We extend the POP algorithm to allow for a moving target and to optimize the number of steps to reach the goal. One tool that we develop in this paper to increase efficiency of the POP algorithm is a second order closed-form uncertainty propagation formula. This formula is utilized to quickly propagate the mean and covariance of nonparametrized distributions for planar systems. The modified POP algorithm is demonstrated on a simple rolling disc example with a moving goal.