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In 2002 Mauduit and Sarkozy started to study finite sequences of \begin{document}$ k $\end{document} symbols \begin{document}$ E_{N} = \left(e_{1},e_{2},\cdots,e_{N}\right)\in \mathcal{A}^{N}, $\end{document} where \begin{document}$ \mathcal{A} = \left\{a_{1},a_{2},\cdots,a_{k}\right\}(k\in \mathbb{N},k\geq 2) $\end{document} is a finite set of \begin{document}$ k $\end{document} symbols. Later many pseudorandom sequences of \begin{document}$ k $\end{document} symbols have been given and studied by using number theoretic methods. In this paper we study the pseudorandom properties of the \begin{document}$ k $\end{document} -ary Sidel'nikov sequences with length \begin{document}$ q-1 $\end{document} by using the estimates for certain character sums with exponential function, where \begin{document}$ q $\end{document} is a prime power. Our results show that Sidel'nikov sequences enjoy good well-distribution measure and correlation measure. Furthermore, we prove that the set of size \begin{document}$ \phi(q-1) $\end{document} of \begin{document}$ k $\end{document} -ary Sidel'nikov sequences is collision free and possesses the strict avalanche effect property provided that \begin{document}$ k = o(q^{\frac{1}{4}}) $\end{document} , where \begin{document}$ \phi $\end{document} denotes Euler's totient function.

In drilling, the tool path is usually generated according to the workpiece geometry and the arrangement of holes. To perform drilling, majority of Computer-Aided Manufacturing (CAM) software offer a set of predefined drilling strategies. In this context, tool traveling time between the holes is considered as a non-value-adding movement and thus must be minimized. However, generating the optimum tool path with the shortest possible traveling distance in the presence of obstacles received little attention and therefore, CAM-generated tool paths are not necessarily optimum. This paper introduces a new algorithm based upon Traveling Salesman Problem (TSP) to minimize the tool path length while considering collision avoidance. The developed optimization model considers multiple constraints, including the location of tool origin and the presence of obstacles along the tool path, to generate a collision-free trajectory with minimum length. Performance of the proposed model was compared to the tool path generated by HSMWorks CAM software and the results confirmed the ability of the algorithm in generating an optimum or near-optimum, collision-free tool path for real-world drilling applications with a minimal computational time.

In this letter, we have studied how to use simultaneous collision-free duplexing (SCD) in point-to-multipoint environment. SCD is a method exchanging uplink and downlink signals simultaneously using the same resource for each link and has the advantages in that it does not need complicated self-interference cancellation unlike full duplexing. In addition, SCD is different from dynamic time division duplexing (D-TDD) in which interlink interference can be completely avoided. Therefore, to analyze the effect of interlink interference on SCD, we have derived the upper bound of link capacity and the required value of interlink isolation level for better SCD performance than D-TDD. We have verified the analyzed isolation level and confirmed that SCD has good performance even in practical point-to-multipoint environment through simulation.

Although multi-axis bead deposition-based additive manufacturing processes have been investigated in many aspects in the literature, a general process planning approach to address collision detecti...

When operating in confined spaces or near obstacles, collision‐free path planning is an essential requirement for autonomous exploration in unknown environments. This study presents an autonomous exploration technique using a carefully designed collision‐free local planner. Using LiDAR range measurements, a local end‐point selection method is designed, and the path is generated from the current position to the selected end‐point. The generated path showed the consistent collision‐free path in real‐time by adopting the Euclidean signed distance field‐based grid‐search method. The results consistently demonstrated the safety and reliability of the proposed path‐planning method. Real‐world experiments are conducted in three different mines, demonstrating successful autonomous exploration flights in environment with various structural conditions. The results showed the high capability of the proposed flight autonomy framework for lightweight aerial robot systems. In addition, our drone performed an autonomous mission in the tunnel circuit competition (Phase 1) of the DARPA Subterranean Challenge.

Unmanned aerial vehicles (UAVs) have become essential tools for exploring, mapping and inspection of unknown three-dimensional (3D) tunnel-like environments which is a very challenging problem. A computationally light navigation algorithm is developed in this paper for quadrotor UAVs to autonomously guide the vehicle through such environments. It uses sensors observations to safely guide the UAV along the tunnel axis while avoiding collisions with its walls. The approach is evaluated using several computer simulations with realistic sensing models and practical implementation with a quadrotor UAV. The proposed method is also applicable to other UAV types and autonomous underwater vehicles.

Instead of using the tedious process of manual positioning, an off-line path planning algorithm has been developed for military turrets to improve their accuracy and efficiency. In the scope of this research, an algorithm is proposed to search a path in three different types of configuration spaces which are rectangular-, circular-, and torus-shaped by providing three converging options named as fast, medium, and optimum depending on the application. With the help of the proposed algorithm, 4-dimensional (D) path planning problem was realized as 2-D + 2-D by using six sequences and their options. The results obtained were simulated and no collision was observed between any bodies in these three options.

Planning a feasible, and safe trajectory is a crucial procedure for autonomous parking which remains to be fully solved. Generally, a trajectory is depicted by a sequence of configurations which include positions, and orientations. However, existing approaches usually design parking trajectories without considering the evolution from one configuration to the next. Hence, these trajectories are practically infeasible in some scenarios, and safety risks may exist. In this paper, a guaranteed collision‐free trajectory planning method is proposed for autonomous parking. A dynamic optimisation problem is built, which includes vehicle kinematics, collision avoidance constraints, and physical restraints. Then the dynamic optimisation problem is discretised into a finite‐dimensional nonlinear programming problem. To describe collision avoidance constraints, the concepts of the virtual protection frame, and the magnification parameter are introduced. It is highlighted that a novel collision detection criterion is raised from the view of geometry. Tests in three common scenarios, and a complex scenario illustrate the effectiveness of the proposed approach. Moreover, the stability of the algorithm is discussed in this paper. Via the proposed approach, an integrated design of planning, and control is possible.

The co-existence of collision avoidance and time-asymptotic flocking of multi-particle systems with measurement delay is considered. Based on Lyapunov stability theory and some auxiliary differential inequalities, a delay-related sufficient condition is established for this system to admit a time-asymptotic flocking and collision avoidance. The estimated range of the delay is given, which may affect the flocking performance of the system. An analytical expression was proposed to quantitatively analyze the upper bound of this delay. Under the flocking conditions, the exponential decay of the relative velocity of any two particles in the system is characterized. Particularly, the collision-free flocking conditions are also given for the case without delay. This work verifies that both collision avoidance and flocking behaviors can be achieved simultaneously in a delay system.

Autonomous mobile robot path planning is considered as a complex task in unknown, highly uncertain and dynamic environments. The presence of diverse and uncertain objects present in the environment makes the autonomous navigation of a mobile robot a difficult and expensive task. Artificial potential field (APF) provides a good and easy solution to the path planning problem resulting in a collision free navigation of a mobile robot from source to destination. One of the inherent problems in APF based path planning is the Local Minima problem. This paper provides a fuzzy based approach to path planning in addition to steering a robot out of local minima configuration with a comparative analysis of some non-fuzzy approaches.

Blisks with the integral structure are key parts used in new jet engines to promote the performance of aircrafts, which also increases the complexity of tool orientation planning in the five-axis machining. It is an essential task to find the collision-free tool orientation when the tool holder is pushed deep into the channel of blisk to increase rigidity and reduce vibration. Since the radius of the holder varies with the height, the line-visibility is no longer applicable when constructing collision-free regions of tool orientation. In this paper, a method of constructing collision-free regions without interference checking is proposed. The work of finding collision-free regions resorts to solving the local contact curves on the checking surfaces of blisk. And it further transforms into searching the locally tangent points (named critical points) between the holder and surface. Then a tracking-based algorithm is proposed to search the sample critical points on these local contact curves. And the corresponding critical vectors are also calculated synchronously. Besides, the safety allowance, discrete precision and acceptable deviation are introduced in the algorithm to ensure accuracy by controlling the angle between two adjacent critical vectors properly. After that, the searched critical vectors are mapped orderly to two-dimensional space and the collision-free regions are constructed. This method is finally verified and compared with a referenced method. The results show that the proposed method can efficiently construct collision-free regions for holder under the given accuracy.

St. Petersburg Institute for Informatics and Automation of the Russian Academy of Sciences An algorithm for collision-free robot reconfiguration is presented, based on search for short mappings between start and target positions, which minimizes the total length of straight robotic paths. Modeling results for a swarm up to 10000 agents are presented.

This paper presents a method for real-time collision-free path planning that uses a new navigation function for environments in which humans and robots cooperate or coexist, which guarantees the sa...

This paper presents a new surveillance video synopsis method which performs much better than previous approaches in terms of both compression ratio and artifact. Previously, a surveillance video was usually compressed by shifting the moving objects of that video forward along the time axis, which inevitably yielded serious collision and chronological disorder artifacts between the shifted objects. The main observation of this paper is that these artifacts can be alleviated by changing the speed or size of the objects, since with varied speed and size the objects can move more flexibly to avoid collision points or to keep chronological relationships. Based on this observation, we propose a video synopsis method that performs object shifting, speed changing, and size scaling simultaneously. We show how to integrate the three heterogeneous operations into a single optimization framework and achieve high-quality synopsis results. Unlike previous approaches that usually use alternative optimization strategies to solve synopsis optimizations, we develop a Metropolis sampling algorithm to find the solution for our three-variable optimization problem. A variety of experiments demonstrate the effectiveness of our method.

This paper focuses on the application of surveillance and monitoring using unmanned aerial vehicles (UAVs). A novel coverage model is proposed to characterize the quality of coverage (QoC) of a target by a UAV. On the basis of this model, a reactive collision free three-dimensional deployment algorithm is proposed, with the goal of maximizing the overall QoC of targets by a network of UAVs. The algorithm consists of two navigation laws for the horizontal movement and the vertical movement, both of which are easily implementable in real time. The convergence of the algorithm is proved, and the computational complexity is analyzed. Computer simulations are conducted to demonstrate the performance of the proposed method.

This study focuses on the trajectory planning problem for automatic lane-change maneuvers, for which we propose a nonlinear programing model to generate the collision-avoidance lane-change trajecto...

With the significant advance of vehicle-to-everything (V2X) techniques, unsignalized intersection coordination has been widely recognized to facilitate the development of automated vehicles (AVs) for the intelligent transportation system. However, how to guarantee driving safety while improving the unsignalized intersection management efficiency is a challenging issue. In this article, we investigate the collision-free and efficient V2X-enabled AV scheduling problem at unsignalized intersections. First, by dividing the intersection zone into different collision sections (CSs), we formulate the intersection collision-free model into an absolute value programming (AVP) problem, which is proved to be NP-hard. We consider both nonplatoon and platoon traffic scenarios, and unlike previous algorithms, which require to control all the AVs at each scheduling step with computational intractability, our scheduling algorithm can assign a feasible time for each arriving AV with low complexity. Further, we propose an alternately iterative descent method (AIDM) to solve the AVP problem by assigning the optimal entering time for each arriving AV. Through extensive simulations with various traffic data generated by SUMO, we demonstrate that our proposed AIDM algorithm can significantly enhance the scheduling performance in terms of passing delay and scheduling throughput. Even though the AIDM algorithm achieves the same level of transportation performances with the state-of-the-art algorithm, it advances dramatically in computational complexity and communication overhead, which is easier to be implemented in practice.

Measurement path planning plays an essential role in on-machine measurement, which is often required to be time-saving and collision-free. This paper proposes a novel path planning methodology and develops an automatic collision avoidance strategy for measurement. Measurement points are generated by Contour section sampling (CSS), Grid mesh sampling (GMS), and Locally dense sampling (LDS) on the free-form surface. Afterwards, a shortest path algorithm (SPA) and a non-interference path algorithm (NIPA) are developed respectively. The simulations show that the proposed method can reduce the total inspection distance to nearly 7.82% than the original one. The presented path planning method can measure the surface of large aerospace parts directly by using a trigger probe.

Mobile robots have become popular in many application areas over the last few decades. In order to perceive their environment in which they move autonomously, various sensors such as depth cameras are used. The processing of 3D information from depth images is very computationally expensive due to the large amount of data. However, for many mobile robots, navigation in a simplified 2D world is sufficient. For this purpose, the depth images of the environment can first be reduced to 2D information in the form of a laserscan line and then processed with algorithms for localization and mapping. This paper improves an existing algorithm that converts depth images into laserscans and tests it on a real robot in a real world scenario. In contrast to the original algorithm, the improved algorithm considers 3D information such as the height of the robot and obstacles when creating the laserscan line. This allows a mobile robot to navigate in a simplified 2D world without colliding with obstacles in the real 3D world. Since processing the 3D information is computationally expensive, the algorithm was optimized to be executable on low-cost single-board computers.

The paper was based on research tasks in the field of robotics. It approaches solving the collision states of a robot while operating equipment and applies the knowledge in the CATIA system environment. Motion Planning is of paramount importance in robotics, where a goal is to determine a collision-free, unobstructed path for a robot that works in an environment which contains obstacles. An obstacle can be an object that is found in the robot’s workspace.

The autonomous navigation of robots in unknown environments is a challenge since it needs the integration of a several subsystems to implement different functionality. It needs drawing a map of the environment, robot map localization, motion planning or path following, implementing the path in real-world, and many others; all have to be implemented simultaneously. Thus, the development of autonomous robot navigation (ARN) problem is essential for the growth of the robotics field of research. In this paper, we present a simulation of a swarm intelligence method is known as Particle Swarm Optimization (PSO) to develop an ARN system that can navigate in an unknown environment, reaching a pre-defined goal and become collision-free. The proposed system is built such that each subsystem manipulates a specific task which integrated to achieve the robot mission. PSO is used to optimize the robot path by providing several waypoints that minimize the robot traveling distance. The Gazebo simulator was used to test the response of the system under various envirvector representing a solution to the optimization problem.onmental conditions. The proposed ARN system maintained robust navigation and avoided the obstacles in different unknown environments. vector representing a solution to the optimization problem.

In five-axis machining of blisk, the filleted end mill has attracted more and more attention because of its larger cutting width. However, it is still a hard work to find the tool posture without interference. In this paper, a method is proposed to solve the collision-free regions. Based on the visibility of free-form surface, a tool-surface tangent model of the filleted end mill is established. With the model, only critical points on profiles of checking surface are searched with a self-adapting step length and the corresponding critical vectors are calculated and mapped to construct the collision-free regions. Firstly, critical points on the boundaries are searched according to the given precision. Meanwhile, the corresponding critical vectors are calculated and some special searched points are selected as the endpoints of each profile. Then, the adjacent critical points are searched along the profile by adjusting iteratively with a self-adapting step length in the parameter domain one by one. During the search, the corresponding critical vectors are calculated too. After that, the critical vectors are mapped to construct the subinterval collision-free regions in two-dimensions. And a method is adopted to combine collision-free regions. This algorithm is finally verified with a closed blisk and compared with a referenced method. The results show that it can efficiently solve collision-free regions in five-axis milling of blisk with a filleted end mill.

We present a second-order formulation of the LWR model based on Phillips' model (Phillips, 1979); but the model is nonstandard with a hyperreal infinitesimal relaxation time. Since the original Phillips model is unstable with three different definitions of stability in both Eulerian and Lagrangian coordinates, we cannot use traditional methods to prove the equivalence between the second-order model, which can be considered the zero-relaxation limit of Phillips' model, and the LWR model, which is the equilibrium counterpart of Phillips' model. Instead, we resort to a nonstandard method based on the equivalence relationship between second-order continuum and car-following models established in (Jin, 2016) and prove that the nonstandard model and the LWR model are equivalent, since they have the same anisotropic car-following model and stability property. We further derive conditions for the nonstandard model to be forward-traveling and collision-free, prove that the collision-free condition is consistent with but more general than the CFL condition (Courant et al., 1928), and demonstrate that only anisotropic and symplectic Euler discretization methods lead to physically meaningful solutions. We numerically solve the lead-vehicle problem and show that the nonstandard second-order model has the same shock and rarefaction wave solutions as the LWR model for both Greenshields and triangular fundamental diagrams; for a non-concave fundamental diagram we show that the collision-free condition, but not the CFL condition, yields physically meaningful results. Finally we present a correction method to eliminate negative speeds and collisions in general second-order models, and verify the method with a numerical example., Comment: 34 pages, 6 figures

The electroacoustic waves, particularly ion-acoustic waves (IAWs), and their expansion in the medium of a magnetized collision-free plasma system has been investigated theoretically. The plasma system is assumed to be composed of both positively and negatively charged mobile ion species and kappa-distributed hot electron species. In the nonlinear perturbation regime, the magnetized Korteweg–de Vries (KdV) and magnetized modified KdV (mKdV) equations are derived by using reductive perturbation method. The prime features (i.e., amplitude, phase speed, width, etc.) of the IAWs are studied precisely by analyzing the stationary solitary wave solutions of the magnetized KdV and magnetized mKdV equations, respectively. It occurs that the basic properties of the IAWs are significantly modified in the presence of the excess superthermal hot electrons, obliqueness, the plasma particle number densities, etc. It is also observed that, in case of magnetized KdV solitary waves, both compressive and rarefactive structures are formed, whereas only compressive structures are found for the magnetized mKdV solitary waves. The implication of our results in some space and laboratory plasma situations is concisely discussed.

An EAST Articulated Maintenance Arm (EAMA), upgraded based on an articulated inspection arm (AIA), which was successfully operated in Tore Supra in 2008, was developed for the purpose of the inspection and maintenance of damaged internal components during plasma discharges without breaking the East Advanced Superconducting Tokamak (EAST) ultra-high vacuum condition. However, the coupling structure and high redundancy of the EAMA, due to the requirement of coverage ratio and the limitation of the EAST environment, produces a limited accuracy in positioning control. Therefore, the optimal design of the geometric parameters plays a vital role in the EAMA’s performance. In this paper, the main characteristics of the EAMA system are investigated to formulate the optimization into a multi-objective problem. Furthermore, an approach based on the Monte Carlo method, integrated with a dedicated collision detection algorithm in the EAST environment, is elaborated on, which is utilized to calculate the collision-free workspace of the EAMA. With the knowledge of the workspace, the coverage ratio is obtained by a progressive meshing technique. Finally, several groups of geometric parameters are sampled to calculate the corresponding value of the objective functions, and the optimized combination of the geometric parameters is obtained by comparing the results.

Collision-freeness is an important structural property of particle dynamics. A nonlinear ODE system ẋ(t) = f(x(t)) is called collision-free if the solution to the initial value problem with x(0)=x° has distinct components for all times t whenever the initial state x° has distinct components. Both the general case of a C1–function f and the special case of a polynomial (or even linear) function f will be addressed.

This paper reports initial collision avoidance results regarding density-based feedback control for swarm robotics from our previous works. The method controls the density distribution of the agents via smooth velocity fields synthesised in a decentralised fashion. Local estimates of density around each agent are compared with the desired swarm density and the difference is fed to the density based feedback controller to generate the velocity commands to be tracked. The continuity of the resulting velocity field promotes smooth and organised behaviour, and as the mathematical analyses reveals, it facilitates collision-free trajectories for each agent.

Any vehicle needs to be aware of its localization, destination, and neighboring vehicles’ state information for collision free navigation. A centralized controller computes controls for cooperative adaptive cruise control (CACC) vehicles based on the assumed behavior of manually driven vehicles (MDVs) in a mixed vehicle scenario. The assumed behavior of the MDVs may be different from the actual behavior, which gives rise to a model mismatch. The use of erroneous localization information can generate erroneous controls. The presence of a model mismatch and the use of erroneous controls could potentially result into collisions. A controller robust to issues such as localization errors and model mismatches is thus required. This paper proposes a robust model predictive controller, which accounts for localization errors and mitigates model mismatches. Future control values computed by the centralized controller are shared with CACC vehicles and are stored in a buffer. Due to large localization errors or model mismatches when control computations are infeasible, control values from the buffer are used. Simulation results show that the proposed robust controller with buffer can avoid almost the same number of collisions in a scenario impacted by localization errors as that in a scenario with no localization errors despite model mismatch.

In this letter, we introduce a surveillance model for multi domain IoT environment, which is supported by reinforced barriers with collision-avoidance using heterogeneous smart UAVs. Formally, we define a problem whose goal is minimizing the maximum movement of smart UAVs on condition that collision-avoidance among UAVs is assured when they fly between initial positions and specific spots in order to build reinforced barrier in multi domain. After ILP formulation of the defined problem, a novel approach is proposed to solve the problem. Also, we analyze the performance of the developed scheme through extensive simulations with various scenarios.