Time-optimal Solution Research Articles

Real-time optimal trajectory planning for autonomous vehicles and lap time simulation using machine learning

Widespread development of driverless vehicles has led to the formation of autonomous racing, where technological development is accelerated by the high speeds and competitive environment of motorsport. A particular challenge for an autonomous vehicle is that of identifying a target trajectory – or, in the case of a competition vehicle, the racing line. Many existing approaches to finding the racing line are either not time-optimal solutions, or are computationally expensive – rendering them unsuitable for real-time application using on-board processing hardware. This study describes a machine learning approach to generating an accurate prediction of the racing line in real-time on desktop processing hardware. The proposed algorithm is a feed-forward neural network, trained using a dataset comprising racing lines for a large number of circuits calculated via traditional optimal control lap time simulation. The network predicts the racing line with a mean absolute error of ±0.27 m, and just ±0.11 m at corner apex – comparable to human drivers, and autonomous vehicle control subsystems. The approach generates predictions within 33 ms, making it over 9000 times faster than traditional methods of finding the optimal trajectory. Results suggest that for certain applications data-driven approaches to find near-optimal racing lines may be favourable to traditional computational methods.

THE TRAVELING SALESMAN PROBLEM WITH MULTI-VISIT DRONE

This paper deals with the Traveling Salesman Problem with Multi-Visit Drone (TSP-MVD) in which a truck works in collaboration with a drone that can serve up to q > 1 customers consecutively during each sortie. We propose a Mixed Integer Linear Programming (MILP) formulation and a metaheuristic based on Iterated Local Search to solve the problem. Benchmark instances collected from the literature of the special case with q = 1 are used to test the performance of our algorithms. The obtained results show that our MILP model can solve a number of instances to optimality. This is the first time optimal solutions for these instances are reported. Our ILS performs better other algorithms in terms of both solution quality and running time on several class of instances. The numerical results obtained by testing the methods on new randomly generated instances show again the effectiveness of the methods as well as the positive impact of using the multi-visit drone.

Situated Temporal Planning Using Deadline-aware Metareasoning

We address the problem of situated temporal planning, in which an agent's plan can depend on scheduled exogenous events, and thus it becomes important to take the passage of time into account during the planning process. Previous work on situated temporal planning has proposed simple pruning strategies, as well as complex schemes for a simplified version of the associated metareasoning problem. Although even the simplified version of the metareasoning problem is NP-hard, we provide a pseudo-polynomial time optimal solution to the case with known deadlines. We leverage intuitions emerging from this case to provide a fast greedy scheme that significantly improves upon previous schemes even for the case of unknown deadlines. Finally, we show how this new method can be applied inside a practical situated temporal planner. An empirical evaluation suggests that the new planner provides state-of-the-art results on problems where external deadlines play a significant role.

Various extensions in resource-constrained project scheduling with alternative subgraphs

In this research, we present several extensions for the resource-constrained project scheduling problem with alternative subgraphs (RCPSP-AS). First of all, we investigate more complex variants of the alternative project structure. More precisely, we consider nested alterative subgraphs, linked alternative branches, multiple selection, caused and closed choices, and split choices. Secondly, we introduce non-renewable resources in the RCPSP-AS in order to implicitly avoid certain combinations of alternatives given a limited availability of this resource over the complete project horizon. We formulate both the basic RCPSP-AS and its extensions as an ILP model and solve it using Gurobi. The computational experiments are conducted on a large set of artificial project instances as well as three case studies. The results show the impact of the different extensions on the project makespan and the computational complexity. We observe that combinations of the proposed extensions might imply complex alternative project structures, resulting in an increasing computational complexity or even infeasible solutions. The analysis of the three case studies shows that it is hard to find feasible solutions with a small time limit or optimal solutions with a larger time limit for projects with a realistic size in terms of the number of activities or alternatives.

Collaborative mission optimization for ship rapid search by multiple heterogeneous remote sensing satellites

<p style='text-indent:20px;'>Multiple heterogeneous satellites mission optimization is a typical kind of non-deterministic polynomial-time hard (NP-hard) problem, and some complicated scenarios bring new challenges. A novel method of missing ship rapid search using multiple grouped heterogeneous satellites is introduced in this paper. The focus is on optimization of collaborative mission optimization for various satellites including low-earth orbit (LEO) satellite and geostationary orbit (GEO) satellites. A fast coverage of the wide sea area using imaging satellites with narrow coverage range has become the most important part to tackle this problem. However, due to different imaging mechanisms of heterogeneous satellites and other constraints, it brings a great challenge to construct the optimization model. A constrained optimization problem model considering the cooperation between LEO and GEO satellites is constructed. A solution strategy based on bi-level metaheuristic algorithm is designed. The time optimal solution of the collaborative task planning between LEO and GEO satellites can be obtained based on the optimal attitude maneuver path of GEO satellites. Thus, wide-area search for missing ships can be conducted in an effective way. The effectiveness of the proposed method is verified by an example.</p>

A homotopy approach connecting time-optimal with fuel-optimal trajectories

This paper describes a novel homotopy method to compute fuel-optimal trajectories starting from a time-optimal solution. The time-optimal problem is proposed to serve as a gateway for solving the minimum thrust problem. Homotopy is used to link the original low-thrust fuel-optimal problem with the minimum thrust problem. Two new variables are introduced in the dynamic model. The first is a logarithm of mass variable and the second is an acceleration magnitude variable. The analytic expression of the logarithm of mass co-state is solved. For the time-optimal problem, initial co-state of logarithm of mass can be expressed by thrust magnitude and transfer time. Then, the number of unknown initial co-states decreased. The effectiveness and optimality of the proposed method is validated through simulations of two rendezvous missions.

Time-optimal variational control of a bright matter-wave soliton

Motivated by recent experiments, we present the time-optimal variational control of bright matter-wave soliton trapped in a quasi-one-dimensional harmonic trap by manipulating the atomic attraction through Feshbach resonances. More specially, we first apply a time-dependent variational method to derive the motion equation for capturing the soliton's shape, and secondly combine inverse engineering with optimal control theory to design the atomic interaction for implementing time-optimal decompression. Since the time-optimal solution is of bang-bang type, the smooth regularization is further adopted to smooth the on-off controller out, thus avoiding the heating and atom loss, induced from magnetic field ramp across a Feshbach resonance in practice.

A dynamic VM consolidation approach based on load balancing using Pearson correlation in cloud computing

In recent years, cloud data centers are rapidly growing with a large number of finite heterogeneous resources to meet the ever-growing user demands with respect to the SLA (service level agreement). However, the potential growth in the number of large-scale data centers leads to large amounts of energy consumption, which is constantly a major challenge. In addition to this challenge, intensive number of VM (virtual machine) migrations can decrease the performance of cloud data centers. Thus, how to minimize energy consumption while satisfying SLA and minimizing the number of VM migrations becomes an important challenge classified as NP-hard optimization problem in data centers. Most VM scheduling schemes have been proposed for this problem, such as dynamic VM consolidation. However, most of them failed in low time complexity and optimal solution. Hence, this paper proposes a dynamic VM consolidation approach-based load balancing to minimize the trade-off between energy consumption, SLA violations and VM migrations while keeping minimum host shutdowns and low time complexity in heterogeneous environment. Specifically, the proposed approach consists of four methods which include: BPSO meta-heuristic-based load balancing to impact on energy consumption and number of host shutdowns, overloading host detection and VM placement-based Pearson correlation coefficient to impact on SLA, and VM selection based on imbalance degree to impact on number of VM migration. Moreover, Pearson correlation coefficient and imbalance degree correlate CPU, RAM and bandwidth, respectively, in each host and each VM. Through extensive analysis and simulation experiments using real PlanetLab and random workloads, the performance results demonstrate that the proposed approach exhibits excellent results for the NP-problem.

Spiking neural P ant optimisation: a novel approach for ant colony optimisation

This Letter introduces an optimisation method that is based on parallelism to simulate the behaviour of foraging ants using spiking neural P (SN P) systems. The proposed method is designed by collaborating several SN P systems to obtain a polynomial time optimal solution. The complexity and reliability of the method have been verified. A theoretical analysis has been performed on the measures of complexity and proved the efficiency of the scheme.

Time optimal control of triple integrator with input saturation and full state constraints

Multiple integrator systems with input saturation and state constraints ubiquitously exist in practical problems such as trajectory planning in CNC (computer numerical control) systems, robots, automotive systems and industrial processes. Without state constraints, the optimal control of the multiple integrator with only input saturation is well solved in classic optimal control theory. However, if state constraints are considered, it is still challenging to obtain a global time optimal analytical solution for multiple integrator systems with even higher than second order, e.g., a double integrator plant. In this paper, the global time optimal control law for triple integrator with input saturation and full state constraints is considered. The system has a serial structure of three integral elements, while the control input and system states are within box constraints. A bang-singular-bang time optimal control law is synthesized according to Pontryagin minimum principle. Then, costates and jump conditions are analyzed in detail. Based on Bellman’s principle of optimality, switching surfaces and curves in phase space are obtained through dynamic programming method. The time optimal control law is then obtained in analytical state feedback form, and its global convergence property is proved. Through the comparison with numerical solutions, the effectiveness of the proposed control strategy is verified. The proposed scheme will be useful for trajectory planning under input saturation and full state constraints in practical applications.

Efficient Hamiltonian programming in qubit arrays with nearest-neighbor couplings

We consider the problem of selectively controlling couplings in a practical quantum processor with always-on interactions that are diagonal in the computational basis, using sequences of local NOT gates. This methodology is well-known in NMR implementations, but previous approaches do not scale efficiently for the general fully-connected Hamiltonian, where the complexity of finding time-optimal solutions makes them only practical up to a few tens of qubits. Given the rapid growth in the number of qubits in cutting-edge quantum processors, it is of interest to investigate the applicability of this control scheme to much larger scale systems with realistic restrictions on connectivity. Here we present an efficient scheme to find near time-optimal solutions that can be applied to engineered qubit arrays with local connectivity for any number of qubits, indicating the potential for practical quantum computing in such systems.

Purity speed limit of open quantum systems from magic subspaces

We introduce the concept of Magic Subspaces for the control of dissipative N- level quantum systems whose dynamics are governed by Lindblad equation. For a given purity, these subspaces can be defined as the set of density matrices for which the rate of purity change is maximum or minimum. Adding fictitious control fields to the system so that two density operators with the same purity can be connected in a very short time, we show that magic subspaces allow to derive a purity speed limit, which only depends on the relaxation rates. We emphasize the superiority of this limit with respect to established bounds and its tightness in the case of a two-level dissipative quantum system. The link between the speed limit and the corresponding time-optimal solution is discussed in the framework of this study. Explicit examples are described for two- and three- level quantum systems.

Retraction Note: Exploring the quantum speed limit with computer games

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Minimum Time—Minimum Jerk Optimal Traffic Management for AGVs

A combined minimum time - minimum jerk traffic management system for the vehicle coordination in an automated warehouse is presented. The algorithm is organised in two steps: in the first, a simple minimum time optimisation problem is solved, in the second step, this time-optimal solution is refined into a smooth minimum jerk plan for the autonomous forklifts in order to avoid impulsive forces that may unbalance the vehicle. For the first step, we propose a novel approach based on Linear Programming, which guarantees convergence to the optimal solution starting from a feasible point, and a low computational overhead, which makes it suitable for real-time applications. The output of this step is a piecewise constant velocity profile for all the moving robots that ensures collision avoidance. The second step takes such speed profile and generates its smoothed version, which minimises the jerk while respecting the same levels of safety of the solution generated by the first step. We discuss the different solutions with simulation and experimental data.

Optimal time task in saccadic eye movement

This article is devoted to fast goal-directed human eye movements. Such movements are described in few ways. One of them is the time-optimal problem model. It this work, the saccade – fast single conformable ballistic eye movement, is under consideration. Saccadic eye trajectory is described by time-optimal task solution. Differential equations system are based on pendulum model. It defines control moment applied from extraocular muscles to eye globe and movement of it. Main feature of the system is all values in suggested system have physical meaning and were found in published experimental investigations. Consideration of the moment applied from extraocular muscles to eye glob as control is main difference of the system from other models for eye movement in submitted works. In this case, the open-loop system has two real roots and one zero. The particular case of the ratio of real roots of 1:3 is analyzed in the article. As a result of modelling, trajectory characteristics closed to the saccades observed in experimental studies is obtained. On the basis of the constructed model, the parameters of the synthesized saccades were compared with the parameters obtained on the experimental sample. The obtained models can be used both for problems of physiology and medicine, and for constructing virtual reality environments. For example, when developing 3D interfaces, the use of a mathematical model makes it possible to optimize the elements arrangement using game theory.

Rescaling Interactions for Quantum Control

A powerful control method in experimental quantum computing is the use of spin echoes, employed to select a desired term in the system's internal Hamiltonian, while refocusing others. Here, we address a more general problem, describing a method to not only turn on and off particular interactions but also to rescale their strengths so that we can generate any desired effective internal Hamiltonian. We propose an algorithm based on linear programming for achieving time-optimal rescaling solutions in fully coupled systems of tens of qubits, which can be modified to obtain near-time-optimal solutions for rescaling systems with hundreds of qubits.

Research on Integrated Scheduling Optimization of Double-trolley Quay Crane and AGV in Automated Terminal

With the upsizing of ships, the operating efficiency of automated container terminals is becoming increasingly important. Based on the operation mode of loading and unloading synchronization, we first established an integrated scheduling optimization model of Double-trolley Quay Crane (QC) and AGV. Secondly, we designed a genetic algorithm embedded in tabu search to improve its local optimization ability. Finally, we conduct an empirical analysis. In the same case size, compared with the traditional genetic algorithm, the genetic algorithm embedded in tabu search has shorter model solving time and lower model optimal solution fitness. The maximum difference of the model solving time and the optimal solution fitness value can reach 165.113% and 7.71%, respectively. The results verify the rationality of the model and the effectiveness of the algorithm.

Near-optimal search-and-rescue path planning for a moving target

Discrete search and rescue path planning for a moving target problem is computationally hard. Despite heuristic methods proposed so far, for which efficiency is further plagued by random episodic target kinematic behavior, qualifying real solution goodness and specifying optimality gap still remain elusive. In this paper a new alternate formulation is proposed to solve the search path planning problem for a moving target. Rather than tackling explicitly the original problem model, a remarkable property is exploited to solve a conjugate mixed-integer linear programming problem. The approach lies on a compact open-loop search path planning problem model with anticipated feedback to efficiently minimize probability of detection failure as opposed to traditionally maximize cumulative probability of success. Preserving path solution optimality, solving the conjugate problem proves very valuable in significantly reducing computational complexity. This is mainly achievable by virtue of the resulting problem objective property which concisely defines the function to be minimized in terms of terminal belief contributions only. For the first time optimal or upper bound solution computation are made possible in reasonable time for practical size problems. A network representation is further utilized to simplify modeling and facilitate constraint specification. Computational results show the strength of the approach for one and two searching agent problem instances.

A Location Method for Partial Discharge Using Time Reversal and Improved Whale Optimization Algorithm

Time difference of arrival method is commonly used in the location of partial discharges. In this method, the main problem are as follows: (1) time delay error is inevitable. (2) location algorithm is sensitive to time delay error. To solve the problems above, an ultra-high frequency localization method for transformer partial discharge based on time reversal and improved whale optimization algorithm is proposed in this article. The method is consisted of three parts, that including time delay extraction, time reversal imaging and optimal solution. Firstly, the time delay is extracted by energy accumulation method. And then the approximate position of partial discharge source is determined by time reversal imaging. Combined with the time reversal imaging, the strategy of initial population selection and weight setting in the whale optimization algorithm is improved. Finally, the improved whale optimization algorithm is used to solve the optimal solution. The results are demonstrated through simulation and experiment. Compared with other localization algorithms, it is shown that the improved whale optimization algorithm has a better control performance in stability and accuracy.

A Planning Method for Multi-Axis Point-to-Point Synchronization Based on Time Constraints

In this paper, a third-order S-curve is used to model the motion issue. A closed method of solving is derived for the optimal point-to-point(P2P) time issue based on the model. Based on the P2P time-optimal solution, a closed multi-axis synchronization algorithm (MASA) method is proposed. This method considers the kinematic equation of the S-curve based on the inverse function of the multivariate function. Therefore, the inverse function of the execution time is derived via the kinematic equation of the P2P time optimization issue and solving a set of smaller bandwidth parameters is an important attempt in this paper. Otherwise, based on the MASA proposed in this paper, a synchronous computing framework suitable for the planning of robot space poses was designed. This framework can effectively solve problems with robot pose planning. The innovations of this article can be summarized as:(1)Based on the third-order S-curve, this paper deduced a complete method for solving the P2P time-optimal curve.(2) Based on the method for solving the time-optimal curve, this paper further derived three synchronization methods based on time constraints.(3) Based on the MASA proposed in this paper, a synchronous computing framework suitable for the planning of robot space poses was designed. The continuity and smoothness of the robot joint spatial motion can be guaranteed in the Descartes space. Few scholars have studied the closed solution method of multi-axis synchronization. The research in this paper promotes the theoretical research of motion control.