Jeff McGough

Pattern formation in the Gray-Scott model

Abstract We investigate an elliptic system that arises in cubic autocatalytic reactions known as the Gray–Scott model. Complicated patterns were reported by Pearson in a numerical study of this system. We produce the bifurcation analysis to support the existing numerical evidence for patterns. Specifically bifurcation results and C 2 bounds for nonuniform steady states are derived.

A priori bounds for reaction-diffusion systems arising in chemical and biological dynamics

The authors investigate reaction-diffusion equations which arise in chemical and biological dynamics. It is shown that several common systems share a useful property, a structure on the non-linearity which arises from conservation of mass or population. This conservation property is used to demonstrate a priori bounds for the parabolic problems and the associated elliptic problem. The types of systems included in the analysis are the Gray-Scott system, SIR model, and the Selkov model of glycolysis.

Depth mapping using a low-cost camera array

Computer vision has the potential to discern a large amount of information about the environment. This intelligence can be used to make decisions on navigation and obstacle avoidance. One of the core problems in machine vision is determining the distance from the camera to different objects for a given scene. Stereo-vision is one technique for solving this problem. Typically, two cameras are used for this algorithm. Using more than two cameras, however, has the ability to provide even better results. Here, a low-cost array of cameras was used which was built from commonly available, inexpensive hardware. The information from the multiple cameras was combined to provide a dense real-time depth map of the environment. The results of single stereo camera pairs versus multiple stereo camera pairs were compared and it was found that using multiple pairs does provide a denser depth map over that of a single pair.

A distributed manipulation concept using selective braking

This paper introduces a new distributed manipulation concept whereby objects operating under the action of a uniform force field are positioned perpendicular to the force field and oriented by selectively applying braking forces at various locations on the object. We assume that the braking locations do not slip, which gives the object dynamics the familiar form of the pendulum equation, but with the pendulum hinge location changing as a function of time. Such a system may find applications in parts handling or in the control of robots descending on inclines. This paper discusses the dynamics of such a robotic system and the sequential control of lateral object position and orientation. Simulation results show the effectiveness of the developed control laws.

Simulation of detecting and climbing a ladder for a humanoid robot

The most recent DARPA challenge presents an industrial accident scenerio for a humanoid robot to traverse and then perform human oriented tasks. In the fifth stage of the challenge, the robot must climb a wall mounted metal rung ladder. To accomplish this task, the robot must first recognize and localize the ladder prior to grasping and climbing. This paper presents the localization of the rungs using point cloud data from a simulated Microsoft Kinect sensor. It also presents grasping and climbing manuveur using PR2 Robot. The basic approach is to first segment out the background planes. We apply a voxel grid filter to make the computation faster. Then using the RANSAC algorithm, lines that represent the legs and the interior rung midline are extracted. Vertical lines are thrown away and only the lines that represent the rungs are retained. The center of the computed line is our estimated location for the rung centroid. We then can use the centroid information for the PR2 grasping.

Handling occlusion with an inexpensive array of cameras

The topic of computer vision is of interest due to its ability to provide a great deal of information about the physical world. One problem that plagues many vision applications is that of occlusion. Occlusion is the situation where the view of an object is being blocked by one or more other objects. In this work, a multi-view approach was taken to solve the problem. The tool used was a low-cost array of cameras that was designed and built in house. Results of the project are reviewed and it is shown that the algorithm used has the potential to recover many details that would otherwise be lost due to occlusion.

Low-cost camera array for mitigating lighting range effects

Lighting is a constant issue for computer vision applications. The range of light in a scene typically exceeds what an image can accurately represent. Typically, multiple images are taken with each image at a different exposure level. These images are then combined together in order to display more detail than a single image at a single exposure. For computer vision applications using a mutli-view approach it would require a substantial amount of bandwidth to perform these routines on each camera individually. This work looked at using multiple views in a camera array to each capture a different exposure level and then used that information to mitigate the lighting issues in a central view. A weighted averaging approach and a radiometric calibration based approach were both implemented and compared. In contrast to existing methods, this work looked at handling depth planes that were not considered to be on or near the plane at infinity. It was found that much of the detail that was lost due to lighting issues could be recovered.

Replacing Servos With Braking in an Omnidirectional Vehicle

We present an underactuated approach for steering a vehicle which reduces the number of required servos. This method replaces steering servos with braking actuators which can reduce energy use, weight and support electronics. The design of the steering system, the control system and comparison to traditional steering is considered.Copyright

Design and Development of a Vector Thrusting Quadrotor for Minimally Induced Pitch and Roll Motions

Due to its hovering capabilites and maneuverability, the quadrotor provides an excellent platform for unmanned systems and robotics research. Localization of the vehicle is typically done via laser ranging or photometric and depth cameras. The design of the quadrotor introduces a problem, however, when it is to travel parallel to the ground plane. Due to the rigid body of the quadrotor and the fixed orientation of the thrusters it is impossible for the quadrotor to undergo this motion without inducing a change in the pitch and/or roll orientation. This introduces a problem in finding the true orientation at which sensor measurements are taken, requiring advanced computer vision algorithms, mechanical gimbal systems or other means to compensate for the motion. This paper focuses on the design of a quadrotor that has the capability to travel parallel to the ground plane while minimizing the induced pitch and roll motion. The unique contribution to the quadrotor design is to allow each of the quadrotor arms to rotate about their respective horizontal axis in order to accomplish thrust vectoring of the individual motors. By controlling both the magnitude and direction of each of the motor thrusts, pure translational maneuvers are possible without inducing pitch and/or roll motions. Simulation results are presented as well as the controller used to govern the behavior of the craft.Copyright

Symbolic Computation of Lyapunov Functions using Evolutionary Algorithms

This paper is concerned with the question of stability in dynamical systems, specifically the issue of computing symbolic forms of Lyapunov functions for given dynamical systems. Due to the non-constructive form of the the Lyapunov constraints, we employ a type of evolutionary algorithm to construct candidate Lyapunov functions. Evolutionary Algorithms have demonstrated results in a vast array of optimization problems and are regularly employed in engineering design. We study the application of a variant of Genetic Programming known as Grammatical Evolution (GE). GE distinguishes itself from more traditional forms of genetic programs in that it separates the internal representation of a potential solution from the actual target expression. Strings of integers are evolved, with the candidate expressions being generated by performing a mapping using a problemspecific grammar. Traditional approaches using Genetic Programming have been plagued by unrestrained expression growth, stagnation and lack of convergence. These are addressed by the more biologically realistic gene representation and variations in the genetic operators. Illustrative examples are presented to validate the proposed technique.