Matthew S. Moses

Kinematic state estimation and motion planning for stochastic nonholonomic systems using the exponential map

A nonholonomic system subjected to external noise from the environment, or internal noise in its own actuators, will evolve in a stochastic manner described by an ensemble of trajectories. This ensemble of trajectories is equivalent to the solution of a Fokker-Planck equation that typically evolves on a Lie group. If the most likely state of such a system is to be estimated, and plans for subsequent motions from the current state are to be made so as to move the system to a desired state with high probability, then modeling how the probability density of the system evolves is critical. Methods for solving Fokker-Planck equations that evolve on Lie groups then become important. Such equations can be solved using the operational properties of group Fourier transforms in which irreducible unitary representation (IUR) matrices play a critical role. Therefore, we develop a simple approach for the numerical approximation of all the IUR matrices for two of the groups of most interest in robotics: the rotation group in three-dimensional space, SO(3), and the Euclidean motion group of the plane, SE(2). This approach uses the exponential mapping from the Lie algebras of these groups, and takes advantage of the sparse nature of the Lie algebra representation matrices. Other techniques for density estimation on groups are also explored. The computed densities are applied in the context of probabilistic path planning for kinematic cart in the plane and flexible needle steering in three-dimensional space. In these examples the injection of artificial noise into the computational models (rather than noise in the actual physical systems) serves as a tool to search the configuration spaces and plan paths. Finally, we illustrate how density estimation problems arise in the characterization of physical noise in orientational sensors such as gyroscopes.

Design of a new independently-mobile reconfigurable modular robot

A new self-reconfigurable robot is presented. The robot is a hybrid chain/lattice design with several novel features. An active mechanical docking mechanism provides inter-module connection, along with optical and electrical interface. The docking mechanisms function additionally as driven wheels. Internal slip rings provide unlimited rotary motion to the wheels, allowing the modules to move independently by driving on flat surfaces, or in assemblies negotiating more complex terrain. Modules in the system are mechanically homogeneous, with three identical docking mechanisms within a module. Each mechanical dock is driven by a high torque actuator to enable movement of large segments within a multi-module structure, as well as low-speed driving. Preliminary experimental results demonstrate locomotion, mechanical docking, and lifting of a single module.

Robotic Self-replication in Structured Environments: Physical Demonstrations and Complexity Measures

In this paper we define a complexity ratio that measures the degree to which a robot is self-replicating based on the number and complexity of subsystems that it can assemble to form a functional replica. We also quantify how structured the environment must be in order for a robot to function. This calculation uses Sandersons concept of parts entropy. Together, the complexity measure of the robot and environmental entropy provide quantitative benchmarks to assess the state of the art in the subfield of self-replicating robotic systems, and provide goals for the design of future systems. We demonstrate these principles with three prototype systems that show different degrees of robotic self-replication. The first robot is controlled by a microprocessor and consists of five subsystems. The second has no microprocessor and is implemented as a finite-state machine consisting of discrete logic chips that are distributed over five subsystems. The third design consists of six subsystems and is able to handle greater environmental entropy. These systems demonstrate the desired progression towards self-replicating robots consisting of greater numbers of subsystems, each of lower complexity, and which are able to function in environments with increasing levels of disorder.

Constrained workspace generation for snake-like manipulators with applications to minimally invasive surgery

Osteolysis is a debilitating condition that can occur behind the acetabular component of total hip replacements due to wear of the polyethylene liner. Conventional treatment techniques suggest replacing the component, while less-invasive approaches attempt to access and clean the lesion through the screw holes in the component. However, current rigid tools have been shown to access at most 50% of the lesion. Using a recently developed dexterous manipulator, we have adapted a group-theoretic convolution framework to define the manipulators workspace and its ability to fully explore a lesion. We compared this with the experimental exploration of a printed model of the lesion. This convolution approach successfully contains the experimental results and shows over 98.8% volumetric coverage of a complex lesion. The results suggest this manipulator as a possible solution to accessing much of the area unreachable to the conventional less-invasive technique.

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.

A continuum manipulator made of interlocking fibers

A new type of continuum manipulator is presented, in which the body of the device is made up of identical, repeated interlocking fibers. A working prototype is demonstrated. Basic models describing the kinematics and mechanical properties of the device are developed, and their predictions are compared with the performance of the physical prototype. Advantages of the interlocking design include improved strength due to better load distribution, controllable stiffness, and a large open lumen.

Towards cyclic fabrication systems for modular robotics and rapid manufacturing

A cyclic fabrication system (CFS) is a network of materials, tools, and manufacturing processes that can produce all or most of its constituent components. This paper proposes an architecture for a robotic CFS based on modular components. The proposed system is intended to self-replicate via producing necessary components for replica devices. Some design challenges unique to self-replicating machines are discussed. Results from several proof-of-principle experiments are presented, including a manipulator designed to handle and assemble modules of the same type it is constructed from, a DC brush motor fabricated largely from raw materials, and basic manufacturing tools made with a simple CFS.

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.

Modeling Cable and Guide Channel Interaction in a High-Strength Cable-Driven Continuum Manipulator

This paper presents several mechanical models of a high-strength cable-driven dexterous manipulator designed for surgical procedures. A stiffness model is presented that distinguishes between contributions from the cables and the backbone. A physics-based model incorporating cable friction is developed and its predictions are compared with experimental data. The data show that under high tension and high curvature, the shape of the manipulator deviates significantly from a circular arc. However, simple parametric models can fit the shape with good accuracy. The motivating application for this study is to develop a model so that shape can be predicted using easily measured quantities such as tension, so that real-time navigation may be performed, especially in minimally-invasive surgical procedures, while reducing the need for hazardous imaging methods such as fluoroscopy.

Robotic Self-Replication in a Structured Environment without Computer Control

The ability to self-replicate is one of the distinctive features of living organisms. Robots capable of self-replication would have a profound impact on the field of robotics by improving lifetime and robustness. In the past our lab has built several prototypes of self-replicating robotic systems including semi-autonomous and fully-autonomous robots with microprocessor-based control, and a self-replicating electromechanical circuit composed of basic electronic elements (transistors, resistors, etc.). These previous efforts demonstrated that man-made systems with simple behaviors are capable of self-replication. Extending our previous results, in this paper, we present an autonomous self-replicating robotic system with distributed electronic components in a structured environment. Using simple discrete electronic components allows for a more uniform decomposition of each robot into simpler parts than for microprocessor-controlled systems. Ultimately, we would like to demonstrate robots that replicate from the most basic parts, and this paper represents one more step toward achieving this goal.