Showing papers on "Obstacle published in 2018"
TL;DR: This paper proposes a decentralized behavior-based formation control algorithm for multiple robots considering obstacle avoidance using only the information of the relative position of a robot between neighboring robots and obstacles that can significantly simplify the step of the information process.
Abstract: This paper proposes a decentralized behavior-based formation control algorithm for multiple robots considering obstacle avoidance. Using only the information of the relative position of a robot between neighboring robots and obstacles, the proposed algorithm achieves formation control based on a behavior-based algorithm. In addition, the robust formation is achieved by maintaining the distance and angle of each robot toward the leader robot without using information of the leader robot. To avoid the collisions with obstacles, the heading angles of all robots are determined by introducing the concept of an escape angle, which is related with three boundary layers between an obstacle and the robot. The layer on which the robot is located determines the start time of avoidance and escape angle; this, in turn, generates the escape path along which a robot can move toward the safe layer. In this way, the proposed method can significantly simplify the step of the information process. Finally, simulation results are provided to demonstrate the efficiency of the proposed algorithm.
156 citations
TL;DR: The results illustrate that the proposed MPC-based simultaneous trajectory planning and tracking approach achieves acceptable obstacle avoidance performance for an intelligent vehicle.
Abstract: As a typical example of cyber-physical systems, intelligent vehicles are receiving increasing attention, and the obstacle avoidance problem for such vehicles has become a hot topic of discussion. This paper presents a simultaneous trajectory planning and tracking controller for use under cruise conditions based on a model predictive control (MPC) approach to address obstacle avoidance for an intelligent vehicle. The reference trajectory is parameterized as a cubic function in time and is determined by the lateral position and velocity of the intelligent vehicle and the velocity and yaw angle of the obstacle vehicle at the start point of the lane change maneuver. Then, the control sequence for the vehicle is incorporated into the expression for the reference trajectory that is used in the MPC optimization problem by treating the lateral velocity of the intelligent vehicle at the end point of the lane change as an intermediate variable. In this way, trajectory planning and tracking are both captured in a single MPC optimization problem. To evaluate the effectiveness of the proposed simultaneous trajectory planning and tracking approach, joint veDYNA-Simulink simulations were conducted in the unconstrained and constrained cases under leftward and rightward lane change conditions. The results illustrate that the proposed MPC-based simultaneous trajectory planning and tracking approach achieves acceptable obstacle avoidance performance for an intelligent vehicle.
153 citations
TL;DR: Results demonstrate a feasible, fast, oscillation-free and collision-free path planning of the proposed method, which is practically feasible that can be applied to both static and dynamic environments.
Abstract: This paper deals with the mobile robots path planning problem in the presence of scattered obstacles in a visually known environment. Utilizing the theory of charged particles’ potential fields and inspired by a key idea of the authors’ recent work, an optimization based approach is proposed to obtain an optimal and robust path planning solution. By assigning a potential function for each individual obstacle, the interaction of all scattered obstacles are integrated in a scalar potential surface (SPS) which strongly depends on the physical features of the mobile robot and obstacles. The optimum path is then obtained from a cost function optimization by attaining a trade-off between traversing the shortest path and avoiding collisions, simultaneously. Hence, irrespective of any physical constraints on the obstacles/mobile-robot and the adjacency of the target to the obstacles, the achieved results demonstrate a feasible, fast, oscillation-free and collision-free path planning of the proposed method. Utilizing a scalar decision variable makes it extremely simple in terms of mathematical computations and thus practically feasible that can be applied to both static and dynamic environments. Finally, simulation results verified the performance and fulfillment of the mentioned objectives of the approach.
96 citations
TL;DR: This is the fastest lightweight aerial vehicle to perform collision avoidance using three‐dimensional geometric information and a complete working system detecting obstacles at 120 Hz and avoiding trees at up to 14 m/s (31 MPH).
Abstract: We present the design and implementation of a small autonomous unmanned aerial vehicle capable of high-speed flight through complex natural environments. Using only onboard GPS-denied sensing and computation, we perform obstacle detection, planning, and feedback control in real time. We present a novel integrated approach to perception and control using pushbroom stereo, which exploits forward motion to enable efficient obstacle detection and avoidance using lightweight processors on an unmanned aerial vehicle. Our use of model-based planning and control techniques allows us to track precise trajectories that avoid obstacles identified by the vision system. We demonstrate a complete working system detecting obstacles at 120 Hz and avoiding trees at up to 14 m/s (31 MPH). To the best of our knowledge, this is the fastest lightweight aerial vehicle to perform collision avoidance using three-dimensional geometric information.
78 citations
TL;DR: The proposed method can perform safe and timely dynamic avoidance for redundant manipulators in human-robot interaction and is implemented in Robot Operating System (ROS) using C++.
Abstract: In order to avoid dynamic obstacle timely during manufacturing tasks performed by manipulators, a novel method based on distance calculation and discrete detection is proposed. The nearest distances between the links of a manipulator and the convex hull of an arbitrarily-shaped dynamic obstacle obtained from Kinect-V2 camera in real-time are calculated by Gilbert–Johnson–Keerthi algorithm, and the minimum one is defined as the closest distance between the manipulator and the obstacle. When the closest distance is less than a safe value, whether the dynamic obstacle is located in the global path of the manipulator is determined by improved discrete collision detection, which can adjust detection step-size adaptively for accuracy and efficiency. If the obstacle will collide with the manipulator, set a local goal and re-plan a local path for the manipulator. The proposed method is implemented in Robot Operating System (ROS) using C++. The experiments indicate that the proposed method can perform safe and timely dynamic avoidance for redundant manipulators in human-robot interaction.
67 citations
TL;DR: An innovative hybrid encoder that integrates deep Boltzmann machines (DBM) and auto-encoders (AE) is designed that combines the greedy learning features of DBM with the dimensionality reduction capacity of AE to accurately and reliably detect the presence of obstacles.
67 citations
TL;DR: This paper proposes a collision avoidance control algorithm based on the virtual structure and the “leader–follower” control strategy in 3-D space that can avoid the obstacle effectively and then track the motion target and provide a new concept for multi-UAV formation avoidance of an obstacle.
Abstract: This paper addresses a local minima problem for multiple unmanned aerial vehicles (UAVs) in the process of collision avoidance by using the artificial potential field method, thereby enabling UAVs to avoid the obstacle effectively in 3-D space. The main contribution is to propose a collision avoidance control algorithm based on the virtual structure and the “leader–follower” control strategy in 3-D space that can avoid the obstacle effectively and then track the motion target. The three UAVs constitute the regular triangular formation as the control object, the virtual leader flight trajectory as the expected path, the obstacles as the simplified cylinders, and the artificial potential fields around them as approximately spherical surfaces. The attractive force of the artificial potential field can guide the virtual leader to track the target. At the same time, the follower tracks the leader to maintain the formation flight. The effect of the repulsive force can avoid the collision between the UAVs and arrange the followers such that they are evenly distributed on the spherical surface. Moreover, the follower’s specific order and position are not required. The collision path of the UAV formation depends on the artificial potential field with the two composite vectors, and every UAV may choose the optimal path to avoid the obstacle and reconfigure the regular triangular formation flight after passing the obstacle. The effectiveness of the proposed collision avoidance control algorithm is fully proved by simulation tests. Meanwhile, we also provide a new concept for multi-UAV formation avoidance of an obstacle.
66 citations
TL;DR: A deep stacked auto-encoders (DSA) model that combines the greedy learning features with the dimensionality reduction capacity and employs an unsupervised nearest neighbors (KNN) algorithm to accurately and reliably detect the presence of obstacles in urban environment is proposed.
Abstract: Obstacle detection is an essential element for the development of intelligent transportation systems so that accidents can be avoided. In this paper, we propose a stereovision-based method for detecting obstacles in urban environment. The proposed method uses a deep stacked auto-encoders (DSA) model that combines the greedy learning features with the dimensionality reduction capacity and employs an unsupervised $k$ -nearest neighbors (KNN) algorithm to accurately and reliably detect the presence of obstacles. We consider obstacle detection as an anomaly detection problem. We evaluated the proposed method by using practical data from three publicly available data sets, the Malaga stereovision urban data set, the Daimler urban segmentation data set, and the Bahnhof data set. Also, we compared the efficiency of DSA-KNN approach to the deep belief network-based clustering schemes. Results show that the DSA-KNN is suitable to visually monitor urban scenes.
65 citations
TL;DR: In this paper, a nonlinear model predictive control (MPC) formulation for obstacle avoidance in high-speed, large-size autono-mous ground vehicles (AGVs) with high center of gravity (CoG) that operate in unstructured environments, such as military vehicles, is presented.
Abstract: This paper presents a nonlinear model predictive control (MPC) formulation for obstacle avoidance in high-speed, large-size autono-mous ground vehicles (AGVs) with high centre of gravity (CoG) that operate in unstructured environments, such as military vehicles. The term ‘unstructured’ in this context denotes that there are no lanes or traffic rules to follow. Existing MPC formulations for passenger vehicles in structured environments do not readily apply to this context. Thus, a new nonlinear MPC formulation is developed to navigate an AGV from its initial position to a target position at high-speed safely. First, a new cost function formulation is used that aims to find the shortest path to the target position, since no reference trajectory exists in unstructured environments. Second, a region partitioning approach is used in conjunction with a multi-phase optimal control formulation to accommodate the complicated forms the obstacle-free region can assume due to the presence of multiple obstacle...
62 citations
TL;DR: A generic framework that integrates an autonomous obstacle detection module and a reinforcement learning (RL) module to develop reactive obstacle avoidance behavior for a UAV and shows that the proposed saliency detection algorithm performs better than state-of-the-art, and the RL algorithm can learn the avoidance behavior from the manual experiences.
58 citations
10 Sep 2018
TL;DR: A novel collision-free motion planning method is proposed not only to keep robot body from colliding with objects but also to preserve the execution of robot's original task under the Cartesian constraint of the environment.
Abstract: This paper presents a real-time motion planning and control design of a robotic arm for human-robot collaborative safety. A novel collision-free motion planning method is proposed not only to keep robot body from colliding with objects but also preserve the execution of robot's original task under the Cartesian constraint of the environment. Multiple KinectV2 depth cameras are utilized to model and track dynamic obstacles (e.g. Humans and objects) inside the robot workspace. Depth images are applied to generate point cloud of segmented objects in the environment. A K-nearest neighbor (KNN) searching algorithm is used to cluster and find the closest point from the obstacle to the robot. Then a Kalman filter is applied to estimate the obstacle position and velocity. For the collision avoidance in collaborative operation, attractive and repulsive potential is generated for robot end effector based on the task specification and obstacle observation. Practical experiments show that the 6-DOF robot arm can effectively avoid an obstacle in a constrained environment and complete the original task.
TL;DR: A novel approach to analytically compute the path in an efficient and effective manner is introduced, showing that the method can adapt in real time the robot’s path in order to avoid several types of obstacles, while producing a map of the surroundings.
TL;DR: An obstacle avoidance problem where the USVs are confronted with a moving ship is focused on and a two-level dynamic obstacle avoidance algorithm is introduced by combining the velocity obstacle (VO) algorithm with the improved artificial potential field (APF) method in a non-emergency situation.
21 May 2018
TL;DR: This work finds that obstacle collisions can be beneficial for open-loop navigation of growing robots because the obstacles passively steer the robot, both reducing the uncertainty of the location of the robot and directing the robot to targets that do not lie on a straight path from the starting point.
Abstract: For many types of robots, avoiding obstacles is necessary to prevent damage to the robot and environment As a result, obstacle avoidance has historically been an important problem in robot path planning and control Soft robots represent a paradigm shift with respect to obstacle avoidance because their low mass and compliant bodies can make collisions with obstacles inherently safe Here we consider the benefits of intentional obstacle collisions for soft robot navigation We develop and experimentally verify a model of robot-obstacle interaction for a tip-extending soft robot Building on the obstacle interaction model, we develop an algorithm to determine the path of a growing robot that takes into account obstacle collisions We find that obstacle collisions can be beneficial for open-loop navigation of growing robots because the obstacles passively steer the robot, both reducing the uncertainty of the location of the robot and directing the robot to targets that do not lie on a straight path from the starting point Our work shows that for a robot with predictable and safe interactions with obstacles, target locations in a cluttered, mapped environment can be reached reliably by simply setting the initial trajectory This has implications for the control and design of robots with minimal active steering
TL;DR: This work presents efficient algorithms that use shadows to prove that trajectories or policies are safe with much tighter bounds than in previous work, and designs a safe variant of the rapidly exploring random tree (RRT) planning algorithm.
Abstract: As drones and autonomous cars become more widespread, it is becoming increasingly important that robots can operate safely under realistic conditions. The noisy information fed into real systems me...
08 Feb 2018
TL;DR: A fast and robust obstacle detection and tracking approach by integrating an adaptive obstacle detection strategy within a kernelized correlation filter (KCF) framework in this paper, which significantly outperforms the state-of theart methods in terms of tracking speed and accuracy.
Abstract: Obstacle detection and tracking is an important research topic in computer vision with a number of practical applications. Though an ample amount of research has been done in this domain, implementing automatic obstacle detection and tracking in real time is still a big challenge. To address this issue, we propose a fast and robust obstacle detection and tracking approach by integrating an adaptive obstacle detection strategy within a kernelized correlation filter (KCF) framework in this paper. A suitable salient object detection method autoinitializes the KCF tracker for this purpose. Moreover, an adaptive obstacle detection strategy is proposed to refine the location and boundary of the object when the confidence value of the tracker drops below a predefined threshold. In addition, a reliable postprocessing technique is implemented to accurately localize the obstacle from a saliency map recovered from the search region. The proposed approach has been extensively tested through quantitative and qualitative evaluations on a number of challenging datasets. The experiments demonstrate that the proposed approach significantly outperforms the state-of-the-art methods in terms of tracking speed and accuracy.
TL;DR: The results demonstrated that the self-tuning method is an appropriate strategy to increase the reliability of the sensor network while minimizing detection thresholds.
Abstract: On-chip LiDAR sensors for vehicle collision avoidance are a rapidly expanding area of research and development. The assessment of reliable obstacle detection using data collected by LiDAR sensors has become a key issue that the scientific community is actively exploring. The design of a self-tuning methodology and its implementation are presented in this paper, to maximize the reliability of LiDAR sensors network for obstacle detection in the ‘Internet of Things’ (IoT) mobility scenarios. The Webots Automobile 3D simulation tool for emulating sensor interaction in complex driving environments is selected in order to achieve that objective. Furthermore, a model-based framework is defined that employs a point-cloud clustering technique, and an error-based prediction model library that is composed of a multilayer perceptron neural network, and k-nearest neighbors and linear regression models. Finally, a reinforcement learning technique, specifically a Q-learning method, is implemented to determine the number of LiDAR sensors that are required to increase sensor reliability for obstacle localization tasks. In addition, a IoT driving assistance user scenario, connecting a five LiDAR sensor network is designed and implemented to validate the accuracy of the computational intelligence-based framework. The results demonstrated that the self-tuning method is an appropriate strategy to increase the reliability of the sensor network while minimizing detection thresholds.
TL;DR: Simulation results performed confirm the viability of the proposed E-APF algorithm that it can be effectively utilized in trajectory planning of wheeled mobile robots and can be applied in real-time scenarios.
01 Dec 2018
TL;DR: This work presents a unified optimization-based motion planning and control solution, that can navigate in the presence of both static and dynamic obstacles, and can precompute optimal motion primitives, and allow real-time planning of physically-feasible trajectories in complex environments with dynamic obstacles.
Abstract: A key requirement of autonomous vehicles is the capability to safely navigate in their environment. However, outside of controlled environments, safe navigation is a very difficult problem. In particular, the real-world often contains both complex 3D structure, and dynamic obstacles such as people or other vehicles. Dynamic obstacles are particularly challenging, as a principled solution requires planning trajectories with regard to both vehicle dynamics, and the motion of the obstacles. Additionally, the real-time requirements imposed by obstacle motion, coupled with real-world computational limitations, make classical optimality and completeness guarantees difficult to satisfy. We present a unified optimization-based motion planning and control solution, that can navigate in the presence of both static and dynamic obstacles. By combining optimal and receding-horizon control, with temporal multi-resolution lattices, we can precompute optimal motion primitives, and allow real-time planning of physically-feasible trajectories in complex environments with dynamic obstacles. We demonstrate the framework by solving difficult indoor 3D quadcopter navigation scenarios, where it is necessary to plan in time. Including waiting on, and taking detours around, the motions of other people and quadcopters.
01 Jan 2018
TL;DR: This paper surveys the different methods developed to handle dynamic changes in an indoor environment for effective localization and mapping in the presence of moving obstacles.
Abstract: The emergence of indoor applications of mobile robotics has led to the development of various algorithms for effective localization and mapping in the presence of moving obstacles. A mobile robot needs to simultaneously solve many problems like sensing, mapping, localization, path planning, obstacle detection and avoidance for a completely autonomous system. This paper surveys the different methods developed to handle dynamic changes in an indoor environment.
TL;DR: In this paper, a constrained interpolation profile (CIP) based on Cartesian grid method is introduced to solve the Navier-Stokes equations, and free surface is captured accurately by the Tangent of Hyperbola for INterface Capturing (THINC) scheme.
TL;DR: The conclusion is that the geometrical path planning method has good adaptability and does not require grid modeling, and it can find a shorter path in 2D/3D complex environment within a short time, so it has the ability of real-time path planning.
Abstract: This paper presents a geometrical path planning method, and it can help unmanned aerial vehicle to find a collision-free path in two-dimensional and three-dimensional (2D and 3D) complex environment quickly. First, a list of tree is designed to describe obstacles, and it is used to query the obstacles which block the line from starting point to finishing point (blocking obstacle). Specially, the list also stores the edge information of blocking obstacle. For the obstacles with short distance, a reasonable way to fly over is studied. Then, a shortest path planning method based on geometrical computation is proposed according to different shapes of obstacles. The obstacles are convex and divided into two cases of 2D and 3D. 2D environment includes rectangular obstacle, trapezoidal obstacle, triangular obstacle, circular obstacle and elliptic obstacle. In 3D, it includes cuboid, sphere and ellipsoid. To compare with other methods, the simulation is made in different environments. In 2D environment with circular obstacles, the method is similar to the artificial potential field. In 2D environment with rectangular obstacles, the performance of the proposed method is better than A-star. Compared with genetic algorithm, the proposed method gives a better result in 3D environment with cuboid obstacles. In 3D environment with hybrid obstacles, it is similar to interfered fluid dynamical system. Through comprehensive comparison and analysis, the conclusion is that the method has good adaptability and does not require grid modeling. It can find a shorter path in 2D/3D complex environment within a short time, so it has the ability of real-time path planning.
TL;DR: This paper investigates the effect of the form of an obstacle on the time that a crowd takes to evacuate a room, using a toy model, and results indicate that the evacuation-completion time depends on the shape of the obstacle.
Abstract: This paper investigates the effect of the form of an obstacle on the time that a crowd takes to evacuate a room, using a toy model. Pedestrians are modeled as active soft matter moving toward a point with intended velocities. An obstacle is placed in front of the exit, and it has one of four shapes: a cylindrical column, a triangular prism, a quadratic prism, or a diamond prism. Numerical results indicate that the evacuation-completion time depends on the shape of the obstacle. Obstacles with a circular cylinder (C.C.) shape yield the shortest evacuation-completion time in the proposed model.
TL;DR: A novel attractive field and repulsive field calculation method and direction decision approach for obstacle avoidance in autonomous vehicles and shows that ODG-PF performed the best in most cases.
Abstract: A new obstacle avoidance method for autonomous vehicles called obstacle-dependent Gaussian potential field (ODG-PF) was designed and implemented. It detects obstacles and calculates the likelihood of collision with them. In this paper, we present a novel attractive field and repulsive field calculation method and direction decision approach. Simulations and the experiments were carried out and compared with other potential field-based obstacle avoidance methods. The results show that ODG-PF performed the best in most cases.
TL;DR: In this paper, the influence of obstacle blockage on explosion venting was studied in a small-sized experimental duct containing an obstacle with different blockages in different positions, and the methane/air explosion characteristics affected by side venting in the duct were analyzed.
Abstract: To study the influence of obstacle blockage on explosion venting, a small sized experimental duct containing an obstacle with different blockages in different positions was built, and the methane/air explosion characteristics affected by side venting in the duct were studied. The explosion characteristics, including flame propagation, propagation velocity and overpressure profile, were analysed. The experimental results indicated that as the flame propagates upstream of an obstacle, flame propagation is little affected by the obstacle; when the flame passes the obstacle, flame propagation velocity and overpressure will always increase due to the incentive effect of the obstacle. Enlarging the blockage ratio increases the promoting effect of the obstacle. The relative position of a side vent and an obstacle affects side venting effect and the incentive effect of the obstacle. For a side vent in front of an obstacle, the explosion can be effectively discharged through the side vent before the flame reaches the obstacle, thus greatly weakening explosion intensity and decreasing the sensitivity of the explosion to the obstacle blockage. Whereas a side vent behind an obstacle is a disadvantage for the side vent to discharge the explosion, and the explosion intensity is very sensitive to the obstacle blockage.
TL;DR: A method to combine a low-cost 16 beam solid state laser sensor and a conventional video camera for obstacle detection is presented and results show that the method accurately detects the presence of obstacles and the direction of their movement.
Abstract: In this paper, a method to combine a low-cost 16 beam solid state laser sensor and a conventional video camera for obstacle detection is presented. The system is intended to form a non-intrusive virtual barrier at both sides of an intelligent wheelchair, in order to protect the user in everyday outdoor and indoor environments, like office, home, or pedestrian areas. In this type of environments, the shape of the obstacles is very heterogeneous (for instance, having a variable width along their height), so their detection via the conventional sensors installed in the wheelchair presents difficulties, especially in the most exposed areas of the user that are the sides of their torso. With the proposed system, when an obstacle intersects a beam, the intersection point is projected in the associated image and optical flow is calculated at both sides of this point. Using the optical flow, several classifiers have been trained and tested in order to automatically discern between intersections produced by the user and those produced by external obstacles. Results show that the method accurately detects the presence of obstacles and the direction of their movement.
27 Dec 2018
TL;DR: Experimental evaluation under two real-world environments with different types of phones and obstacles shows that ObstacleWatch achieves over 92% accuracy in predicting obstacle collisions with distance estimation errors at about 2 cm.
Abstract: Walking while using a smartphone is becoming a major pedestrian safety concern as people may unknowingly bump into various obstacles that could lead to severe injuries. In this paper, we propose ObstacleWatch, an acoustic-based obstacle collision detection system to improve the safety of pedestrians who are engaged in smartphone usage while walking. ObstacleWatch leverages the advanced audio hardware of the smartphone to sense the surrounding obstacles and infers fine-grained information about the frontal obstacle for collision detection. In particular, our system emits well-designed inaudible beep signals from the smartphone built-in speaker and listens to the reflections with the stereo recording of the smartphone. By analyzing the reflected signals received at two microphones, ObstacleWatch is able to extract fine-grained information of the frontal obstacle including the distance, angle and size for detecting the possible collisions and to alert users. Our experimental evaluation under two real-world environments with different types of phones and obstacles shows that ObstacleWatch achieves over 92% accuracy in predicting obstacle collisions with distance estimation errors at about 2 cm. Results also show that ObstacleWatch is robust to different sizes of objects and is compatible to different phone models with low energy consumption.
01 Oct 2018
TL;DR: A dataset of 6k synthetic depth maps of drones has been generated and used to train a state-of-the-art deep learning-based drone detection model, which enables full 3D localization of the obstacle and is extremely useful for collision avoidance.
Abstract: Obstacle avoidance is a key feature for safe Unmanned Aerial Vehicle (UAV) navigation. While solutions have been proposed for static obstacle avoidance, systems enabling avoidance of dynamic objects, such as drones, are hard to implement due to the detection range and field-of-view (FOV) requirements, as well as the constraints for integrating such systems on-board small UAVs. In this work, a dataset of 6k synthetic depth maps of drones has been generated and used to train a state-of-the-art deep learning-based drone detection model. While many sensing technologies can only provide relative altitude and azimuth of an obstacle, our depth map-based approach enables full 3D localization of the obstacle. This is extremely useful for collision avoidance, as 3D localization of detected drones is key to perform efficient collision-free path planning. The proposed detection technique has been validated in several real depth map sequences, with multiple types of drones flying at up to 2 m/s, achieving an average precision of 98.7 %, an average recall of 74.7 % and a record detection range of 9.5 meters.
TL;DR: The purpose of this paper is to develop a direct imaging algorithm to reconstruct the location and shape of the obstacle from the phaseless far-field data corresponding to infinitely many sets of superpositions of two plane waves with a fixed frequency as the incident fields.
Abstract: This paper is concerned with the inverse obstacle scattering problem with phaseless far-field data at a fixed frequency. The main difficulty of this problem is the so-called translation invariance property of the modulus of the far-field pattern or the phaseless far-field pattern generated by one plane wave as the incident field, which means that the location of the obstacle cannot be recovered from such phaseless far-field data at a fixed frequency. It was recently proved in our previous work Xu et al 2018 (SIAM J. Appl. Math. 78 1737–53) that the obstacle can be uniquely determined by the phaseless far-field patterns generated by infinitely many sets of superpositions of two plane waves with different directions at a fixed frequency if the obstacle is a priori known to be a sound-soft or an impedance obstacle with real-valued impedance function. The purpose of this paper is to develop a direct imaging algorithm to reconstruct the location and shape of the obstacle from the phaseless far-field data corresponding to infinitely many sets of superpositions of two plane waves with a fixed frequency as the incident fields. Our imaging algorithm only involves the calculation of the products of the measurement data with two exponential functions at each sampling point and is thus fast and easy to implement. Further, the proposed imaging algorithm does not need to know the type of boundary conditions on the obstacle in advance and is capable to reconstruct multiple obstacles with different boundary conditions. Numerical experiments are also carried out to illustrate that our imaging method is stable, accurate and robust to noise.
TL;DR: A novel model predictive control strategy for controlling autonomous motion systems moving through an environment with obstacles of general shape is presented, validated by extensive numerical simulations and shown to outperform state-of-the-art solvers in runtime and robustness.