Worst-case Computation Time Research Articles

Friction-adaptive stochastic nonlinear model predictive control for autonomous vehicles

This paper addresses the trajectory-tracking problem under uncertain road-surface conditions for autonomous vehicles. We propose a stochastic nonlinear model predictive controller (SNMPC) that learns a tyre–road friction model online using standard automotive-grade sensors. Learning the entire tyre–road friction model in real time requires driving in the nonlinear, potentially unstable regime of the vehicle dynamics, using a prediction model that may not have fully converged. To handle this, we formulate the tyre-friction model learning in a Bayesian framework and propose two estimators that learn different aspects of the tyre–road friction. The estimators output the estimate of the tyre-friction model as well as the uncertainty of the estimate, which expresses the confidence in the model for different driving regimes. The SNMPC exploits the uncertainty estimate in its prediction model to take proper action when the uncertainty is large. We validate the approach in an extensive Monte Carlo study using real vehicle parameters and in CarSim. The results when comparing to various MPC approaches indicate a substantial reduction in constraint violations, as well as a reduction in closed-loop cost. We also demonstrate the real-time feasibility in automotive-grade processors using a dSPACE MicroAutoBox-II rapid prototyping unit, showing a worst-case computation time of roughly 40 ms.

Control-Based Tension Distribution Scheme for Fully Constrained Cable-Driven Robots

Control inputs of fully constrained cable-driven parallel robots (CDPRs) are constrained by the positiveness of the cables tension, as cables merely apply tensile forces. The positive tension distribution (PTD) in CDPRs is usually guaranteed with iterative optimization techniques, utilizing the redundant actuation of the CDPR. The iterative nature of the conventional PTD limits their real-time application since the worst-case computation time of the iterative methods is not predictable. In addition, optimization methods are prone to model uncertainties. This article addresses the PTD problem in the fully constrained CDPRs with a control viewpoint. In the proposed approach, the PTD algorithm is an integral part of the controller, which explicitly generates positive values for the cables tension. To this aim, a saturation-type function is coupled with the controller, and its effect is compensated using a nonlinear disturbance observer. The stability of the proposed control scheme is also investigated in detail through Lyapunov’s second method, considering a nonsingular terminal sliding mode controller. Furthermore, the performance of the proposed methodology is compared with the conventional method for a six-degrees-of-freedom CDPR, in the presence of uncertainties. Finally, the effectiveness of the proposed control scheme is investigated through experiments.

A Hierarchical Motion Planning Framework for Autonomous Driving in Structured Highway Environments

This paper presents an efficient hierarchical motion planning framework with a long planning horizon for autonomous driving in structured environments. A 3D motion planning with time information is a non-convex problem because there exists more than one local minimum point and various constraints such as roads and obstacles. Accordingly, to deal with high computational complexity and the problem of falling into a local minimum in an enormous solution space, a decoupled method is utilized, that consists of two steps: <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Long-term</i> planning and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">short-term</i> planning. First, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">long-term</i> planner provides reasonable far-sighted behavior through two processes. In the first process, a rough path that includes a driving strategy is generated in the 2D spatial space. Then, the jump point search algorithm is utilized with time information on the path to reduce the computational burden of A*, giving an acceptable quality of solution at the same time. In this step, a safe, comfortable, and dynamically feasible trajectory is generated. Next, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">short-term</i> planner optimizes a short-sighted trajectory using particle swarm optimization. In this method, a steering angle set is encoded as a particle, resulting in a safe, comfortable, and kinodynamically feasible trajectory. The proposed algorithm is implemented and evaluated in a range of vehicle-in-the-loop simulation scenarios, which include various virtual static and dynamic obstacles generated by Intelligent Driver Model. In the evaluation results, the proposed method reduced the computation time by up to 0.696 s with increasing the step cost by up to about 3%. The proposed algorithm is executed every 100 ms for a planning horizon of 10 seconds, and the average computation time is 31 ms with the worst-case computation time of 94 ms.

Uncertainty Propagation by Linear Regression Kalman Filters for Stochastic NMPC

Abstract Stochastic nonlinear model predictive control (SNMPC) allows to directly take model uncertainty into account, e.g., by including probabilistic chance constraints. This paper proposes linear-regression Kalman filtering to perform high-accuracy propagation of mean and covariance information for the nonlinear system dynamics in a tractable approximation of the stochastic optimal control problem. In addition, a tailored adjoint-based sequential quadratic programming (SQP) algorithm is presented to considerably reduce the computational cost and allow a real-time implementation of the resulting SNMPC. The prediction accuracy and control performance of the proposed approach are illustrated on a vehicle control application subject to external disturbances, while highlighting a worst-case computation time of 10 ms for SNMPC which is close to that of deterministic NMPC for this particular case study.

Exact Complexity Certification of Active-Set Methods for Quadratic Programming

Active-set methods are recognized to often outperform other methods in terms of speed and solution accuracy when solving small-size quadratic programming (QP) problems, making them very attractive in embedded linear model predictive control (MPC) applications. A drawback of active-set methods is the lack of tight bounds on the worst-case number of iterations, a fundamental requirement for their implementation in a real-time system. Extensive simulation campaigns provide an indication of the expected worst-case computation load, but not a complete guarantee. This paper solves such a certification problem by proposing an algorithm to compute the exact bound on the maximum number of iterations and floating point operations required by a state-of-the-art dual active-set QP solver. The algorithm is applicable to a given QP problem whose linear term of the cost function and right-hand side of the constraints depend linearly on a vector of parameters, as in the case of linear MPC. In addition, a new solver is presented that combines explicit and implicit MPC ideas, guaranteeing improvements of the worst-case computation time. The ability of the approach to exactly quantify memory and worst-case computation requirements is tested on a few MPC examples, also highlighting when online optimization should be preferred to explicit MPC.

Heuristic Optimization of Consumer Electricity Costs Using a Generic Cost Model

Many new demand response strategies are emerging for energy management in smart grids. Real-Time Energy Pricing (RTP) is one important aspect of consumer Demand Side Management (DSM), which encourages consumers to participate in load scheduling. This can help reduce peak demand and improve power system efficiency. The use of Intelligent Decision Support Systems (IDSSs) for load scheduling has become necessary in order to enable consumers to respond to the changing economic value of energy across different hours of the day. The type of scheduling problem encountered by a consumer IDSS is typically NP-hard, which warrants the search for good heuristics with efficient computational performance and ease of implementation. This paper presents an extensive evaluation of a heuristic scheduling algorithm for use in a consumer IDSS. A generic cost model for hourly pricing is utilized, which can be configured for traditional on/off peak pricing, RTP, Time of Use Pricing (TOUP), Two-Tier Pricing (2TP) and combinations thereof. The heuristic greedily schedules controllable appliances to minimize smart appliance energy costs and has a polynomial worst-case computation time. Extensive computational experiments demonstrate the effectiveness of the algorithm and the obtained results indicate the gaps between the optimal achievable costs are negligible.

Load Balanced Resampling for Real-Time Particle Filtering on Graphics Processing Units

The application of particle filters to real-time systems is often limited because of their computational complexity, and hence the use of graphics processing units (GPUs) that contain hundreds of processing elements on a chip is very promising. However, parallel implementations of particle filters with state-of-the-art systematic resampling on a GPU suffer from a severe workload imbalance problem, which results in fluctuation of the computation speed and hinders their application to real-time systems. We analyze the computational load imbalance of the systematic resampling method in conventional implementations, and show that the workload imbalance is proportional to the variance of weights in particle filters. Then, we propose a load balanced particle replication (LBPR) algorithm for systematic resampling, which shows almost constant execution speed and outperforms the conventional algorithm in terms of the worst-case computation time. The proposed algorithm has been implemented on an NVIDIA GTX580 GPU.

Counting Integer Points in Parametric Polytopes Using Barvinok's Rational Functions

Many compiler optimization techniques depend on the ability to calculate the number of elements that satisfy certain conditions. If these conditions can be represented by linear constraints, then such problems are equivalent to counting the number of integer points in (possibly) parametric polytopes. It is well known that the enumerator of such a set can be represented by an explicit function consisting of a set of quasi-polynomials, each associated with a chamber in the parameter space. Previously, interpolation was used to obtain these quasi-polynomials, but this technique has several disadvantages. Its worst-case computation time for a single quasi-polynomial is exponential in the input size, even for fixed dimensions. The worst-case size of such a quasi-polynomial (measured in bits needed to represent the quasi-polynomial) is also exponential in the input size. Under certain conditions this technique even fails to produce a solution. Our main contribution is a novel method for calculating the required quasi-polynomials analytically. It extends an existing method, based on Barvinok's decomposition, for counting the number of integer points in a non-parametric polytope. Our technique always produces a solution and computes polynomially-sized enumerators in polynomial time (for fixed dimensions).

An upper bound on the hardness of exact matrix based motif discovery

Motif discovery is the problem of finding local patterns or motifs from a set of unlabeled sequences. One common representation of a motif is a Markov model known as a score matrix. Matrix based motif discovery has been extensively studied but no positive results have been known regarding its theoretical hardness. We present the first non-trivial upper bound on the complexity (worst-case computation time) of this problem. Other than linear terms, our bound depends only on the motif width w (which is typically 5–20) and is a dramatic improvement relative to previously known bounds. We prove this bound by relating the motif discovery problem to a search problem over permutations of strings of length w, in which the permutations have a particular property. We give a constructive proof of an upper bound on the number of such permutations. For an alphabet size of σ (typically 4) the trivial bound is n ! ≈ ( n e ) n , n = σ w . Our bound is roughly n ( σ log σ n ) n . We relate this theoretical result to the exact motif discovery program, TsukubaBB, whose algorithm contains ideas which inspired the result. We describe a recent improvement to the TsukubaBB program which can give a speed up of nine or more and use a dataset of REB1 transcription factor binding sites to illustrate that exact methods can indeed be used in some practical situations.

Quality of service guarantee for temporal consistency of real-time transactions

The more-less (ML) scheme has been shown to be an efficient approach for maintaining temporal consistency of real-time data objects. Although ML provides a deterministic guarantee in temporal consistency, the number of update transactions that can be supported in a system is limited. This is due to its use of the worst-case computation time in deriving deadlines and periods of update transactions. This paper studies the problem of temporal consistency maintenance where a certain degree of temporal inconsistency is tolerable. A suite of statistical more-less (SML) approaches are proposed to explore the trade-off between quality of service (QoS) of temporal consistency and the number of supported transactions. It begins with a baseline algorithm, SML-BA, which provides the requested QoS of temporal consistency. Then, SML with optimization (SML-OPT) is proposed to further improve the QoS by better utilizing the excess processor capacity. Finally, SML-OPT is enhanced with a slack reclaiming scheme (SML-SR). The reclaimed slacks are used to process jobs whose required computation time is larger than the guaranteed computation time. Simulation experiments are conducted to compare the performance of these schemes (SML-BA, SML-OPT, and SML-SR) together with the deterministic more-less and half-half schemes. The results show that the SML schemes are effective in trading the schedulability of transactions for the QoS guaranteed. Moreover, SML-SR performs best and offers a significant QoS improvement over SML-BA and SML-OPT.

Scheduling algorithms based on weakly hard real-time constraints

The problem of scheduling weakly hard real-time tasks is addressed in this paper. The paper first analyzes the characters of µ-pattern and weakly hard real-time constraints, then, presents two scheduling algorithms, Meet Any Algorithm and Meet Row Algorithm, for weakly hard real-time systems. Different from traditional algorithms used to guarantee deadlines, Meet Any Algorithm and Meet Row Algorithm can guarantee both deadlines and constraints. Meet Any Algorithm and Meet Row Algorithm try to find out the probabilities of tasks breaking constraints and increase task's priority in advance, but not till the last moment. Simulation results show that these two algorithms are better than other scheduling algorithms dealing with constraints and can largely decrease worst-case computation time of real-time tasks.

DHARMA: A tool for evaluating dynamic scheduling algorithms for real-time multiprocessor systems

A majority of today's real-time systems assume a priori knowledge of task characteristics and hence are based on static designs which contribute to their high cost and inflexibility. The next generation of hard real-time systems must be designed to be dynamic and flexible. This provides the motivation to study various dynamic scheduling proposals. In this paper, we evaluate new algorithms for scheduling and resource reclaiming in a dynamic multiprocessor system with fault-tolerant requirements. Resource reclaiming refers to the problem of utilizing resources left unused by a task when its actual computation time is less than its worst case computation time, or when a task is deleted in a fault-tolerant schedule. We also describe the design and implementation of a tool, called Dynamic (Heuristic) scheduling Algorithms for Real-time Multiprocessor systems (DHARMA), to study various dynamic scheduling algorithms, with or without fault-tolerance requirements, and associated resource reclaiming algorithms in a multiprocessor real-time system.

A New Strategy for Improving the Effectiveness of Resource Reclaiming Algorithms in Multiprocessor Real-Time Systems

The scheduling of tasks in multiprocessor real-time systems has attracted the attention of many researchers in the recent past. Tasks in such systems have deadlines to be met, and most real-time scheduling algorithms use worst case computation times to schedule these tasks. Many resources will be left unused if the tasks are dispatched purely based on the schedule produced by these scheduling algorithms, since most of the tasks will take less time to execute than their respective worst case computation times. Resource reclaiming refers to the problem of reclaiming the resources left unused by a real-time task when it takes less time to execute than its worst case computation time. Several resource reclaiming algorithms such as Basic, Early Start, and RV algorithms have been proposed in the recent past. But these pay very little attention to the strategy by which the scheduler can better utilize the benefits of reclaimed resources. In this paper, we propose an esti- mation strategy which can be used along with a particular class of resource reclaiming algorithms (such as Early Start and RV algorithms) by which the scheduler can estimate the minimum time by which any scheduled but unexecuted task will start or finish early, based solely on the start and finish times of tasks that have started or finished execution. We then propose an approach by which dynamic scheduling strategies, which append or reschedule new tasks into the schedules, can use this estimation strategy to achieve better schedulability. Extensive simulation studies are carried out to investigate the effectiveness of this estimation strategy versus its cost.

An efficient dynamic scheduling algorithm for multiprocessor real-time systems

Many time-critical applications require predictable performance and tasks in these applications have deadlines to be met. In this paper, we propose an efficient algorithm for nonpreemptive scheduling of dynamically arriving real-time tasks (aperiodic tasks) in multiprocessor systems. A real-time task is characterized by its deadline, resource requirements, and worst case computation time on p processors, where p is the degree of parallelization of the task. We use this parallelism in tasks to meet their deadlines and, thus, obtain better schedulability compared to nonparallelizable task scheduling algorithms. To study the effectiveness of the proposed scheduling algorithm, we have conducted extensive simulation studies and compared its performance with the myopic scheduling algorithm. The simulation studies show that the schedulability of the proposed algorithm is always higher than that of the myopic algorithm for a wide variety of task parameters.

A New Approach for Scheduling of Parallelizable Tasks inReal-Time Multiprocessor Systems

In a parallelizable task model, a task can be parallelized and the component tasks can be executed concurrently on multiple processors. We use this parallelism in tasks to meet their deadlines and also obtain better processor utilisation compared to non-parallelized tasks. Non-preemptive parallelizable task scheduling combines the advantages of higher schedulability and lower scheduling overhead offered by the preemptive and non-preemptive task scheduling models, respectively. We propose a new approach to maximize the benefits from task parallelization. It involves checking the schedulability of periodic tasks (if necessary, by parallelizing them) off-line and run-time scheduling of the schedulable periodic tasks together with dynamically arriving aperiodic tasks. To avoid the run-time anomaly that may occur when the actual computation time of a task is less than its worst case computation time, we propose efficient run-time mechanisms. We have carried out extensive simulation to study the effectiveness of the proposed approach by comparing the schedulability offered by it with that of dynamic scheduling using Earliest Deadline First (EDF), and by comparing its storage efficiency with that of the static table-driven approach. We found that the schedulability offered by parallelizable task scheduling is always higher than that of the EDF algorithm for a wide variety of task parameters and the storage overhead incurred by it is less than 3.6% of the static table-driven approach even under heavy task loads.

Routing with multiple QoS requirements for supporting multimedia applications

Distributed multimedia applications usually require multiple QoS performance guarantees. However, in general, searching such a route in the network, to support multimedia applications, is known to be NP?complete. In this paper, we propose a new heuristic QoS routing algorithm, called "QoSRDKS", for supporting multimedia applications in high?speed networks. QoSRDKS is a modification of rule?based Fallback routing and Dijkstra algorithms. It can search a unicast route that would have enough network resources so that multiple QoS requirements (bandwidth, delay, and delay jitter) of the requested flow could be guaranteed. Its worst case computation time complexity is the same as that of the Dijkstra algorithm, i.e., O(?V?2), where ?V? is the number of nodes in the network. Extensive simulations were done with various network sizes, upto 500 nodes networks, where each node uses Weighted Fair Queueing (WFQ) service discipline. Results show that QoSRDKS is very efficient. It could always find the QoS satisfying route, whenever there exists one (success rate is optimal), and its average computation time is near to simple shortest path Dijkstra algorithm.

New Algorithms for Resource Reclaiming from Precedence Constrained Tasks in Multiprocessor Real-Time Systems

The scheduling of tasks in multiprocessor real-time systems has attracted many researchers in the recent past. Tasks in these systems have deadlines to be met, and most of the real-time scheduling algorithms use worst case computation times to schedule these tasks. Many resources will be left unused if the tasks are dispatched purely based on the schedule produced by these scheduling algorithms, since most of the tasks will take less time to execute than their respective worst case computation times. Resource reclaiming refers to the problem of reclaiming the resources left unused by a real-time task when it takes less time to execute than its worst case computation time. In this paper, we propose two algorithms to reclaim these resources from real-time tasks that are constrained by precedence relations and resource requirements, in shared memory multiprocessor systems. We introduce a notion called a restriction vector for each task which captures its resource and precedence constraints with other tasks. This will help not only in the efficient implementation of the algorithms, but also in obtaining an improvement in performance over the reclaiming algorithms proposed in earlier work [2]. We compare our resource reclaiming algorithms with the earlier algorithms and, by experimental studies, show that they reclaim more resources, thereby increasing the guarantee ratio (the ratio of the number of tasks guaranteed to meet their deadlines to the number of tasks that have arrived), which is the basic requirement of any resource reclaiming algorithm. From our simulation studies, we demonstrate that complex reclaiming algorithms with high reclaiming overheads do not lead to an improvement in the guarantee ratio.

Transformations that preserve malignness of universal distributions

A function μ( x) that assigns a nonnegative real number μ( x) to each bit string x is said to be malign if, for any algorithm, the worst-case computation time and the average-case computation time of the algorithm are functions of the same order when each bit string x is given to the algorithm as an input with the probability that is proportional to the value μ( x). M. Li and P.M.B. Vitányi found that functions that are known as “universal distributions” are malign. We say that a function ƒ(x) preserves malignness of universal distributions if ƒ(μ(x)) is malign for any universal distribution μ( x). We show one necessary and sufficient condition for ƒ(x) to preserve malignness of universal distributions under the assumption that ƒ(x) satisfies some additional conditions. As an application of this result, we show that ƒ(x) = x t preserves malignness of universal distributions or does not according as t⩾ 1 or 0 < t < 1.

Resource reclaiming in multiprocessor real-time systems

Most real-time scheduling algorithms schedule tasks with regard to their worst case computation times. Resources reclaiming refers to the problem of utilizing the resources left unused by a task when it executes in less than its worst case computation time, or when a task is deleted from the current schedule. Dynamic resource reclaiming algorithms that are effective, avoid any run time anomalies, and have bounded overhead costs that are independent of the number of tasks in the schedule are presented. Each task is assumed to have a worst case computation time, a deadline, and a set of resource requirements. The algorithms utilize the information given in a multiprocessor task schedule and perform online local optimization. The effectiveness of the algorithms is demonstrated through simulation studies. >

Efficient scheduling algorithms for real-time multiprocessor systems

Efficient scheduling algorithms based on heuristic functions are developed for scheduling a set of tasks on a multiprocessor system. The tasks are characterized by worst-case computation times, deadlines, and resources requirements. Starting with an empty partial schedule, each step of the search extends the current partial schedule by including one of the tasks yet to be scheduled. The heuristic functions used in the algorithm actively direct the search for a feasible schedule, i.e. they help choose the task that extends the current partial schedule. Two scheduling algorithms are evaluated by simulation. To extend the current partial schedule, one of the algorithms considers, at each step of the search, all the tasks that are yet to be scheduled as candidates. The second focuses its attention on a small subset of tasks with the shortest deadlines. The second algorithm is shown to be very effective when the maximum allowable scheduling overhead is fixed. This algorithm is hence appropriate for dynamic scheduling in real-time systems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>