Tamás Kalmár-Nagy

Near-optimal dynamic trajectory generation and control of an omnidirectional vehicle

Abstract This paper describes a computationally inexpensive, yet high performance trajectory generation algorithm for omnidirectional vehicles. It is shown that the associated non-linear control problem can be made tractable by restricting the set of admissible control functions. The resulting problem is linear with coupled control efforts and a near-optimal control strategy is shown to be piecewise constant (bang–bang type). A very favorable trade-off between optimality and computational efficiency is achieved. The proposed algorithm is based on a small number of evaluations of simple closed-form expressions and is thus extremely efficient. The low computational cost makes this method ideal for path planning in dynamic environments.

Subcritical Hopf Bifurcation in the Delay Equation Model for Machine Tool Vibrations

We show the existence of a subcritical Hopf bifurcation in thedelay-differential equation model of the so-called regenerative machine toolvibration. The calculation is based on the reduction of the infinite-dimensional problem to a two-dimensional center manifold. Due to the specialalgebraic structure of the delayed terms in the nonlinear part of the equation,the computation results in simple analytical formulas. Numerical simulationsgave excellent agreement with the results.

Nonlinear models for complex dynamics in cutting materials

This paper reviews the prediction of complex, unsteady and chaotic dynamics associated with material–cutting processes through nonlinear dynamical models. The status of bifurcation phenomena such as subcritical Hopf instabilities is assessed. A new model using hysteresis in the cutting force is presented, which is shown to exhibit complex quasi–periodic solutions. In addition, further evidence for chaotic dynamics in non–regenerative cutting of polycarbonate plastic is reviewed. The authors draw the conclusion that single–degree–of–freedom models are not likely to predict low–level cutting chaos and that more complex models, such as multi–degree–of–freedom systems based on careful cutting–force experiments, are required.

Benchmarking and standardization of intelligent robotic systems

To design and develop capable, dependable, and affordable intelligent systems, their performance must be measurable. Scientific methodologies for standardization and benchmarking are crucial for quantitatively evaluating the performance of emerging robotic and intelligent systems’ technologies. There is currently no accepted standard for quantitatively measuring the performance of these systems against user-defined requirements; and furthermore, there is no consensus on what objective evaluation procedures need to be followed to understand the performance of these systems. The lack of reproducible and repeatable test methods has precluded researchers working towards a common goal from exchanging and communicating results, inter-comparing system performance, and leveraging previous work that could otherwise avoid duplication and expedite technology transfer. Currently, this lack of cohesion in the community hinders progress in many domains, such as manufacturing, service, healthcare, and security. By providing the research community with access to standardized tools, reference data sets, and open source libraries of solutions, researchers and consumers will be able to evaluate the cost and benefits associated with intelligent systems and associated technologies. In this vein, the edited book volume addresses performance evaluation and metrics for intelligent systems, in general, while emphasizing the need and solutions for standardized methods.From mundane and repetitive tasks to assisting first responders in saving lives of victims in disaster scenarios, robots are expected to play an important role in our lives in the coming years. Despite recent advances in mobile robotic systems, lack of widely accepted performance metrics and standards hinder the progress in many application areas such as manufacturing, healthcare, and search and rescue. In this paper, we outline the importance of the development of standardized methods and objective performance evaluation/benchmarking of existing and emerging robotic technologies. We provide a survey of significant past efforts by researchers and developers around the globe and discuss how we can leverage such efforts in advancing the state-of-the-art. Using an example of designing a ‘standard’ evaluation toolkit for robotic mapping, we illustrate some of the problems faced in developing objective performance metrics whilst accommodating the requirements and restrictions imposed by the intended domain of operation and other practical considerations.

Cut Detection in Wireless Sensor Networks

A wireless sensor network can get separated into multiple connected components due to the failure of some of its nodes, which is called a “cut.” In this paper, we consider the problem of detecting cuts by the remaining nodes of a wireless sensor network. We propose an algorithm that allows 1) every node to detect when the connectivity to a specially designated node has been lost, and 2) one or more nodes (that are connected to the special node after the cut) to detect the occurrence of the cut. The algorithm is distributed and asynchronous: every node needs to communicate with only those nodes that are within its communication range. The algorithm is based on the iterative computation of a fictitious “electrical potential” of the nodes. The convergence rate of the underlying iterative scheme is independent of the size and structure of the network. We demonstrate the effectiveness of the proposed algorithm through simulations and a real hardware implementation.

Nonlinear Stability of a Delayed Feedback Controlled Container Crane

A simplified model of a container crane subject to a delayed feedback is investigated. The conditions for a Hopf bifurcation to stable/unstable limit-cycle solutions are determined. It is shown that a subcritical Hopf bifurcation to unstable oscillations cannot be ruled out and the undesired coexistence of stable large amplitude oscillations and a stable equilibrium endangers the robustness of time-delay control strategies. The bifurcation is analyzed both analytically and numerically using a continuation method.

High-dimensional Harmonic Balance Analysis for Second-order Delay-differential Equations

This paper demonstrates the utility of the high-dimensional harmonic balance (HDHB) method for locating limit cycles of second-order delay-differential equations (DDEs). A matrix version of the HDHB method for systems of DDEs is described in detail. The method has been successfully applied to capture the stable and/or unstable limit cycles in three different models: a machine tool vibration model, the sunflower equation and a circadian rhythm model. The results show excellent agreement with collocation and continuation-based solutions from DDE-BIFTOOL. The advantages of HDHB over the classical harmonic balance method are highlighted and discussed.

Real-time trajectory generation for omnidirectional vehicles

We discuss a method of generating near-optimal trajectories for a robot with omnidirectional drive capabilities, taking the second-order dynamics of the vehicle into account. The relaxation of optimality results in immense computational savings, critical in dynamic environments. In particular, a decoupling strategy for each of the three degrees of freedom of the vehicle is presented, along with a method for coordinating the degrees of freedom. A nearly optimal trajectory for the vehicle can typically be calculated in less than 1000 floating point operations, which makes it attractive for real-time control in dynamic and uncertain environments.

Graph decomposition methods for uncertainty propagation in complex, nonlinear interconnected dynamical systems

Uncertainty propagation in complex, interconnected dynamical systems can be performed more efficiently by decomposing the network based on the hierarchy and/or the strength of coupling. In this paper, we first present a structural decomposition method that identifies the hierarchy of subsystems. We briefly review the notion of horizontal-vertical decomposition (HVD) or strongly connected components (SCC) decomposition of a dynamical system and describe algorithms based on Markov chain theory and graph theory to obtain the HVD from the equation graph of the system. We also present a non-structural decomposition method to identify the weakly connected subsystems of a system based on the Laplacian of a graph derived from the Jacobian. While most of prior efforts in this direction concentrated on stability, robustness and concrete results were limited to linear systems, we use it for uncertainty propagation and study of asymptotic behavior of nonlinear interconnected systems. We illustrate the two methods using a fuel cell system example. These two methods provide a framework for efficient propagation of uncertainty in complex nonlinear systems.

Genetic Algorithm for Combinatorial Path Planning: The Subtour Problem

The purpose of this paper is to present a combinatorial planner for autonomous systems. The approach is demonstrated on the so-called subtour problem, a variant of the classical traveling salesman problem (TSP): given a set of 𝑛 possible goals/targets, the optimal strategy is sought that connects 𝑘≤𝑛 goals. The proposed solution method is a Genetic Algorithm coupled with a heuristic local search. To validate the approach, the method has been benchmarked against TSPs and subtour problems with known optimal solutions. Numerical experiments demonstrate the success of the approach.