Optimal Collision Avoidance Research Articles

The Optimal Collision Avoidance Trajectory Planning of Redundant Manipulators in the Process of Grinding Ceramic Billet Surface

The intelligent manufacturing system (IMS) is widely used in the surface machining of the workpiece. In the process of ceramic surface grinding, the intelligent machine (manipulator) in IMS is required to automatically plan the collision avoidance trajectory in a complex environment. This paper presents an optimal trajectory planning method of the use of redundant manipulators in the surface grinding of ceramic billet, which is based on trajectory evaluation. The collision avoidance trajectory can be optimized, taking into account several parameters in the trajectory, including the length of the collision avoidance path, the weighted sum of the strokes of all joints, and the duration of the collision avoidance trajectory. Firstly, get the planning task. Secondly, set the planning parameters and obtain a number of collision avoidance trajectories. Finally, the evaluation function is used to evaluate the collision avoidance trajectories and get the optimal collision avoidance trajectory. The performance of the proposed optimal collision avoidance trajectory planning method is validated in different evaluation functions.

Implementing Conditional Inequality Constraints for Optimal Collision Avoidance

Current Federal Aviation Administration regulations require that passing aircraft must either meet a specified horizontal or vertical separation distance. However, solving for optimal avoidance trajectories with conditional inequality path constraints is problematic for gradient-based numerical nonlinear programming solvers since conditional constraints typically possess non-differentiable points. Further, the literature is silent on robust treatment of approximation methods to implement conditional inequality path constraints for gradient-based numerical nonlinear programming solvers. This paper proposes two efficient methods to enforce conditional inequality path constraints in the optimal control problem formulation and compares and contrasts these approaches on representative airborne avoidance scenarios. The first approach is based on a minimum area enclosing superellipse function and the second is based on use of sigmoid functions. These proposed methods are not only robust, but also conservative, that is, their construction is such that the approximate feasible region is a subset of the true feasible region. Further, these methods admit analytically derived bounds for the over-estimation of the infeasible region with a demonstrated maximum error of no greater than 0.3% using the superellipse method, which is less than the resolution of typical sensors used to calculate aircraft position or altitude. However, the superellipse method is not practical in all cases to enforce conditional inequality path constraints that may arise in the nonlinear airborne collision avoidance problem. Therefore, this paper also highlights by example when the use of sigmoid functions are more appropriate.

Optimal Satellite-Formation Collision-Avoidance Maneuver Based on Relative E/I Vectors

AbstractThe optimal satellite-formation collision-avoidance maneuver problem is investigated in terms of relative eccentricity and inclination vectors (E/I vectors) in relative E/I vectors plane. Using the relative E/I vectors theory and under the relative inclination vector unchanged assumption, first, the fuel-optimal collision-avoidance maneuver problem to maneuver the final target configuration with predefined passive safety parameters using minimal fuel is transferred to the geometrical problem to find the shortest distance from the initial point determined by the current relative eccentricity vector to the hyperbolic curve, which is determined by a predefined passive safety parameter in the relative E/I vectors plane. This case is solved using the Newton interaction method. Second, the optimal collision-avoidance maneuver problem to maneuver the final target configuration having maximum passive safety parameter under limiting fuel constraint is interpreted as the geometrical problem to find the opti...

Real-Time Crowd Simulation Integrating Potential Fields and Agent Method

Crowd simulation is studied extensively in computer graphics, animation, and safety. A real-time crowd simulator has been developed based on potential fields and agent approach in this article. This simulator produces realistic complex heterogeneous motion and improves the simulation rates by at least 32% in comparison with the potential field results. The model of this simulator can efficiently tackle the problems in global optimal navigation, collision avoidance, and dynamic interaction; furthermore, it allows an agent to make independent decisions.

UAS Sense and Avoid System Interface Design and Evaluation

A key challenge to integrating unmanned aerial systems (UASs) into the National Airspace is providing a means for UASs to sense and avoid (SAA) other aircraft. Additionally, successful applications of a SAA system will depend on the degree to which the operator understands the rationale for its maneuvers/decision aids and can interact with the system to tailor and/or override the automation. This paper describes two interface prototypes for the Jointly Optimal Collision Avoidance (JOCA) SAA system that differed in feedback provided on the algorithm’s state and planned maneuvers. Results from an operator-in-the-loop simulation are also presented. Although performance was generally similar with both interface types, the participants rated their ability to maintain safe separation from other aircraft and overall situation awareness as better with the interface that provided more visibility into the SAA algorithm’s intent.

Collision avoidance strategy optimization based on danger immune algorithm

Marine collision accidents cause a great loss of lives and property. As a possible solution, the danger immune algorithm is used to achieve ship collision avoidance strategy optimization, which is a multi-objective problem concerning safety and economy. Collision avoidance operations are encoded as the individuals of optimization algorithm. In the system, ship domain and ship arena, among others, are used for collision risk evaluation to assess the fitness of individuals. Through the optimization, the navigator will obtain the optimal collision avoidance strategy to achieve safe and efficient collision avoidance. The simulations indicate that the optimization algorithm is valid.

V2X 및 환경 센서 융합 기반 교차로 안전 시스템 알고리즘 개발

This paper describes the development and verification of control algorithms for V2X and environmental sensor integrated intersection support and safety systems. The objective of the research is to develop core technologies for effective fusion of V2X and environmental sensors and to develop new safety function for intersection safety. One of core technologies is to achieve the improvement of GPS accuracy, and the other is to develop the algorithm of a vehicle identification which matches all data from V2X, vehicle sensors and environmental sensors to specific vehicles. A intersection optimal pass (IOP) algorithm is designed based on these core technologies. IOP recommends appropriate speed to pass the intersection in the consideration of traffic light signal and preceeding vehicle existence. Another function is developed to prevent a collision avoidance when car crash caused by traffic violation of surrounding vehicles is expected. Finally all functions are implemented and tested in three test vehicles. It is shown that IOP can support convenient and comfortable driving with recommending optimal pass speed and collision avoidance algorithm can effectively prevent collision caused by traffic sign violation of surrounding vehicles.

Multiobjective Optimization Based Vessel Collision Avoidance Strategy Optimization

The vessel collision accidents cause a great loss of lives and property. In order to reduce the human fault and greatly improve the safety of marine traffic, collision avoidance strategy optimization is proposed to achieve this. In the paper, a multiobjective optimization algorithm NSGA-II is adopted to search for the optimal collision avoidance strategy considering the safety as well as economy elements of collision avoidance. Ship domain and Arena are used to evaluate the collision risk in the simulation. Based on the optimization, an optimal rudder angle is recommended to navigator for collision avoidance. In the simulation example, a crossing encounter situation is simulated, and the NSGA-II searches for the optimal collision avoidance operation under the Convention on the International Regulations for Preventing Collisions at Sea (COLREGS). The simulation studies exhibit the validity of the method.

Planning of Optimal Collision Avoidance Trajectories with Timed Elastic Bands

This paper is concerned with the planning of optimal trajectories for vehicle collision avoidance with a Timed Elastic Band (TEB) framework. The avoidance trajectory is represented by a TEB which is optimized with respect to multiple partially conflicting objectives. The resulting trajectory constitutes the optimal compromise between a mere braking and a lane change maneuver that avoids the collision with the smoothest feasible path. The approach is applicable to general critical traffic situations as the TEB considers the constraints imposed by the vehicle dynamics, road boundaries, static obstacles and moving vehicles.

Computation of bang-bang and singular controls in collision avoidance

We study optimal cooperative collision avoidance strategies for twoparticipants in a planar close proximity encounter. Previousresearch focused on special cases of this problem and showed thatbang-bang strategies without switching are optimal in mostsituations, while singular controls only appear for the case ofparticipants with unequal linear speeds under certain conditions.This paper extends the earlier analyses to a general case of acoplanar close proximity encounter, for which both parameters of theproblem may take arbitrary admissible values. For such a case, wepresent a theoretical and numerical study of the structure ofoptimal controls. We prove that both controls can not be singularsimultaneously and that the only possible singular control is a zerocontrol. We derive formulas for the singular surfaces and verifythat sufficient conditions hold for the computed extremal solutions.We identify different types of structural changes of the controlstrategies and show how the control structure changes with thechange in the model parameters and initial conditions.

Model based real-time collision-free motion planning for nonholonomic mobile robots in unknown dynamic environments

In this paper, by explicitly considering a dynamic model of the robots, the coefficients of trajectories are determined by boundary conditions, optimal performance index and collision avoidance conditions. The planned trajectory is feasible and has a closed loop expression, which is efficient for real-time updating. There are two main improvements compared with existing parametric approaches. Firstly, most of existing methods use the kinematic models of the robots, which could cause curvature discontinuities when trajectories are updated in real-time. Secondly, in some existing parametric methods, the initial position and ending waypoints cannot be aligned vertically due to singularities. The approach proposed in this paper overcomes this limitation. Computer simulations verified the effectiveness of the proposed method.

Collision monitoring and optimal collision avoidance manoeuvre for formation flying satellites

PurposeThe purpose of this paper is to evaluate the safety of formation flying satellites, and propose a method for practical collision monitoring and collision avoidance manoeuvre.Design/methodology/approachA general formation description method based on relative orbital elements is proposed, and a collision probability calculation model is established. The formula for the minimum relative distance in the crosstrack plane is derived, and the influence of J2 perturbation on formation safety is analyzed. Subsequently, the optimal collision avoidance manoeuvre problem is solved using the framework of linear programming algorithms.FindingsThe relative orbital elements are illustrative of formation description and are easy to use for perturbation analysis. The relative initial phase angle between the in‐plane and cross‐track plane motions has considerable effect on the formation safety. Simulations confirm the flexibility and effectiveness of the linear programming‐based collision avoidance manoeuvre method.Practical implicationsThe proposed collision probability method can be applied in collision monitoring for the proximity operations of spacecraft. The presented minimum distance calculation formula in the cross‐track plane can be used in safe configuration design. Additionally, the linear programming method is suitable for formation control, in which the initial and terminal states are provided.Originality/valueThe relative orbital elements are used to calculate collision probability and analyze formation safety. The linear programming algorithms are extended for collision avoidance, an approach that is simple, effective, and more suitable for on‐board implementation.

Collision avoidance for general aviation

This presented the development and simulation of optimized collision avoidance logic to operate on-board general aviation aircraft. Framing the collision avoidance problem as a Markov decision process allows the logic to be generated using a specified encounter model and performance metrics. Past work has focused on using this framework to develop an improved collision avoidance system for non-GA aircraft. This presented results using the framework to optimize logic for lower performance GA aircraft and comparing its performance to the existing version of TCAS, as well as a simple Descend/Climb responsive logic. The results presented herein show that the optimized logic, issuing only climb, descend, and level-off advisories, was able to outperform the current version of TCAS and the Descend/Climb responsive logic against intruders that are equipped with TCAS. The optimized logic issuing 1000 feet = min advisories resulted in the best performance with respect to safety and alerting. For encounters where two GA aircraft are equipped with a collision avoidance system, the optimized logic was 3.1 times safer than TCAS for 500 feet = min advisories and 3.6 times safer for 1000 feet = min advisories. Both of the optimized methods resulted in lower probabilities of alert and reversal than TCAS and the Descend/Climb logic, which is desirable from an operational standpoint. The optimized logic that resulted in the best performance had a relatively high cost of reversing. This resulted in a very low probability of reversing for the GA aircraft, as low as zero in one case. The reversal rate for a TCAS-equipped intruder aircraft was slightly higher, but this was offset by a lower probability of strengthening advisories on the TCAS aircraft.

A Study on the Collision Avoidance Maneuver Optimization with Multiple Space Debris

In this paper, the authors introduced a new approach to find the optimal collision avoidance maneuver considering multi threatening objects within short period, while satisfying constraints on the fuel limit and the acceptable collision probability. A preliminary effort in applying a genetic algorithm (GA) to those kinds of problems has also been demonstrated through a simulation study with a simple case problem and various fitness functions. And then, GA is applied to the complex case problem including multi-threatening objects. Two distinct collision avoidance maneuvers are dealt with: the first is in-track direction of collision avoidance maneuver. The second considers radial, in-track, cross-track direction maneuver. The results show that the first case violates the collision probability threshold, while the second case does not violate the threshold with satisfaction of all conditions. Various factors for analyzing and planning the optimal collision avoidance maneuver are also presented.

Singular controls in optimal collision avoidance for participants with unequal linear speeds

This article studies optimal collision avoidance strategies for participants with unequal linear speeds in a planar close proximity encounter. It is known that bang-bang collision avoidance strategies are optimal for encounters of participants with equal linear speeds. However, as shown recently, bang-bang collision avoidance strategies are not necessarily optimal when the linear speeds of the participants are not equal. We study the structure of optimal singular controls for collision avoidance of participants with unequal linear speeds, but equal turn capabilities. We prove that both controls cannot be singular simultaneously, and that the only possible singular control is a zero control. We use several optimization techniques compute optimal state, control and adjoint variables. Numerical simulations suggest that a zero control strategy only exists for a slower participant and that, at most, one switching from a bang-bang to a singular control occurs. Different types of structural changes of the controls with change in the initial conditions are identified via the numerical simulations. References U. Ledzewicz, H. Maurer, and H. Schattler, Optimal and suboptimal protocols for a mathematical model for tumor anti-angiogenesis in combination with chemotherapy, Mathematical Biosciences and Engineering , 8 , 2011, 307--328. doi:10.3934/mbe.2011.8.307 U. Ledzewicz, H. Maurer, H. Schattler, On optimal delivery of combination therapy for tumors, Mathematical Biosciences , 22 , 2009, 13--26. doi:10.1016/j.mbs.2009.08.004 H. Maurer, C. Buskens, J.-H. R. Kim, Y. Kaya, Optimization methods for the verification of second-order sufficient conditions for bang-bang controls. Optimal Control Applications and Methods , 26 , 2005, 129--156. doi:10.1002/oca.756 A. W. Merz, Optimal aircraft collision avoidance. Proceedings of the Joint Automatic Control Conf. , Paper 15-3, pages 449--454, 1973. A. W. Merz, Optimal evasive manoeuvres in maritime collision avoidance. Navigation , 20 (2), 1973, 144--152. T. Tarnopolskaya, and N. L. Fulton, Optimal cooperative collision avoidance strategy for coplanar encounter: Merz's solution revisited, J. Optim. Theory Appl. , 140 (2), 2009, 355--375. doi:10.1007/s10957-008-9452-9 T. Tarnopolskaya, and N. L. Fulton, Parametric behavior of the optimal control solution for collision avoidance in a close proximity encounter, In R. S. Andersson et al., editors, 18th World IMACS Congress and MODSIM09 International Congress on Modelling and Simulation , pages 425--431, 2009. http://www.mssanz.org.au/modsim09/A7/tarnopolskaya_A7.pdf T. Tarnopolskaya, and N. L. Fulton, Synthesis of optimal control for cooperative collision avoidance for aircraft (ships) with unequal turn capabilities, J. Optim. Theory Appl. , 144 (2), 2010, 367--390. doi:10.1007/s10957-009-9597-1 T. Tarnopolskaya, and N. L. Fulton, Dispersal Curves for Optimal Collision Avoidance in a Close Proximity Encounter: a Case of Participants with Unequal Turn Rates, Lecture Notes in Engineering and Computer Science: Proceedings of The World Congress on Engineering 2010 , WCE 2010, pages 1789--1794. IAENG, 2010. http://www.iaeng.org/publication/WCE2010/WCE2010_pp1789-1794.pdf T. Tarnopolskaya, and N. L. Fulton, Non-unique Optimal Collision Avoidance Strategies for Coplanar Encounter of Participants with Unequal Turn Capabilities, IAENG International Journal of Applied Mathematics , 40 (4), 2010, 289--296. http://www.iaeng.org/IJAM/issues_v40/issue_4/IJAM_40_4_10.pdf T. Tarnopolskaya, and N. L. Fulton, Synthesis of Optimal Control for Cooperative Collision Avoidance in a Close Proximity Encounter: Special Cases, Proceedings of the 18th World Congress of the International Federation of Automatic Control (IFAC) , Milan (Italy), August 28--September 2, 2011, 18 (1), 9775--9781. T. Tarnopolskaya, N. L. Fulton, and H. Maurer, Synthesis of optimal bang-bang control for cooperative collision avoidance for aircraft (ships) with unequal linear speeds. J. Optim. Theory Appl. , to appear, 2012.

Decomposition Methods for Optimized Collision Avoidance with Multiple Threats

Aircraft collision avoidance systems assist in the resolution of collision threats from nearby aircraft by issuing avoidance maneuvers to pilots. Encounters where multiple aircraft pose a threat, though rare, can be difficult to resolve because a maneuver that might resolve a conflict with one aircraft might induce conflicts with others. Recent efforts to develop robust collision avoidance systems for single-threat encounters have involved modeling the problem as a Markov decision process and applying dynamic programming to solve for the optimal avoidance strategy. Because this methodology does not scale well to multiple threats, this paper evaluates a variety of decomposition methods that leverage the optimal avoidance strategy for single-threat encounters.

Synthesis of Optimal Control for Cooperative Collision Avoidance in a Close Proximity Encounter: Special Cases

AbstractThe paper studies the optimal cooperative collision avoidance strategies in a planar close proximity encounter, with turning rates of the participants as the control functions. The maximization of the terminal miss distance is adopted as a performance criterion. This paper extends earlier analyses to the important special case when participants have unequal linear speeds but equal turn capabilities. The analysis is based on the Pontryagin maximum principle and the study of the properties of the extremals. The analysis is outlined in a unified manner that covers all special cases of the problem, including the cases of identical participants and the participants with unequal turn capabilities but equal linear speeds. The distinctive features of the mathematical structure of the problem and the optimal control solutions for different special cases of the problem are identified. The results of this paper are useful for setting and validating air traffic rules and for benchmarking and validating automated proximity management and collision avoidance systems.

Optimal cooperative collision avoidance between multiple robots based on Bernstein–Bézier curves

In this paper a new cooperative collision-avoidance method for multiple, nonholonomic robots based on Bernstein–Bézier curves is presented. The main contribution focuses on an optimal, cooperative, collision avoidance for a multi-robot system where the velocities and accelerations of the mobile robots are constrained and the start and the goal velocity are defined for each robot. The optimal path of each robot, from the start pose to the goal pose, is obtained by minimizing the penalty function, which takes into account the sum of all the path lengths subjected to the distances between the robots, which should be larger than the minimum distance defined as the safety distance, and subjected to the velocities and accelerations, which should be lower than the maximum allowed for each robot. The model-predictive trajectory tracking is used to drive the robots on the obtained reference paths. The results of the path planning, real experiments and some future work ideas are discussed.

Optimal Cooperative Collision Avoidance Strategy for Coplanar Encounter: Merz’s Solution Revisited

Analytic solutions for optimal collision avoidance strategies are of great importance when setting and validating air traffic rules and as a benchmark when validating automated proximity management and collision avoidance systems. Such a solution for optimal air collision avoidance strategies for a coplanar cooperative encounter between two identical aircraft (or ships) was first presented by Merz (Proc. Joint Automatic Control Conf., Pap. 15-3:449---454, 1973; Navigation 20(2):144---152, 1973). Unfortunately, Merz provided only a very brief indicative justification for his solution. This paper presents a rigorous analysis of the problem. New results include a characterization of a complete set of extremals, justification for optimal strategies and an analysis of the properties of the regions of different optimal strategies. A simple, practical and sufficiently accurate closed form approximation for dispersal curves that partition the plane of initial positions into the regions of different optimal strategies is also presented.

UAV Optimal Cooperative Target Tracking and Collision Avoidance of Moving Objects

Effective target tracking and collision avoidance schemes are essential to the success of unmanned aerial vehicle (UAV) missions. In a dynamic environment, UAV path planning often relies on predicted obstacle and target motion. This paper presents an algorithm that predicts the trajectory of a moving object (target or obstacle) detected by a UAV. An extended Kalman filter is first employed to estimate the states of the object from its measured spatial position. The optimal object trajectory and its associated position prediction error are then calculated using the state equation defined for Kalman filtering. The proposed trajectory prediction scheme is afterward tested in a path planner which relies on decentralized cooperative predictive control to select optimal UAV trajectories as a function of the predicted target and obstacle trajectories. Simulation results are presented to demonstrate the effectiveness of the proposed approach.