TOP: Trajectory Optimization via Parallel Optimization Towards Constant Time Complexity

Optimal sizing of residential battery energy storage systems for long-term operational planning

Unmanned Aerial Vehicles (UAVs), in multi-UAV collaborative search systems, need to realize adaptive autonomous trajectory planning based on their own state and surrounding environmental conditions. To allow for a fast trajectory planning of multiple UAVs from the current state to the target state, this paper proposes a trajectory planning method for multi-UAV collaborative search tasks based on genetic algorithm (GA). And using genetic algorithm, the UAV's trajectory can be optimized online based on the current mission. Through the analysis of the tasks of the multi-UAV collaborative decision-making part and the autonomous trajectory planning part, the genetic algorithm is used to model and optimize the trajectory planning problem to obtain a feasible and efficient optimal search trajectory from the current state to the decision-making target state. Finally, through specific simulation experiments, the optimal trajectory from the current state to the target state of the UAV i in the multi-UAV system is obtained, which verifies the effectiveness of the algorithm.

Purpose The purpose of this paper is to improve the positional accuracy, smoothness on motion and productivity of industrial robot through the proposed optimal joint trajectory planning method. Also a new improved algorithm, i.e. non-dominated sorting genetic algorithm-II (NSGA-II) with achievement scalarizing function (ASF) has been proposed to obtain better optimal results compared to previously used optimization methods. Design/methodology/approach The end effector positional errors can be reduced by limiting the uncertainties of dynamic parameter variations like torque rate of joints. The jerk induced in robot joints due to acceleration variations are need to be minimized which otherwise induces vibrations in the manipulator that causes deviation in the encoders. But these lead to a vast increase in total travel time which affects the cost function of trajectory planning. Therefore, these three objectives need to be minimized individually so that an optimal trajectory path can be achieved with minimum positional error. Findings The simulation results have been obtained by running the proposed hybrid NSGA-II with ASF in MATLAB R2017a software. The optimal time intervals have been used to calculate jerk, acceleration and torque values for consecutive points on the trajectory path. From the simulation and experimental results, it can be concluded that the optimization technique could be used effectively for the trajectory planning of six-axis industrial manipulator in the joint space on the basis of minimum time-jerk-torque rate criteria. Originality/value In this paper, a new approach based on hybrid multi-objective optimization technique by combining NSGA-II with ASF has been applied to find the minimal time-jerk- torque rate joint trajectory of a six-axis industrial robot for obtaining higher positional accuracy. The results obtained from the execution of algorithm have been validated through experimentation using Kawasaki RS06L industrial robot for a particular defined path.

We consider a global variable consensus ADMM algorithm for solving large-scale PDE parameter estimation problems asynchronously and in parallel. To this end, we partition the data and distribute the resulting subproblems among the available workers. Since each subproblem can be associated with different forward models and right-hand-sides, this provides ample options for tailoring the method to different applications including multi-source and multi-physics PDE parameter estimation problems. We also consider an asynchronous variant of consensus ADMM to reduce communication and latency. Our key contribution is a novel weighting scheme that empirically increases the progress made in early iterations of the consensus ADMM scheme and is attractive when using a large number of subproblems. This makes consensus ADMM competitive for solving PDE parameter estimation, which incurs immense costs per iteration. The weights in our scheme are related to the uncertainty associated with the solutions of each subproblem. We exemplarily show that the weighting scheme combined with the asynchronous implementation improves the time-to-solution for a 3D single-physics and multiphysics PDE parameter estimation problems.

PurposeThis paper aims to present an optimal trajectory planning for industrial MOTOMAN MA1440A gas metal arc welding system. A new and efficient evolutionary algorithm, enhanced multi-objective teaching learning-based optimization (EMOTLBO) method, i.e. TLBO with non-dominated sorting approach has been proposed to obtain the optimal joint trajectory for the defined weld seam path.Design/methodology/approachThe joint trajectory of the welding robot need to be computed in an optimal manner for proper torch orientation, smooth travel of the robot along the weld path and for achieving higher positional accuracy. This can be achieved by limiting the kinematic and dynamic variations of the robot joints like joint jerks, squared acceleration and torque induced in the joints while travel of the robot along the weld path. Also, the robot travel should be done within minimum possible time for maintaining productivity. This leads to a multi-objective optimization problem which needs to be solved for maintaining proper orientation of the robot end effector. EMOTLBO has been proposed to obtain the Pareto front consisting of optimal solutions. The fuzzy membership function has been used to obtain the optimal solution from the Pareto front with best trade-off between objectives.FindingsThe proposed method has been implanted in MATLAB R2017a for simulation results. The joint positions have been used to program the robot for performing welding operation along the weld seam. From the simulation and experimental results, it can be concluded that the proposed approach can be effectively used for optimal trajectory planning of MOTOMAN MA 1440 A arc welding robot system as a very smooth and uniform weld bead has been obtained with maximum weld quality.Originality/valueIn this paper, a novel approach for optimal trajectory planning welding arc robot has been performed. Though trajectory planning of industrial robots has been done before, it has not been done yet for welding robot. The objectives are formulated taking in consideration of requirement of welding process like minimization of joint jerks and torques induced during welding operation due to travel of robot with the effect of arc spatter, minimization of squared acceleration for maintaining constant joint velocity and finally minimization of total travel time for maintaining productivity.

The aviation industry contributes to global warming by releasing CO2 and non-CO2 species into the atmosphere. The climate impacts of non-CO2 emissions have been claimed to be two times higher than the effects of CO2 alone [1]. Unlike CO2 emission, the climate impacts of non-CO2 species highly depend on geographical location, altitude, and time of the emissions. Thus, performing more efficient maneuvers to avoid climate hotspots can potentially mitigate their associated climate effects. So far, several studies have been conducted on micro-scale climate optimal aircraft trajectory planning (i.e., trajectory level) [2]. However, generating a climatically optimal flight plan for each aircraft is not the ultimate solution to this problem when it comes to global traffic scenarios.     Besides increasing the operating costs as the aircraft fly longer routes ( mainly due to the tendency to avoid climate-sensitive regions), the climate-optimal trajectories also alter the traffic pattern by increasing the congestion around climate hotspots, which may have negative implications, including, but not limited to, high traffic density, increased workload, complexity, and conflicts. Therefore, the evolution toward an environmentally friendly trajectory planning framework required a holistic perspective on the consequences of adopting climate-optimal routes at network scale. Nonetheless, in the literature, the problem of aircraft trajectory planning for the benefits of climate at a network scale is explored only in a free-routing airspace, considering a regional scenario (i.e., only Spain airspace), and constant altitude for trajectory optimization [3].    In this study, we aim to explore this problem considering a real large-scale scenario including ≈ 6000 flights on December 20th, 2018, from 12:00 to 16:00 over European airspace. The flight information, including the time and altitude of the first crossed waypoint within the considered time interval, has been extracted from the DDR2 dataset. For flights that start or land outside ECAC airports, we model only the segment of the flight that takes place within ECAC airspace. The algorithmic climate change functions proposed by [4] are employed to quantify the climate impact of each species, including contrails, and emissions of nitrogen oxides, CO2, and water vapor, in terms of average temperature response over the next 20 years. Our recently developed tool for climate-optimal aircraft trajectory planning, ROOST, is then used to optimize each trajectory 1 within the current structured airspace [5]. The effects of adopting climate optimized trajectories are assessed in terms of complexity, demand, and the number of conflicts. A performance map associated with each indicator is generated to spatially analyze the overall behavior of optimized trajectories and detect congested areas.      For the considered scenario, the results indicate that by adopting trajectories with less climate impact, the complexity, demand, and conflicts are increased around climate hotspots. This trend is mainly due to the tendency to avoid climate-sensitive regions. In order to mitigate such changes in traffic patterns, an efficient resolution strategy is needed to find the optimal mechanisms to manage the ATM system from a climatic perspective.  

This work offers an overview of the effective communication techniques for space exploration of ground, aerial, and underwater vehicles. We not only comprehensively summarize the trajectory planning, space exploration, optimization, and other challenges encountered but also present the possible directions for future work. Because a detailed study like this is uncommon in the literature, an attempt has been made to fill the gap for readers interested in path planning. This paper also includes optimization strategies that can be used to implement terrestrial, underwater, and airborne applications. This study addresses numerical, bio-inspired, and hybrid methodologies for each dimension described. Throughout this study, we endeavored to establish a centralized platform in which a wealth of research on autonomous vehicles (on the land and their trajectory optimizations), airborne vehicles, and underwater vehicles, is published.

Autonomous systems have achieved great success over the last couple of decades. They have bring the revolutionary change in the world, either its ground vehicles, aerial systems or underground vehicles. Number of research papers have been written on the importance of autonomous systems and their applications in different field. Keeping in view the pattern of research done by authors, an effort has been made to provide a single platform for readers to familiarize themselves with applications involved in terrestrial, aerial and undersea systems along with different sets of dimensions involved in achieving these applications. Therefore, the article provides a summary of the main communication methods used by terrestrial, aerial, and undersea space research vehicles. In addition to providing an exhaustive summary of the difficulties encountered in trajectory planning, space exploration, optimization, and other areas, the research also presents optimization methods applicable to aerial, undersea, and terrestrial applications. As the literature lacks extensive studies like this one, hence an effort has been made to fill the gap for readers interested in path design. This study tackles numerical, bioinspired, and hybrid techniques for each of the dimensions given. With this study, we attempted to provide a single repository for a plethora of research on autonomous land vehicles, their trajectory optimization, as well as research on aerial and undersea vehicles. The article ends with the most practical directions for future research.

Detecting actions in videos have been widely applied in on-device applications, such as cars, robots, etc. Practical on-device videos are always untrimmed with both action and background. It is desirable for a model to both recognize the class of action and localize the temporal position where the action happens. Such a task is called temporal action location (TAL), which is always trained on the cloud where multiple untrimmed videos are collected and labeled. It is desirable for a TAL model to continuously and locally learn from new data, which can directly improve the action detection precision while protecting customers’ privacy. However, directly training a TAL model on the device is nontrivial. To train a TAL model which can precisely recognize and localize each action, tremendous video samples with temporal annotations are required. However, annotating videos frame by frame is exorbitantly time consuming and expensive. Although weakly supervised temporal action localization (W-TAL) has been proposed to learn from untrimmed videos with only video-level labels, such an approach is also not suitable for on-device learning scenarios. In practical on-device learning applications, data are collected in streaming. For example, the camera on the device keeps collecting video frames for hours or days, and the actions of nearly all classes are included in a single long video stream. Dividing such a long video stream into multiple video segments requires lots of human effort, which hinders the exploration of applying the TAL tasks to realistic on-device learning applications. To enable W-TAL models to learn from a long, untrimmed streaming video, we propose an efficient video learning approach that can directly adapt to new environments. We first propose a self-adaptive video dividing approach with a contrast score-based segment merging approach to convert the video stream into multiple segments. Then, we explore different sampling strategies on the TAL tasks to request as few labels as possible. To the best of our knowledge, we are the first attempt to directly learn from the on-device, long video stream. Experimental results on the THUMOS’14 dataset show that the performance of our approach is comparable to the current W-TAL state-of-the-art (SOTA) work without any laborious manual video splitting.

An optimal trajectory is very important to reusable launch vehicle (RLV) which facing the critical heating and aero force in reentry environment. The trajectory planning is a typical large scale and multi-constraint optimization problem. In this paper, an optimal trajectory planning for RLV from the beginning upper atmosphere state to lower atmosphere site with the minimum accumulated heat load or maximum range under multi-constraint reentry condition is studied. To achieve this goal, the dynamics of RLV is first described and the cost function of the optimal problem is formulated with multi reentry constraints. Then, a series of discrete trajectory points were designed on reentry corridor. The process of searching the optimized trajectory for RLV with the Sequential Quadratic Programming(SQP) is proposed. This algorithm is implemented on a RLV which similar the X-33 and its validity is proven by simulation result.

This paper proposed an algorithm to solve major challenges in the domain of autonomous transportation systems. These challenges are trajectory planning and collision avoidance. Generally, in a shared infrastructure where several agents aim to use limited capacity resources, finding a set of optimal and conflict-free paths for each single agent is the most critical part. In such a dynamic environment where continual planning and scheduling are required, we have adopted a coupled (centralized) technique and face the problem by breaking it into two distinct phases: path planning and collision avoidance. In the first phase, the lowest cost path is planned for each agent by a modified version of Dijkstra algorithm. Following that, in the second phase, the head-on collisions can be foreseen and avoided by detecting the agents' common segments of the path choices. Finally, based on the capacity of each resource and the feasibility of each path, the task assignment and scheduling algorithm allocates different tasks between agents.

We present fast and scalable parallel computations for a number of important and fundamental matrix problems on distributed memory systems (DMS). These problems include computing the powers, the inverse, the characteristic polynomial, the determinant, the rank, the Krylov matrix, and an LU- and a QR-factorization of a matrix, and solving linear systems of equations. These parallel computations are based on efficient implementations of the fastest sequential matrix multiplication algorithm on DMS. We show that compared with the best known time complexities on PRAM, our parallel matrix computations achieve the same speeds on distributed memory parallel computers (DMPC), and have an extra polylog factor in the time complexities on DMS with hypercubic networks. Furthermore, our parallel matrix computations are fully scalable on DMPC and highly scalable over a wide range of system size on DMS with hypercubic networks. Such fast and scalable parallel matrix computations were not seen before on any distributed memory systems.

This paper proposes a linear programming approach for onboard optimization of rocket trajectories, motivated by the need for reliable and computationally efficient trajectory optimization methods in real-time applications. To reformulate rocket trajectory optimization problems within a linear programming framework, a polytopal approximation method is developed. The polytopal approximation method approximates the thrust magnitude constraint using a set of artificial variables and linear constraints. Compared with a state-of-the-art approximation method, the polytopal approximation method demonstrates a higher accuracy-to-size ratio, enabling rocket trajectory optimization problems to be cast into linear subproblems without significantly increasing problem sizes. As linear subproblems can be readily solved by linear programming solvers, the proposed trajectory optimization approach inherits the solver’s reliability and computational efficiency, making it potentially useful for critical onboard applications. An ascent trajectory optimization problem is provided as an illustrative example to demonstrate the effectiveness of the proposed linear programming approach.

We introduce a twice differentiable augmented Lagrangian for nonlinear optimization with general inequality constraints and show that a strict local minimizer of the original problem is an approximate strict local solution of the augmented Lagrangian. A novel augmented Lagrangian method of multipliers (ALM) is then presented. Our method is originated from a generalization of the Hestenes-Powell augmented Lagrangian, and is a combination of the augmented Lagrangian and the interior-point technique. It shares a similar algorithmic framework with existing ALMs for optimization with inequality constraints, but it can use the second derivatives and does not depend on projections on the set of inequality constraints. In each iteration, our method solves a twice continuously differentiable unconstrained optimization subproblem on primal variables. The dual iterates, penalty and smoothing parameters are updated adaptively. The global and local convergence are analyzed. Without assuming any constraint qualification, it is proved that the proposed method has strong global convergence. The method may converge to either a Karush-Kuhn-Tucker (KKT) point or a singular stationary point when the converging point is a minimizer. It may also converge to an infeasible stationary point of nonlinear program when the problem is infeasible. Furthermore, our method is capable of rapidly detecting the possible infeasibility of the solved problem. Under suitable conditions, it is locally linearly convergent to the KKT point, which is consistent with ALMs for optimization with equality constraints. The preliminary numerical experiments on some small benchmark test problems demonstrate our theoretical results.

A Nonlinear Least Squares problem is an optimization problem for which the objective function to be minimized has the form() = [∑=1] ƒ2() , ∈ , ≥ The structure of () allows the problem to be solved using Newton-type methods, in which the Hessian is efficiently approximated from the first derivatives, rather than explicitly calculated. In most of the work which has appeared in recent years, it has been assumed that the ƒ's are twice continuously differentiable, that there are no explicit constraints on the variables, and that the Jacobian is small enough to be held in core and factorized. The first part of this thesis presents an overview of some of the algorithms which have been used on this general problem.Special types of nonlinear least squares problems are then examined, in particular (i) problems for which there are general linear inequality constraints on (ii) problems in which the functions ƒ may be nonsmooth (i.e. have discontinuous first partial derivatives) (iii) problems for which the Jacobian matrix () = [ ∂ƒ / ∂ ] =1,.. ; =1,..is sparse; that is, most of the ƒ's are functions of only a small subset of the variables.Algorithms for these three classes of problems are presented in Chapters 2, 3, and 4, together with convergence results and numerical experience.In the final Chapter, we consider the geophysical problem of inverting seismic arrival time data, in order to accurately locate earthquake coordinates and to obtain density information about the earth's crust in the vicinity of the recording stations. This can be formulated as a sparse nonlinear least squares problem, and is solved using a modification of the algorithm of Chapter 4. Numerical results are obtained for two actual data sets, and are compared with the results obtained from a program currently in use at the U. S. Geological Survey.The appendices contain listings of the FORTRAN programs which were used to implement the algorithms of Chapters 2, 3, and 4.