Optimal Trajectory Design Research Articles

Adaptive entry guidance for the Tianwen-1 mission

To meet the requirements of the Tianwen-1 mission, adaptive entry guidance for entry vehicles, with low lift-to-drag ratios, limited control authority, and large initial state bias, was presented. Typically, the entry guidance law is divided into four distinct phases: trim angle-of-attack phase, range control phase, heading alignment phase, and trim-wing deployment phase. In the range control phase, the predictor—corrector guidance algorithm is improved by planning an on-board trajectory based on the Mars Science Laboratory (MSL) entry guidance algorithm. The nominal trajectory was designed and described using a combination of the downrange value and other states, such as drag acceleration and altitude rate. For a large initial state bias, the nominal downrange value was modified onboard by weighing the landing accuracy, control authority, and parachute deployment altitude. The biggest advantage of this approach is that it allows the successful correction of altitude errors and the avoidance of control saturation. An overview of the optimal trajectory design process, including a discussion of the design of the initial flight path angle, relevant event trigger, and transition conditions between the four phases, was also presented. Finally, telemetry data analysis and post-flight assessment results were used to illustrate the adaptive guidance law, create good conditions for subsequent parachute reduction and power reduction processes, and gauge the success of the mission.

Design of well seismic combined with horizontal well and tracking adjustment while drilling in block A

Based on the accurate understanding of the reservoir, oil-water distribution and structure of block A, the main oil layers are locally developed in well blocks A, B and C, the favorable parts of the structure are optimized, and the horizontal wells are deployed according to the principle of “increasing the production of horizontal wells in the main layer, not adding new platforms, and the horizontal section is not easy to be too long”. Apply new drilling data to carry out fine structure interpretation and reservoir inversion prediction, update geological model, and guide horizontal well trajectory optimization design and tracking adjustment.

Joint Trajectory and Resource Optimization for UAV-Aided Two-Way Relay Networks

Unmanned aerial vehicle (UAV)-aided two-way relay networks with multiple terrestrial user pairs is investigated, where a fix-wing UAV is served as a two-way relay to assist information transmission. We aim to maximize the total rate of the two-way relay networks while the quality of service (QoS) being guaranteed. A novel relay strategy, namely <i>time-slots pairing</i>, is proposed by exploiting physical-layer network coding (PNC) protocol. Specifically, the UAV receives and buffers the signals from the scheduled user pair when the UAV approaches one of them, then forwards the modulated signal when the UAV is close to the other. As a result, a non-convex total rate maximization problem is formulated by joint trajectory design and resource optimization. To solve this problem, we first decompose it into three sub-problems, and then a three-step iterative algorithm that can effectively handle the non-convex problem with no worse than a polynomial complexity is developed leveraging the block coordinate descent (BCD) technique and successive convex approximation (SCA) method. Simulation results finally illustrate that: 1) Compared with amplify-and-forward (AF) or decode-and-forward (DF) protocols, the proposed design based on PNC protocol can significantly improve the total rate of the two-way relay networks; 2) the time-slots pairing relay strategy always achieves a significant enhancement on performance than the traditional non-time-slots pairing relay strategy; 3) the time-slots pairing relay strategy is more favorable for the mobile PNC relay networks since it can well resist the degradation of the entire networks caused by users&#x2019; increased service quality requirements.

Cooperative Eco-driving Controller for Battery Electric Vehicle Platooning

Eco-driving and platooning both play an increasingly important role in alleviating range anxiety for battery electric vehicles (BEVs). Pontryagin's Minimum Principle (PMP) has been popularly adopted for designing eco-driving speed planners because of its capability to achieve near optimal solutions at high computational efficiency that brings potential of real-time implementation. However, most of the existing PMP-based eco-driving studies did not consider the change of aerodynamic drag coefficient due to platooning effect, or simply ignore the nonlinear aerodynamic resistance to achieve analytical optimal solutions. Such simplification of aerodynamic resistance model can lead to inaccuracy in vehicle speed optimization, and thus potentially make eco-driving less energy-efficient and cause severe safety issues in car following scenario. In recognition of these issues, this paper proposes an innovative PMP-based cooperative eco-driving controller (CEDC) that incorporates the impact of air drag coefficient change in the optimal speed trajectory design for the circumstance of two-BEV operation. The simulation results reveal noticeable differences in optimal speed profile, when compared to baseline CEDC controller which adopts a constant aerodynamic drag coefficient. It is also shown that implementation of the optimal speed profile from baseline CEDC controller will violate safety constraint and lead to collision. Furthermore, the simulation results demonstrate that, the CEDC can reduce energy consumption by 12.25% and 4.68%, respectively, when compared to intelligent driver model (IDM)-based control and the baseline CEDC.

Trajectory optimization design of ascending stage of RBCC powered hypersonic vehicle

Trajectory optimization design of ascending stage of RBCC powered hypersonic vehicle

UAV Placement and Trajectory Design Optimization: A Survey

UAV Placement and Trajectory Design Optimization: A Survey

Optimal trajectory design accounting for the stabilization of linear time-varying error dynamics

This study is dedicated to the development of a direct optimal control-based algorithm for trajectory optimization problems that accounts for the closed-loop stability of the trajectory tracking error dynamics already during the optimization. Consequently, the trajectory is designed such that the Linear Time-Varying (LTV) dynamic system, describing the controller’s error dynamics, is stable, while additionally the desired optimality criterion is optimized and all enforced constraints on the trajectory are fulfilled. This is achieved by means of a Lyapunov stability analysis of the LTV dynamics within the optimization problem using a time-dependent, quadratic Lyapunov function candidate. Special care is taken with regard to ensuring the correct definiteness of the ensuing matrices within the Lyapunov stability analysis, specifically considering a numerically stable formulation of these in the numerical optimization. The developed algorithm is applied to a trajectory design problem for which the LTV system is part of the path-following error dynamics, which is required to be stable. The main benefit of the proposed scheme in this context is that the designed trajectory trades-off the required stability and robustness properties of the LTV dynamics with the optimality of the trajectory already at the design phase and thus, does not produce unstable optimal trajectories the system must follow in the real application.

Discrete-time flatness-based control of a gantry crane

This article addresses the design of a discrete-time flatness-based tracking control for a gantry crane and demonstrates the practical applicability of the approach by measurement results. The required sampled-data model is derived by an Euler-discretization with a prior state transformation in such a way that the flatness of the continuous-time system is preserved. Like in the continuous-time case, the flatness-based controller design is performed in two steps. First, the sampled-data system is exactly linearized by a discrete-time quasi-static state feedback. Subsequently, a further feedback enforces a stable linear tracking error dynamics. To underline its practical relevance, the performance of the novel discrete-time tracking control is compared to the classical continuous-time approach by measurement results from a laboratory setup. In particular, it turns out that the discrete-time controller is significantly more robust with respect to large sampling times. Moreover, it is shown how the discrete-time approach facilitates the design of optimal reference trajectories, and further measurement results are presented.

Quantitative prediction of the drilling azimuth of horizontal wells in fractured tight sandstone based on reservoir geomechanics in the Ordos Basin, central China

Hydraulic fracturing and horizontal well technology can effectively improve reservoir production but can affect reservoir reconstruction through many factors, including the reservoir lithology, reservoir stress state and natural fractures. Considering tight sandstone as an example, the finite element method (FEM) and the optimal trajectory design scheme for a horizontal well are used in this study to determine the influence of the stress state, mechanical parameters and natural fractures of rock on the effects of hydraulic fracturing. Core reorientation via a paleomagnetic method is used to determine the natural fracture orientations in different well blocks. The in-situ stress magnitudes and directions are determined using microseismic monitoring of hydraulic fracturing, borehole breakout analysis, difference strain analysis and acoustic emission experiments. A heterogeneous geomechanical model is formulated based on log interpretations of the rock mechanical parameters of 111 wells and the results of triaxial mechanical experiments. The FEM is used to determine the in-situ stress field in the Dongrengou block. A predictive model for the hydraulic fracture propagation direction is formulated considering the in-situ stress, geomechanical model and natural fracture orientation. The results show that the mechanical parameters of the Dongrengou block are characterized by planar anisotropy and three-dimensional heterogeneity, where the rock mechanical parameters vary considerably across the plane and are vertically stratified. Using these results in conjunction with the drilling directions and oil production of 14 horizontal wells shows that oil and gas recovery is maximized by orienting horizontal wells perpendicular to the propagation direction of hydraulic fractures.

Robust Co-Design: Coupling Morphology and Feedback Design Through Stochastic Programming

Abstract This article proposes a new framework for the computational design of robots that are robust to disturbances. The framework combines trajectory optimization (TO) and feedback control design to produce robots with improved performance under perturbations by co-optimizing a nominal trajectory alongside a feedback policy and the system morphology. Stochastic programming (SP) methods are used to address these perturbations via uncertainty models in the problem specification, resulting in motions that are easier to stabilize via feedback. Two robotic systems serve to demonstrate the potential of the method: a planar manipulator and a jumping monopod robot. The co-optimized robots achieve higher performance compared to state-of-the-art solutions where the feedback controller is designed separately from the physical system. Specifically, the co-designed controllers show higher tracking accuracy and improved energy efficiency (e.g., 91% decrease in tracking error and ≈5% decrease in energy consumption for a manipulator) compared to linear quadratic regulator applied to a design optimized for nominal conditions.

Novel Optimal Trajectory Design in UAV-Assisted Networks: A Mechanical Equivalence-Based Strategy

Unmanned aerial vehicles (UAVs), also known as drones, have already been widely implemented in wireless networks for promoting network performance and enabling new services. To efficiently explore the diversity introduced by the mobility of UAV, many efforts have been made in the design of the UAV trajectory under various wireless scenarios. However, the continuity of a UAV trajectory in both time and topology forces researchers to approximate the UAV trajectory by a discrete model, which always results in a sub-optimal solution. To tackle the difficulty and obtain the optimal trajectory, in this work we introduce an artificial potential field (APF) to reformulate the objective in trajectory design, with which the UAV trajectory problem can be completely equivalent to a mechanical problem. In such mechanical problem, the UAV trajectory is represented by an extremely soft and thin rope with variable density carrying UAV speed information, and the original objective of optimizing the system performance is transformed to minimizing the overall artificial potential energy on the rope. As a result, the rope in the optimal solution stays in a state of equilibrium and the UAV trajectory can be equivalently optimized by designing the shape of a rope under the APF via mechanical principles. We provide a case study to describe in detail the problem equivalence, i.e., taking a single-user network as an example in which the throughput between UAV and the user is considered as the objective performance. In particular, the optimal trajectory of a UAV is constructed based on mechanical principles, while the global optimality is also rigorously proved and further confirmed via simulations. Moreover, we also highlight that the novel strategy of constructing equivalent mechanical problem has the possibilities to be extended to various UAV trajectory problems under different scenarios with different performance optimization objectives.

Hybrid Rocket Engine Design Optimization at Politecnico di Torino: A Review

Optimization of Hybrid Rocket Engines at Politecnico di Torino began in the 1990s. A comprehensive review of the related research activities carried out in the last three decades is here presented. After a brief introduction that retraces driving motivations and the most significant steps of the research path, the more relevant aspects of analysis, modeling and achieved results are illustrated. First, criteria for the propulsion system preliminary design choices (namely the propellant combination, the feed system and the grain design) are summarized and the engine modeling is presented. Then, the authors describe the in-house tools that have been developed and used for coupled trajectory and propulsion system design optimization. Both deterministic and robust-based approaches are presented. The applications that the authors analyzed over the years, starting from simpler hybrid powered sounding rocket to more complex multi-stage launchers, are then presented. Finally, authors’ conclusive remarks on the work done and their future perspective in the context of the optimization of hybrid rocket propulsion systems are reported.

Residual force polytope: Admissible task-space forces of dynamic trajectories

We propose a representation for the set of forces a robot can counteract using full system dynamics: the residual force polytope. Given the nominal torques required by a dynamic motion, this representation models the forces which can be sustained without interfering with that motion. The residual force polytope can be used to analyze and compare the set of admissible forces of different trajectories, but it can also be used to define metrics for solving optimization problems, such as in trajectory optimization or system design. We demonstrate how such a metric can be applied to trajectory optimization and compare it against other objective functions typically used. Our results show that the trajectories computed by optimizing objectives defined as functions of the residual force polytope are more robust to unknown external disturbances. The computational cost of these metrics is relatively high and not compatible with the short planning times required by online methods, but they are acceptable for planning motions offline.

Bézier Curves-Based Optimal Trajectory Design for Multirotor UAVs with Any-Angle Pathfinding Algorithms.

Multirotor Unmanned Aerial Vehicles (UAVs) play an imperative role in many real-world applications in a variety of scenarios characterized by a high density of obstacles with different heights. Due to the complicated operation areas of UAVs and complex constraints associated with the assigned mission, there should be a suitable path to fly. Therefore, the most relevant challenge is how to plan a flyable path for a UAV without collisions with obstacles. This paper demonstrates how a flyable and continuous trajectory was constructed by using any-angle pathfinding algorithms, which are Basic Theta*, Lazy Theta*, and Phi* algorithms for a multirotor UAV in a cluttered environment. The three algorithms were modified by adopting a modified cost function during their implementation that considers the elevation of nodes. First, suitable paths are generated by using a modified version of the three algorithms. After that, four Bézier curves-based approaches are proposed to smooth the generated paths to be converted to flyable paths (trajectories). To determine the most suitable approach, particularly when searching for an optimal and collision-free trajectory design, an innovative evaluation process is proposed and applied in a variety of different size environments. The evaluation process results show high success rates of the four approaches; however, the approach with the highest success rate is adopted. Finally, based on the results of the evaluation process, a novel algorithm is proposed to increase the efficiency of the selected approach to the optimality in the construction process of the trajectory.

Joint trajectory and transmission optimization for energy efficient UAV enabled eLAA network

Unmanned aerial vehicle (UAV) as a carrier of small cell base station (SBS) becomes a promising solution to reduce infrastructure deployment cost. At the same time, Licensed-assisted Access (LAA) is proposed by 3GPP to apply the Long Term Evolution (LTE) technology into the unlicensed spectrum to expand the available bandwidth. To enhance and supplement the next generation 5G wireless network, this paper integrates LAA technology into UAV network to provide communication service for high-density mobile users. An enhanced LAA (eLAA) network is adopted to coordinate unlicensed band for LTE and WiFi by leveraging IEEE 802.11e protocol. The limited on-board energy is the main challenge for UAV to support mobility and communication. Under the UAV enabled eLAA network, we propose a joint trajectory design and transmission optimization algorithm to maximize the energy efficiency (EE) of the UAV. Firstly, for single UAV network, the formulated nonlinear fractional problem is solved by block coordinate descent (BCD) method and Dinkelbach-type algorithm. Our algorithm is proved to converge to a stationary point of the original nonconvex problem. Then, the proposed algorithm is extended to multi-UAV network through the sum-of-ratios algorithm. Numerical results demonstrate that the EE performance is significantly improved by UAV mobility. Based on the optimal trajectories, frequency reuse among multiple UAVs can further improve the EE performance.

Energy-Efficient UAV Backscatter Communication With Joint Trajectory Design and Resource Optimization

Backscatter communication which enables wireless-powered backscatter devices (BDs) to transmit information by reflecting incident signals, is an energy- and cost-efficient communication technology for Internet-of-Things. This paper considers an unmanned aerial vehicle (UAV)-assisted backscatter communication network (UBCN) consisting of multiple BDs and carrier emitters (CEs) on the ground as well as a UAV. A communicate-while-fly scheme is first designed, in which the BDs illuminated by their associated CEs transmit information to the flying UAV in a time-division-multiple-access manner. Considering the critical issue of the UAV's limited on-board energy and the CEs' transmission energy, we maximize the energy efficiency (EE) of the UBCN by jointly optimizing the UAV's trajectory, the BDs' scheduling, and the CEs' transmission power, subject to the BDs' throughput constraints and harvested energy constraints, as well as other practical constraints. Furthermore, we propose an iterative algorithm based on the block coordinated decent method to solve the formulated mixed-integer non-convex problem, in each iteration of which the variables are alternatively optimized by leveraging the cutting-plane technique, the Dinkelbach's method and the successive convex approximation technique. Also, the convergence and complexity of the proposed algorithm are analyzed. Finally, simulation results show that the proposed communicate-while-fly scheme achieves significant EE gains compared with the hover-and-fly scheme, the state-of-the-art scheme, and the CE-relay scheme. Useful insights on the optimal trajectory design and resource allocation are also obtained.

Optimal Earth-Moon Transfer Trajectory Design via Differential Dynamic Programming with Input Saturation Constraints

Optimal Earth-Moon Transfer Trajectory Design via Differential Dynamic Programming with Input Saturation Constraints

Optimization Design of Propellant Charge for a Medium and Large Caliber High Chamber Pressure Gun

Taking a medium and large caliber high chamber pressure gun as the object and a single charge as an example, the optimization design model of the propellant charge of high chamber pressure gun was established by using the optimization theory, and the trajectory parameters of 100mm gun were optimized, and the optimal trajectory design scheme satisfying the constraints is obtained. The results of this paper have some guiding significance for the optimal design of propellant charge for high chamber pressure gun.

A composite framework for co-optimization of spacecraft trajectory and propulsion system

Indirect optimization methods convert optimal control problems (OCPs) into two- or multi-point boundary-value problems. A highly desirable feature of indirect methods, specifically for space applications, is that high-resolution trajectories can be generated, which satisfy the first-order necessary conditions of optimality. A recently developed Composite Smoothing Control (CSC) framework is utilized to formulate and solve the problem of simultaneous trajectory optimization and propulsion sub-system design of spacecraft. A reasonable parameterized breakdown of the spacecraft mass is adopted, which captures the impact of power produced by the solar arrays and its contribution to the total spacecraft mass. Thus, the implicit trade-offs can be considered in the indirect optimization approach. The function space co-optimization problem of spacecraft power subsystem parameters along with the main trajectory is solved with the objective to maximize the payload delivered. The proposed framework amounts to an invariant embedding that reduces the original, difficult-to-solve, multi-point boundary-value problem into a two-point boundary-value problem with continuous, differentiable control inputs. Utility of the proposed construct is demonstrated through a low-thrust, multi-revolution, multi-year rendezvous maneuver to asteroid Dionysus with a variable-specific-impulse, variable-thrust modeled engine. This is the first time that indirect optimization methods have tackled such a complex co-optimization problem using the CSC framework.

Homotopy-based optimal trajectory design to transfer from Earth orbit to halo orbits

مدارهای هاله‌ای به واسطه ویژگی‌هایی همچون حرکت‌های تناوبی حول نقطه تعادلی برای رصد و مطالعه فضا اهمیت ویژه‌ای دارند. از این رو، مقاله حاضر به طراحی مسیر انتقال بهینه به مدار هاله‌ای پرداخته است. برای حل این مسئله کنترل بهینه از رویکرد هموتوپی در کنار روش پرتابی استفاده شده‌است. این روش باعث بهبود سرعت همگرایی و رسیدن به حدس اولیه بهتری می‌شود. مسیر بهینه طراحی‌شده، فضاپیمایی در مدار حول زمین را به یک مدار هاله‌ای حول نقطه لاگرانژی L1 سیستم سه جسم زمین-ماه منتقل می‌کند. سیستم پیشران فضاپیما از نوع تراست-کم با ضربه ویژه ثابت در نظر گرفته شده است. رویکرد هموتوپی دامنه گسترده‌ای دارد که از آن میان، روش ادامه‌ی هموتوپی در این پژوهش مدنظر قرار گرفته‌است. هدف از مسیر طراحی شده، انتقال با کمینه مصرف سوخت است که به کمک رویکرد هموتوپی از تغییر شکل حل مساله کمینه مصرف انرژی به دست آمده است. در واقع رویکرد هموتوپی سبب تسهیل حل مساله دشوار کمینه مصرف سوخت شده است.