The complexity of the free space for a robot moving amidst fat obstacles

We propose a new definition of fatness of geometric objects and compare it with alternative definitions. We show that, under some realistic assumptions, the complexity of the free space for a robot, with any fixed number of degrees of freedom moving in a d-dimensional Euclidean workspace with fat obstacles, is linear in the number of obstacles. The complexity of motion planning algorithms depends on the complexity of the robot's free space, and theoretically, the complexity of the free space can be very high. Thus, our result opens the way to devising provable efficient motion planning algorithms in certain realistic settings.     

Generating optimal path by level set approach for a mobile robot moving in static/dynamic environments

According to the analogy between the mobile robot navigation path and the heat transferring path under steady state, the robot path planning problem during navigation is converted into identify the heat transferring path that minimizes the thermal compliance across the analysis domain. A new path planning approach which combines the concept of growth simulation and level set based heat conduction topology optimization framework is adopted to determine the heat transferring path. By introducing the concept of growth simulation, the proposed approach could calculate a few steps of the navigation path, which is of great significance for online reactive navigation. The proposed approach could avoid local minima and search for the optimal growth orientation freely without constraints from background mesh since the inherent characteristics of heat conduction and the level set approach, respectively. A new reactive navigation algorithm based on the proposed path planning approach and the concept of temporarily safe path is proposed to navigate the mobile robot from the start point to the goal point in unknown dynamic environment with static and dynamic obstacles. Diverse simulation cases are carried to illustrate the effectiveness of the reactive navigation algorithm.     

Heuristic fuzzy-neuro network and its application to reactive navigation of a mobile robot

A novel pattern recognition approach to reactive navigation of a mobile robot is presented in this paper. A heuristic fuzzy-neuro network is developed for pattern-mapping between quantized ultrasonic sensory data and velocity commands to the robot. The design goal was to enable an autonomous mobile robot to navigate safely and efficiently to a target position in a previously unknown environment. Useful heuristic rules were combined with the fuzzy Kohonen clustering network (FKCN) to build the desired mapping between perception and motion. This method provides much faster response to unexpected events and is less sensitive to sensor misreading than conventional approaches. It allows continuous, fast motion of the mobile robot without any need to stop for obstacles. The effectiveness of the proposed method is demonstrated in a series of practical tests on our experimental mobile robot.     

A findpath problem in the presence of moving obstacles

A solution of the findpath problem in which a moving object is required to avoid moving obstacles and move to the designated target in the plane is provided via the second method of Lyapunov. This paper presents a new control designed by a family of piecewise Lyapunov functions to solve a findpath problem and gives some simulation results of that.     

The existence of the scattering operator for moving obstacles

For solutions of the wave equation outside a moving obstacle, the scattering operator exists if and only if the local energy decays to zero.     

A stochastic optimization approach for robot scheduling

In this paper we are concerned with a stochastic optimization approach for determining the optimal job-sequencing in a robot-handler production system, such that the best value of some performance indices which depend on control parameters are obtained. The idea is to reflect the possible control policies of the system in its Stochastic Petri Net model (SPN) and to select a suitable conflict resolution rule whenever the transitions representing the possible actions of the robot are enabled. This rule would depend on a vectorx ⁿ of control parameters, and the problem results in finding the values of those parameters which would be in some sense optimal for the system.The objective function is defined as a linear combination of several performance indices that are estimated simultaneously.We propose a combined simulation and optimization approach aimed at solving the conflict situations arising in the system due to simultaneous requests of the robot from jobs in different queues; then we establish a stochastic optimization approach for deriving control policies that govern the flow in the SPN model.The theoretical optimization criteria are presented along with a case study.     

Neuro-fuzzy technique for navigation of multiple mobile robots

In this paper, navigation techniques for several mobile robots are investigated in a totally unknown environment. In the beginning, Fuzzy logic controllers (FLC) using different membership functions are developed and used to navigate mobile robots. First a fuzzy controller has been used with four types of input members, two types of output members and three parameters each. Next two types of fuzzy controllers have been developed having same input members and output members with five parameters each. Each robot has an array of sensors for measuring the distances of obstacles around it and an image sensor for detecting the bearing of the target. It is found that the FLC having Gaussian membership function is best suitable for navigation of multiple mobile robots. Then a hybrid neuro-fuzzy technique has been designed for the same problem. The neuro-fuzzy technique being used here comprises a neural network, which is acting as a pre processor for a fuzzy controller. The neural network considered for neuro-fuzzy technique is a multi-layer perceptron, with two hidden layers. These techniques have been demonstrated in simulation mode, which depicts that the robots are able to avoid obstacles and reach the targets efficiently. Amongst the techniques developed neuro-fuzzy technique is found to be most efficient for mobile robots navigation. Experimental verifications have been done with the simulation results to prove the authenticity of the developed neuro-fuzzy technique.     

An efficient direct approach for computing shortest rectilinear paths among obstacles in a two-layer interconnection model

In this paper, we present a direct approach for routing a shortest rectilinear path between two points among a set of rectilinear obstacles in a two-layer interconnection model that is used for VLSI routing applications. The previously best known direct approach for this problem takes O(nlog²n) time and O(nlogn) space, where n is the total number of obstacle edges. By using integer data structures and an implicit graph representation scheme (i.e., a generalization of the distance table method), we improve the time bound to O(nlog^3/2n) while still maintaining the O(nlogn) space bound. Comparing with the indirect approach for this problem, our algorithm is simpler to implement and is probably faster for a quite large range of input sizes.     

Rectilinear paths among rectilinear obstacles

Given a set of obstacles and two distinguished points in the plane the problem of finding a collision-free path subject to a certain optimization function is a fundamental problem that arises in many fields, such as motion planning in robotics, wire routing in VLSI and logistics in operations research. In this survey we emphasize its applications to VLSI design and limit ourselves to the rectilinear domain in which the goal path to be computed and the underlying obstacles are all rectilinearly oriented, i.e., the segments are either horizontal or vertical. We consider different routing environments, and various optimization criteria pertaining to VLSI design, and provide a survey of results that have been developed in the past, present current results and give open problems for future research.     

Directional fields algebraic non-linear solution equations for mobile robot planning

In this study, a novel approach to robot navigation/planning by using half-cell electrochemical potentials is presented. The half-cell electrode’s potential is modelled by the Nernst equation to yield automatic search/detection of pipeline flaws by using the direct current voltage gradient (DCVG) technique. We introduce a theory of spherical volumetric electric density in the soil to sustain our postulates for navigational potential fields. The Nernst potential is correlated with the distance to a pipe’s flaw by proposing a fitted theoretical-empirical nonlinear regression model. From this, volumetric derivatives are solved as gradient-based fields to control wheeled robot’s motion. A nonlinear system for trajectory planning is proposed, and analytically solved by an algebraic solution. This solution directly adjust robot’s speed kinematic values to lead it toward the flaw. The inverse/forward kinematic constraints are non-holonomic, and are recursively integrated into the general potential equation. Analytical modelling is reported, and a set of numerical simulations are presented to prove the feasibility of the proposed formulations.     

A hierarchical method for real-time distance computation among moving convex bodies

This paper presents the Hierarchical Walk, or H-Walk algorithm, which maintains the distance between two moving convex bodies by exploiting both motion coherence and hierarchical representations. For convex polygons, we prove that H-Walk improves on the classic Lin–Canny and Dobkin–Kirkpatrick algorithms. We have implemented H-Walk for moving convex polyhedra in three dimensions. Experimental results indicate that, unlike previous incremental distance computation algorithms, H-Walk adapts well to variable coherence in the motion and provides consistent performance.     

Sequentially switched fuzzy-model-based control for wheeled mobile robot with visual odometry

This study focused on the Takagi–Sugeno (T–S) fuzzy-model-based control design for the differentially-driven wheeled mobile robot with visual odometry. The position and posture of the mobile robot are estimated by visual odometry. The polar kinematic model of the mobile robot is exactly converted to the T–S fuzzy model and then the fuzzy control design is synthesized to the fuzzy model. The sequentially switched fuzzy control design includes turning, forward motion as well as position and posture control modes. The stabilization is guaranteed based on the Lyapunov stability criterion. The practical constraints on the visual odometry are also satisfied in the control design. Finally, the experiment results demonstrate the effectiveness of the fuzzy-model-based control design for the mobile robot with visual odometry.     

A moving window approach for nonparametric estimation of the conditional tail index

We present a nonparametric family of estimators for the tail index of a Pareto-type distribution when covariate information is available. Our estimators are based on a weighted sum of the log-spacings between some selected observations. This selection is achieved through a moving window approach on the covariate domain and a random threshold on the variable of interest. Asymptotic normality is proved under mild regularity conditions and illustrated for some weight functions. Finite sample performances are presented on a real data study.     

A mean-field approach for the asymptotic tracking problem of moving continuum target clouds

We propose a new coupled kinetic system arising from the asymptotic tracking of a continuum target cloud, and study its asymptotic tracking property. For the proposed kinetic system, we present an energy functional which is monotonic and distance between particle trajectories corresponding to kinetic equations for target, and tracking ensembles tend to zero asymptotically under a suitable sufficient framework. The framework is formulated in terms of system parameters and initial data.     

Discrete neural dynamic programming in wheeled mobile robot control

In this paper we propose a discrete algorithm for a tracking control of a two-wheeled mobile robot (WMR), using an advanced Adaptive Critic Design (ACD). We used Dual-Heuristic Programming (DHP) algorithm, that consists of two parametric structures implemented as Neural Networks (NNs): an actor and a critic, both realized in a form of Random Vector Functional Link (RVFL) NNs. In the proposed algorithm the control system consists of the DHP adaptive critic, a PD controller and a supervisory term, derived from the Lyapunov stability theorem. The supervisory term guaranties a stable realization of a tracking movement in a learning phase of the adaptive critic structure and robustness in face of disturbances. The discrete tracking control algorithm works online, uses the WMR model for a state prediction and does not require a preliminary learning. Verification has been conducted to illustrate the performance of the proposed control algorithm, by a series of experiments on the WMR Pioneer 2-DX.     

An approach for solving of a moving boundary problem

In this paper we shall study moving boundary problems, and we introduce an approach for solving a wide range of them by using calculus of variations and optimization. First, we transform the problem equivalently into an optimal control problem by defining an objective function and artificial control functions. By using measure theory, the new problem is modified into one consisting of the minimization of a linear functional over a set of Radon measures; then we obtain an optimal measure which is then approximated by a finite combination of atomic measures and the problem converted to an infinite-dimensional linear programming. We approximate the infinite linear programming to a finite-dimensional linear programming. Then by using the solution of the latter problem we obtain an approximate solution for moving boundary function on specific time. Furthermore, we show the path of moving boundary from initial state to final state.     

A social approach for target localization: simulation and implementation in the marXbot robot

Foraging is a common benchmark problem in collective robotics in which a robot (the forager) explores a given environment while collecting items for further deposition at specific locations. A typical real-world application of foraging is garbage collection where robots collect garbage for further disposal in pre-defined locations. This work proposes a method to cooperatively perform the task of finding such locations: instead of using local or global localization strategies relying on pre-installed infrastructure, the proposed approach takes advantage of the knowledge gathered by a population about the localization of the targets. In our approach, robots communicate in an intrinsic way the estimation about how near they are from a target; these estimations are used by neighbour robots for estimating their proximity, and for guiding the navigation of the whole population when looking for these specific areas. We performed several tests in a simulator, and we validated our approach on a population of real robots. For the validation tests we used a mobile robot called marXbot. In both cases (i.e., simulation and implementation on real robots), we found that the proposed approach efficiently guides the robots towards the pre-specified targets while allowing the modulation of their speed.     

Feasible command strategies for the control of motion of a simple mobile robot

The concept of feasible command strategies is introduced and its applicability is demonstrated by solving a guidance and control problem. This problem concerns the motion of a system which is composed of a rolling disk and a controlled slender rod that is pivoted, through its endpoint, about the disk center. The motion of the disk-rod system is subjected to state and control constraints, and it serves as a model for the motion of a simple mobile robot. In addition, the concept of path controllability is introduced and a condition is derived for the system motion path controllability. The derivation of this condition enables one to design closed-loop control laws for the system motion.