Trajectory Optimization

Specific conditions of on-orbit environment are taken into account in the design of all devices intended to be used in space. Despite this fact malfunctions of satellites occur and sometimes lead to shortening of the satellite operational lifetime. It is considered to use unmanned servicing satellite, that could perform repairs of other satellites. Such satellites equipped with a manipulator, could be used to capture and remove from orbit large space debris. The critical part of planned missions is the capture manoeuvre. In this paper a concept of the control system for the manipulator mounted on the satellite is presented. This control system is composed of the trajectory planning module and model predictive controller (the latter is responsible for ensuring precise realization of the planned trajectory). Numerical simulations performed for the simplified planar case with a 2 DoF manipulator show that the results obtained with the predictive control are better than the results obtained with adaptive control method.

Unmanned Aerial Vehicles (UAVs) Technology recently attracts attention of many researchers; this is due toits numerous potentialities in civil application. One of the key areas of interest by researches is how to achievea total talent of “Sense and Avoid” in the UAV which will enhance safe and efficient trajectory of the vehicle.This is why this paper is going to use an optimization technique to optimize trajectory path of the UAV flight.The chosen optimization algorithm is Genetic algorithm (GA) which is going to be use to optimize the trajectoryof UAV by determine the shortest path of flight as well as obstacle-free path in order to save energy and timeduring flight. MATLAB and Simulink are used to simulate as well as evaluate the algorithm. In the result fromthe experiment, it appeared that an optimized trajectory path is tremendously better than path from the firstrandomly generated population in term of distance covered as well as time taken before triumph the target pointfrom ...

In this paper, the trajectory optimization problem for a multi-aerial base station (ABS) communication network is investigated. The objective is to find the trajectory of the ABSs so that the sum-rate of the users served by each ABS is maximized. To reach this goal, along with the optimal trajectory design, optimal power and subchannel allocation is also of great importance to support the users with the highest possible data rates. To solve this complicated problem, we divide it into two sub-problems: ABS trajectory optimization sub-problem, and joint power and sub-channel assignment sub-problem. Then, based on the Q-learning method, we develop a distributed algorithm which solves these sub-problems efficiently, and does not need significant amount of information exchange between the ABSs and the core network. Simulation results show that although Q-learning is a model-free reinforcement learning technique, it has a remarkable capability to train the ABSs to optimize their trajectories based on the received reward signals, which carry decent information from the topology of the network.

Information on the trajectories of turning vehicles at signalized intersections can be used in numerous applications, such as movement planning of autonomous vehicles, realistic representation of surrounding vehicle movements in driving simulator and virtual reality applications, and in microscopic simulation tools. However, no proper framework is currently available to realistically model and estimate trajectories of turning vehicles reflecting the intersection geometries, which is critical for the reliability of simulation models. This study explores the applicability of the minimum-jerk principle, which has been initially applied in neuroscience and robotics domains, to model and simulate free-flow trajectories of turning vehicles. The modeling method is validated by comparing model outputs with empirical trajectories collected at several signalized intersections in Nagoya, Japan. The capability of the model in realistically capturing the variations in turning trajectories based on intersection geometry (e.g., intersection angle and turning radius) is also explained. Further, the applicability of the modeling framework at intersections with different geometric features under different speeds and accelerations are also discussed.

This paper deals with models of the rockets' motion around mass centre, command laws of vertical and horizontal planes trajectory, stabilisation laws of the roll motion of the rockets and target control laws (1), (2). One also studies the way to choose of the parameters of general command laws which assures state variables simultaneous cancellation. Some automatic control systems, using the previous laws, are also presented. Also, one presents some extremal systems for optimization of aircrafts and rockets' flight using test signals for extreme's search (3), (4).

This paper examines two low thrust insertion options for delivery of a 40-kW solar electric propulsion spacecraft to a Near Rectilinear Halo Orbit (NRHO). One option considered is a trans-lunar injection launch as a co-manifested payload on the Space Launch System. For this option, a reference trajectory is designed and a scan of launch dates is completed to understand the propellant mass sensitivity. A 15-day period cyclical variation in required propellant is observed that is attributed to solar gravity effects. A second option considered is to launch on a smaller commercial launch vehicle to a less energetic elliptical orbit and use SEP to spiral out to NRHO. For this option, analysis is completed to understand the trades between delivered mass to NRHO, total propellant required, time of flight, and solar array degradation. Results show that, while launching to lower altitudes can deliver greater payload mass to NRHO, significant solar array degradation can occur. In addition to a generic dataset that can be applied to any launch vehicle, spiral trajectory results are presented specific to launch on an Atlas V 551 and Falcon 9.

The upcoming DARPA Robotics Challenge (DRC) presents a demanding set of real-world tasks to be accomplished autonomously by robots. In this paper, we describe the de velopment of a system to control an existing humanoid robot to open a door, one of the many tasks of the DRC. Special emphasis is placed upon generating smooth trajectories which minimize unnecessary motion of the robot. We describe methods for generating and optimizing trajectories for the robot, and present preliminary results demonstrated on the physical robotic platform. To the best of our knowledge, we demonstrate the first large scale application of the CHOMP trajectory optimization in a situation with closed kinematic chain constraints.

Specific conditions of on-orbit environment are taken into account in the design of all devices intended to be used in space. Despite this fact malfunctions of satellites occur and sometimes lead to shortening of the satellite operational lifetime. It is considered to use unmanned servicing satellite, that could perform repairs of other satellites. Such satellites equipped with a manipulator, could be used to capture and remove from orbit large space debris. The critical part of planned missions is the capture manoeuvre. In this paper a concept of the control system for the manipulator mounted on the satellite is presented. This control system is composed of the trajectory planning module and model predictive controller (the latter is responsible for ensuring precise realization of the planned trajectory). Numerical simulations performed for the simplified planar case with a 2 DoF manipulator show that the results obtained with the predictive control are better than the results obtained with adaptive control method.

This paper presents a continuous-time optimal control framework for the generation of reference trajectories in driving scenarios with uncertainty. A previous work presented a discrete-time stochastic generator for autonomous vehicles; those results are extended to continuous time to ensure the robustness of the generator in a real-time setting. We show that the stochastic model in continuous time can capture the uncertainty of information by producing better results, limiting the risk of violating the problem's constraints compared to a discrete approach. Dynamic solvers provide faster computation and the continuous-time model is more robust to a wider variety of driving scenarios than the discrete-time model, as it can handle further time horizons, which allows trajectory planning outside the framework of urban driving scenarios.

In this paper, we develop a composite collocation approximation scheme for solving optimal control problems governed by ordinary differential equations with piecewise smooth solutions. For this purpose, we divide the time interval of the problem into some nonequal subintervals and define a piecewise interpolating polynomial on the base of transformed Legendre-Gauss nodes in subintervals. According to the weak representations approach, we derive the corresponding operational matrix of derivative. Using the Legendre-Gauss quadrature formula and the obtained operational matrix, the optimal control problem is discretized as a nonlinear

In this paper, we propose a unified approach to solve the time-energy optimal landing problem on planetary bodies (e.g. planets, moons, and asteroids). In particular, the indirect optimization method, based on the derivation of the first order necessary conditions from the Hamiltonian, is exploited and the Two-Point Boundary Value Problem arising from the application of the Pontryagin Minimum Principle is solved using the Theory of Functional Connections. The optimal landing trajectories are accurately computed with a computational time on the order of 10-100 ms, using a MATLAB implementation. The speed and accuracy of the proposed method makes it suitable for real time applications. The algorithm is applied and validated for the landing on large (Mars and Moon) and small (asteroids Gaspra and Bennu) planetary bodies.

In this paper, we apply a newly developed method to solve boundary value problems for differential equations to solve optimal space guidance problems in a fast and accurate fashion. The method relies on the least-squares solution of differential equations via orthogonal polynomials expansion and constrained expression as derived via Theory of Connection (ToC). The application of the optimal control theory to derive the first order necessary conditions for optimality, yields a Two-Point Boundary Value Problem (TPBVP) that must be solved to find state and costate. Combining orthogonal polynomials expansion and ToC, we solve the TPBVP for a class of optimal guidance problems including energy-optimal landing on planetary bodies and fixed-time optimal intercept for a target-interceptor scenario. The performance analysis in terms of accuracy shows the potential of the proposed methodology as applied to optimal guidance problems.

A time-series flight trajectory technique was developed for use in a civil aircraft during descent. The three-degree-of-freedom (3-DoF) equations of motion were solved via time-series prediction of aerodynamic forces. In the present evaluation, the microburst effect during the descent was considered. The single-objective optimization problem, in which the cost function indicating the trajectory efficiency was minimized, was solved by means of a Kriging model based genetic algorithm (GA) which produces an efficient global optimization process. The optimal trajectory results were compared with those without the microburst condition during the descent. The minimization solution converged well in each case for both conditions plus the differences in flight profiles based on the trajectory history were smaller than those of the solutions before optimization. An analysis of variance and parallel coordinate plot were applied to acquire the quantitative information for the initial condition...

Specific conditions of on-orbit environment are taken into account in the design of all devices intended to be used in space. Despite this fact malfunctions of satellites occur and sometimes lead to shortening of the satellite operational lifetime. It is considered to use unmanned servicing satellite, that could perform repairs of other satellites. Such satellites equipped with a manipulator, could be used to capture and remove from orbit large space debris. The critical part of planned missions is the capture manoeuvre. In this paper a concept of the control system for the manipulator mounted on the satellite is presented. This control system is composed of the trajectory planning module and model predictive controller (the latter is responsible for ensuring precise realization of the planned trajectory). Numerical simulations performed for the simplified planar case with a 2 DoF manipulator show that the results obtained with the predictive control are better than the results obtained with adaptive control method.

The optimal Earth-Moon transfer trajectory considering spacecraft's visibility from the Daejeon ground station visibility at both the trans lunar injection (TLI) and lunar orbit insertion (LOI) maneuvers is designed. Both the TLI and LOI maneuvers are assumed to be impulsive thrust. As the successful execution of the TLI and LOI maneuvers are crucial factors among the various lunar mission parameters, it is necessary to design an optimal lunar transfer trajectory which guarantees the visibility from a specified ground station while executing these maneuvers. The optimal Earth-Moon transfer trajectory is simulated by modifying the Korean Lunar Mission Design Software using Impulsive high Thrust Engine (KLMDS-ITE) which is developed in previous studies. Four different mission scenarios are established and simulated to analyze the effects of the spacecraft's visibility considerations at the TLI and LOI maneuvers. As a result, it is found that the optimal Earth-Moon transfer trajectory, guaranteeing the spacecraft's visibility from Daejeon ground station at both the TLI and LOI maneuvers, can be designed with slight changes in total amount of delta-Vs. About 1% difference is observed with the optimal trajectory when none of the visibility condition is guaranteed, and about 0.04% with the visibility condition is only guaranteed at the time of TLI maneuver. The spacecraft's mass which can delivered to the Moon, when both visibility conditions are secured is shown to be about 534 kg with assumptions of KSLV-2's on-orbit mass about 2.6 tons. To minimize total mission delta-Vs, it is strongly recommended that visibility conditions at both the TLI and LOI maneuvers should be simultaneously implemented to the trajectory optimization algorithm.

The conventional method to send payloads to Mars is by direct trans-Mars injection (TMI) from LEO. NASA is considering an alternative of fueling large Mars-bound cargo transfer vehicles in cis-lunar space with propellants derived from the Moon by in situ propellant production (ISPP) prior to trans-Mars injection from cis-lunar space. A large team of investigators developed an Evolvable Lunar Campaign (ELC) that de ined its strategic objective as follows: "The ELC strategic objective is commercial mining of propellant from lunar poles where it will be transported to lunar orbit to be used by NASA to send humans to Mars." Unfortunately, sending Mars-bound vehicles to cis-lunar space prior to trans-Mars injection saves little mass in LEO, unnecessarily includes lunar ISPP, which is costly, complex, and risky, and at the bottom line, has no bene its. The problem is that the amount of propellant needed to go from LEO to cis-lunar space is roughly comparable to the amount of propellant used for direct TMI from LEO, so the lunar-derived propellants only offset a small amount of propellant used to augment Mars Orbit Insertion and Entry, Descent, and Landing, and the amount of propellant required in LEO is almost the same in both cases. The initial mass in low Earth orbit (IMLEO) is not reduced much by utilizing lunar ISPP. At the bottom line, sending Mars-bound MCTV to cis-lunar space adds complexity, cost, and risk and provides essentially no bene its.

A numerical method for the resolution of a system of ordinary differential equations coupled with a mixed constrained minimization problem is presented. This coupling induces discontinuities of some time-dependent variables when inequality constraints are activated or deactivated. The ordinary differential equations are discretized in time and combined with the first order optimality conditions of the optimization problem. We use a second order multistep method based on a predictorcorrector Adams scheme to detect the discontinuities by extrapolation of the trajectories. Optimization features, namely a sensitivity analysis, are exploited to compute the derivatives of the optimization variables and track the discontinuity points. The main difficulty consists in the impossibility of defining an explicit event function to characterize the activation or deactivation of a constraint. The order of convergence of our method is proved when inequality constraints are activated and numerical results for atmospheric organic particles are presented.

The existence of significant uncertainties in the models and systems required for trajectory prediction represents a major challenge for the Air traffic Management (ATM) system. Weather can be considered as one of the most relevant sources of uncertainty. Understanding and managing the impact of these uncertainties is necessary to increase the predictability of the ATM system. State-ofthe-art probabilistic forecasts from Ensemble Prediction Systems are employed to characterize uncertainty in the wind and potential convective areas. A robust optimal control methodology to produce efficient and predictable aircraft trajectories in the presence of these uncertainties is presented. Aircraft motion is assumed to be at a constant altitude and variable speed, considering BADA4 as the aircraft performance model. A set of Pareto-optimal trajectories is obtained for different preferences among predictability, convective risk, and average cost index running a thorough parametric study on a North Atlantic crossing use case. Results show that the cost of reducing the arrival time window by 10 sec. is between 100 to 200 kg or 3 to 6 min., depending on the cost-index. They also show that reducing the exposure to convection by 50 km is on the order of 5 to 10 min. or 100 to 200 kg. of average fuel consumption.

The design of the robotic arm's trajectory is based on inverse kinematics problem solving, with additional refinements of certain criteria. One common design issue is the trajectory optimization of the robotic arm. Due to the difficulty of the work in the past, many of the suggested ways only resulted in a marginal improvement. This paper introduces two approaches to solve the problem of achieving robotic arm trajectory control while maintaining the minimum reachability time. These two approaches are based on rule-based optimization and a genetic algorithm. The way we addressed the problem here is based on the robot's forward and inverse kinematics and takes into account the minimization of operating time throughout the operation cycle. The proposed techniques were validated, and all recommended criteria were compared on the trajectory optimization of the KUKA KR 4 R600 six-degree-of-freedom robot. As a conclusion, the genetic based algorithm behaves better than the rule-based one in terms of achieving a minimal trip time. We found that solutions generated by the Genetic based algorithm are approximately 3 times faster than the other solutions generated by the rule-based algorithm to the same paths. We argue that as the rule-based algorithm produces its solutions after discovering all the problem's searching space which is time consuming, and it is not the case as per the genetic based algorithm.

In 2007, the Committee on Meeting the Workforce Needs for the National Vision for Space Exploration published findings related to age and skills of the current National Aeronautics and Space Administration (NASA) workforce and projected potential expertise shortages as a result of retirement in the 2014-2015 time frame. In addition, the expanding commercial space industry in both the United States and Europe will likely create further demand for space experts in engineering and a variety of related fields. Although NASA contributes $162 million in funding for education programs annually, those programs target kindergarten through grade 12, not collegiate-level programs. Further, few aeronautical/aerospace departments focused on education related to the development of space technologies, a discipline known as astronautics, exist in the US. In 2009, Doule and Peeters, Professors at the International Space University, sought to determine the need for space-focused knowledge and skills ...

High-Thrust Interplanetary Spacecraft Trajectory Optimization Using Cuda Viktor Wase Global optimization applied to the design of high-thrust interplanetary space trajectories is a computationally expensive task. This thesis investigates the feasibility of combining the Multiple Gravity Assist model of spacecraft trajectory with periodic Lyapunov orbits. The trajectories are designed by optimization, enabled by the computational power of a high-end graphics processing unit.

A scheme is developed for nwnerical solution of minimwn•time trajectories for combat aircraft, undergoing large velocity vector change. The usual six degree-of-freedom aircraft model naturally embeds a point-mass model and a somewhat higher-fidelity "body-rate" model, and can be viewed as consisting of a few "dynamic layers" that exhibit distinct dynamic characteristics. These features. coupled with some classical singular perturbation ideas, allow for time scale separation and interactive sequential multistage optimization. The scheme is illustrated by heading reversal trajectories, computed with a nonlinear programming code.

A scheme is developed for nwnerical solution of minimwn•time trajectories for combat aircraft, undergoing large velocity vector change. The usual six degree-of-freedom aircraft model naturally embeds a point-mass model and a somewhat higher-fidelity "body-rate" model, and can be viewed as consisting of a few "dynamic layers" that exhibit distinct dynamic characteristics. These features. coupled with some classical singular perturbation ideas, allow for time scale separation and interactive sequential multistage optimization. The scheme is illustrated by heading reversal trajectories, computed with a nonlinear programming code.

Robustness and reliability of the designed trajectory are crucial for flight performance of launch vehicles. In this paper, robust trajectory design optimization of a typical LV is proposed. Two formulations of robust trajectory design optimization problem using single-objective and multi-objective optimization concept are presented. Both aleatory and epistemic uncertainties in model parameters and operational environment characteristics are incorporated in the problem, respectively. In order to uncertainty propagation and analysis, the improved Latin hypercube sampling is utilized. A comparison between robustness of the single-objective robust trajectory design optimization solution and deterministic design optimization solution is illustrated using probability density functions. The multi-objective robust trajectory design optimization is executed through NSGA-II and a set of feasible design points with a good spread is obtained in the form of Pareto frontier. The final Pareto fro...

This investigation deals with the problem of spacecraft relative motion control, which is typically associated with the spacecraft rendezvous and proximity maneuvers. Relative position and linear velocity are considered. A distinguishing attribute of the presented approach is consideration of definitely larger relative distance between the satellites than it is commonly addressed in the literature. The presented control method is applicable in the case where the chief satellite moves in a known, highly elliptical orbit. A quasi-optimal control is found by a model predictive control algorithm, where the nonlinear optimization problem is reduced to quadratic optimization by preliminary estimation of the future control trajectory. Significance of the method has been verified using a computer simulation.

In the article, the algorithm optimization trajectory of motion unmanned aerial vehicle (UAVs) is described on the criterion of the least extent of way due to the use theory of the graphs and presentation of flight UAVs as a task of traveling salesman. The prospects of further research and use of algorithm are distinguished. Key words: unmanned aerial vehicle, optimization, trajectory, algorithm of Little's , theory of the graphs.

In collaborative robotics the manipulator trajectory has to be planned to avoid collisions, yet in real-time. In this paper we pose the problem as minimization of a quadratic functional among piecewise linear trajectories in the angular (joint) space. The minimization is subjected to novel nonlinear inequality constraints that simplify the original non-penetration constraints to become cheap to evaluate in real time while still preserving collision-avoidance. The very first and most critical step of the computation is to find an initial trajectory that is free of collisions. To that goal we minimize a weighted sum of the violated constraints until they become feasible or a maximal number of steps is reached. Sometimes an incremental growing of the obstacle helps. By incremental growing we mean that we sequentially solve auxiliary subproblems with obstacles growing from ground or falling from top and use as the initial trajectory the one optimized in the previous step. The initial trajectory is then optimized while preserving feasibility at each step. We solve a sequence of simple-bound constrained quadratic programming problems formulated in the dual space of Lagrange multipliers, which are related to the original linearized inequality constraints that are active or close-to-active. Finally, we refine the trajectory parameterization and repeat the optimization, which we refer to as an hierarchical approach, until an overall prescribed time limit, being well below a second, is reached.

This paper presents a new method that addresses measurement origin uncertainty. Measurement origin uncertainty occurs when the object a measurement originated from is not clear. The systems considered contain multiple bodies which are dynamically indistinguishable other than initial conditions. Each measurement originates from one of the bodies in the system. In the past, recursive data association methods have been used to address problems of this nature. A new technique is presented which treats the measurement association problem as a batch post-processing problem. Reformulating the problem as such, it is possible to transform the data association problem into a trajectory optimization problem. From this point of view it is then possible to solve the measurement association problem using first-and second-order optimization algorithms that rely on having first-and second-order derivatives for cost functions that depend on impulsive trajectories.

The trajectory planning problem in industrial robotic applications has recently attracted the great attention of many researchers. In this paper, an optimal trajectory planning approach is proposed based on optimal time by utilizing the interpolation spline method. The method including a combination of cubic spline and 7th order polynomial is used for generating the trajectory in joint space for robot manipulators. Cuckoo Search (CS) optimization algorithm is chosen to optimize the joint trajectories based on objective, including minimizing total traveling time along the whole trajectory. The spline method has been applied to the PUMA robot for optimizing the joint trajectories with the CS algorithm based on the objective. With the trajectory planning method, the joint velocities, accelerations, and jerks along the whole trajectory optimized by CS meet the requirements of the kinematic constraints in the case of the objective. Simulation results validated that the used trajectory pl...

In this work, we present the integrated structure-control design of a 2-DOF underactuated mechanical system, aiming to achieve a periodic motion of the end-effector. The desired behavior is generated via input-output linearization, followed by structural optimization of the zero dynamics. Inspired by recent works on the control-oriented design of multibody systems, we define an optimization problem based on the simulation of the system's response. In particular, relevant model parameters are used to match the reference with a specific orbit of the zero dynamics, while also penalizing the input energy. For the considered application, the selected parameters are related to the mechanism's elasticities and mass distribution. Notably, we show that it is possible to reach a desirable trade-off between mass reduction and periodic motion accuracy. With an optimal zero dynamics response available, the control scheme can be completed with established orbital stabilization techniques, ensuring a robust oscillating behavior.

This paper is concerned with a robot trajectory optimization approach for thermal barrier coatings. As the requirements of high reproducibility of complex workpieces increase, an optimal thermal spraying trajectory should not only guarantee an accurate control of spray parameters defined by users (e.g., scanning speed, spray distance, scanning step, etc.) to achieve coating thickness homogeneity but also help to homogenize the heat transfer distribution on the coating surface. A mesh-based trajectory generation approach is introduced in this work to generate path curves on a freeform component. Then, two types of meander trajectories are generated by performing a different connection method. Additionally, this paper presents a research approach for introducing the heat transfer analysis into the trajectory planning process. Combining heat transfer analysis with trajectory planning overcomes the defects of traditional trajectory planning methods (e.g., local over-heating), which helps form the uniform temperature field by optimizing the time sequence of path curves. The influence of two different robot trajectories on the process of heat transfer is estimated by coupled FEM models which demonstrates the effectiveness of the presented optimization approach.

This paper is concerned with a robot trajectory optimization approach for thermal barrier coatings. As the requirements of high reproducibility of complex workpieces increase, an optimal thermal spraying trajectory should not only guarantee an accurate control of spray parameters defined by users (e.g., scanning speed, spray distance, scanning step, etc.) to achieve coating thickness homogeneity but also help to homogenize the heat transfer distribution on the coating surface. A mesh-based trajectory generation approach is introduced in this work to generate path curves on a freeform component. Then, two types of meander trajectories are generated by performing a different connection method. Additionally, this paper presents a research approach for introducing the heat transfer analysis into the trajectory planning process. Combining heat transfer analysis with trajectory planning overcomes the defects of traditional trajectory planning methods (e.g., local overheating), which helps form the uniform temperature field by optimizing the time sequence of path curves. The influence of two different robot trajectories on the process of heat transfer is estimated by coupled FEM models which demonstrates the effectiveness of the presented optimization approach.

The work considers and analyzes three main ways of forming trajectory of movement: coordinate trajectory and vector. The choice of description method depends on conditions of specific problem. The specificity of different type's movement of robots is analyzed: wheeled, tracked and walking. One of features in formation of movement trajectory in space with dynamic obstacles is speed. Thus, analysis of impacts is especially important for those robots that are able to achieve significant speeds and accelerations, as well as for robots characterized by large load capacity, while dynamic effects are associated with significant masses in structural elements. Today, there is no unified universal approach to constructing trajectories in environment with obstacles. The analysis showed that formation of rational trajectory taking into account: length and smoothness of trajectory; nature of workspace and map of area; safetydistance to obstacles; type of mobile platform (method of moving robot) will ensure correctness and conflict-free trajectory.

The Origins' Next Generation Space Telescope (NGST) trajectory design is addressed in light of improved methods for attaining constrained orbit parameters and their control at the exterior collinear libration point, L2. The use of a dynamical systems approach, state-space equations for initial libration orbit control, and optimization to achieve constrained orbit parameters are emphasized. The NGST trajectory design encompasses a direct transfer and orbit maintenance under a constant acceleration. A dynamical systems approach can be used to provide a biased orbit and stationkeeping maintenance method that incorporates the constraint of a single axis correction scheme.

In response to the current interest in CubeSats and potential applications for planetary exploration, this work studies the feasibility of using autonomous CubeSats to flyby near-Earth asteroids. Considering the limited performance of current propulsion systems for CubeSats, low-energy (impulsive and low-thrust) trajectories are designed to encounter near-Earth asteroids in the medium-fidelity Circular Restricted Three-Body Problem, and their existence in a high-fidelity ephemeris model is also verified. The use of large ground antennas for deep-space communications might represent a major portion of CubeSat mission budgets, and thus the feasibility of performing optical navigation to autonomously estimate and correct the trajectory of the CubeSat is also evaluated through Monte Carlo simulations. Preliminary results show that approximately 4 asteroids per year could be reached by a 3U CubeSat if deployed around the first or second Sun-Earth Lagrange points. According to the limited...

The expressions substituted for the costate differential equations are the same for the Earth-centered and Moon-centered coordinate frames with the states referenced to the respective frames. Since the trajectory terminates in circular orbits, Vr is zero at both ends. Also, as previously indicated, \g is zero in the two terminal circular orbits. Therefore, equations (C.5) and (C.9) determine the position costates and at both ends of the trajectory given the values u, it, v, and v in circular Earth orbit and circular lunar orbit.

increased service bandwidth. The Intelsat series of ABSTRACT satellites present a good example of these trends. 1 Solar Electric Propulsion (SEP) technology is currently Intelsat 1 and 2, launched during the late sixties, had being used for geostationary satellite station keeping to lifetimes under four years. Intelsats 4 and 5 had seven increase payload mass. Analyses show that advanced year design lifetimes. Intelsat 7 had full capacity design electric propulsion technologies can be used to obtain lifetime of ten years with propellant for 15 years. The additional increases in payload mass by using these same planned Intelsat 8/8A series lifetime is 14-18 years using technologies to perform part of the orbit transfer. In this N2H4 arcjets for station keeping. These results indicate a work three electric propulsion technologies are examined continuing trend toward longer lifetimes, thus a 15 year at two power levels for an Atlas IIAS class spacecraft, lifetime is assumed in these analyses. Satellite masses, The on-board chemical propulsion apogee engine fuel is and the launch vehicles to deliver them, have also gown. reduced in this analysis to allow the use of electric Early Intelsats were well under 1000 kg dry mass. The propulsion. A numerical optimizer is used to determine planned Intelsat 8/8A series will have a 1530kg dry mass. the chemical burns which will minimize the electric End-of-life (EOL) power levels have increased from propulsion transfer time. Results show that for a 1550 kg hundredsof watts for Intelsats 1 to 4, to over 5 kW for Atlas gAS class payload, increases in net mass Intelsat 7A. Intelsat 8/8A will use the Martin Marietta (geostationary satellite mass less wet propulsion system Astro Space Series 7000 which has a beginning of life mass) of 150 to 800 kg are possible using electric (BOL) power level over 7 kW. Finally, communication propulsion for station keeping, advancedchemical engines bandwidthson Intelsat spacecraft have increased from 50 for part of the transfer and electric propulsion for the MHz on Intelsat 1 to 2856 MHz on the planned Intelsat remainderof the transfer. Trip times are between one and 8/8A series. These continuing trends toward larger, more four months, capable, longer life and higher power spacecraft were used to select the spacecraft characteristics in this study. Higher INTRODUCTION power spacecraft permit expansion of the use of electric Solar Electric Propulsion (SEP) is already being used for propulsion systems beyond the already demonstrated station keeping of geostationary satellites, most notably station keeping function to encompass a portion of the hydrazine arcjets on AT&T's Telstar 4 and SPT-'100Hall orbit transfer mission. Successful implementation of thrusters on the Russian GALS spacecraft.1 The next step advanced propulsion systems will enable continued gowth in the development of electric propulsion systems is to use of geostationary satellite capability without requiring these types of thrusters to contribute to placing the growth in spacecraft mass or launch vehicle and will • spacecraft into geostationary orbit. For a given launch permit continued expansion of communicationscapability. vehicle, the fuel mass savings could then be directly used to increase the payload, for instance, the number of Studies by various authors have shown the net mass communication transponders. Even a small increase in benefits of using electric propulsion for transfer from mass might have large revenue impacts, various high Earth orbits2,3,Appendix in order to avoid the long trip times and Van Alien belt radiation damage of The current trend for geostationary spacecraft is towards low Earth orbit (LEO) to geostationary Earth orbit (GEO) longer lifetimes, increased masses, higher powers, and transfers using electric propulsion. 4,5 However, none of This paper is declared a work of the U.S. Government and 1 is not subject to copyright protection in the United States.

FY14 CIF/DIF Focus Areas (please check all that apply): __X__ 1) (CIF Only) High-level of inter-center collaboration __X__ 2) Significant use of Ames SpaceShop __X__ 3) Aligns with Flight Opportunities Program __X__ 4) Aligns with National Initiative ____ 5) (DIF only) Aligns with Center Core Research Areas Hypothesis to be tested (DIF Proposal Only): Proposal Approval: Proposers must inform their Branch and/or Division managers about their CIF/DIF proposals for concurrence on the strategic value, availability of labor resources, and proposal-development support. __X__ TI Branch manager has been informed of this proposal and concurs with its submission. TI Branch Manager name: Kalmanje S. Krishnakumar, Ph.D. __X__ TS Division manager has been informed of this proposal and concurs with its submission. TS Division Manager name: Dean Kontinos, Ph.D. __X__ RE Branch manager has been informed of this proposal and concurs with its submission. REE Branch Manager name: Kuok Ling A SECTION 2 2.1 Science/Technical Objectives: 2.1.1. Objectives: We propose to develop an active guidance and control (G&C) system for the ADEPT (Adaptable Deployable Entry and Placement Technology) entry vehicle for Aerocapture and Entry, Descent and Landing (EDL) missions with large payloads. This is a game changer and will allow extending the current investment beyond simple ballistic entry to accomplish lift guided entries, including Aerocapture at Venus, Mars and other destinations. The ADEPT concept utilizes a mechanically deployable aeroshell with a flexible carbon fabric, a multi-functional element that is drag generating decelerator and thermal protection system, for planetary entry. The goal of proposal, which has never been done, is to utilize ADEPT aeroshell as a controllable G&C effector through innovative aerosurface actuation concepts and real-time optimization based control methods for planetary entry maneuvers. 2.1.2 Current state-of-the-art: The Game Changing Technology program is currently supporting design, manufacture and ground-based verification of a full-scale, 6-m diameter, ADEPT vehicle suitable for ballistic unguided entry of a Venus lander. The low ballistic coefficient of the ADEPT vehicle configuration combined with mechanically articulated aeroshell is a game changer and the G&C aspects of the lift guided planetary entry have never been explored. 2.1.3 Technical challenges: The proposal addresses the three main areas of G&C technical challenges: 1) Venus aerocapture. The upper atmosphere density profile is not sufficiently characterized and this makes targeting to a planned orbit specially challenging. A real-time onboard optimal G&C algorithm and guided lift/drag modulation are required to manage the aerocapture trajectory. 2) Precision landing at Mars with hypersonic/supersonic entry and power descent. For ADEPT vehicle, since the aeroshell remains part of the landed system, additional dynamical complexity needs to be accounted for due to the motion of aeroshell, and the coupling between aeroshell motion and vehicle dynamics further complicates the G&C problem. The set of reachable states, including hazard/obstacle avoidance, via controllable aeroshell needs to be quantified. 3) Development of lift guided mechanisms for ADEPT aeroshell. Given the mission requirements/flight conditions, a viable and effective actuation mechanism to control the ADEPT aeroshell needs to be designed and analyzed. 2.1.4 Relevance of proposal: The proposed research aligns well with the three technical areas in the Space Technology Roadmaps, they are: TA09 Entry, Descent and Landing; TA04 Robotics and Autonomous Systems; and TA12 Materials, Mechanical Systems and Manufacturing. They have identified "sample return, autonomous G&C, deployable hypersonic decelerators" and "innovative, multifunctional, lightweight concepts" as game changing technologies for planetary entry missions. The proposal also addresses all of CIF Focus Areas: 1) The proposal leverages on existing collaboration with researchers of other centers and academia. Letters of support/advocacy from LaRC, GSFC, APL, and ADEPT Project Manager; please see Appendix B, indicated that the proposed G&C research complements to their efforts in Venus aerocapture mission and contributes significantly to the Advancement of Exploration Class Human Mars Missions. In particular, the EDL Principal Investigator Michelle Munk advocates that the product of proposed research

We introduce a new trajectory optimization method for robotic grasping based on a point-cloud representation of robots and task spaces. In our method, robots are represented by 3D points on their link surfaces. The task space of a robot is represented by a point cloud that can be obtained from depth sensors. Using the point-cloud representation, goal reaching in grasping can be formulated as point matching, while collision avoidance can be efficiently achieved by querying the signed distance values of the robot points in the signed distance field of the scene points. Consequently, a constrained nonlinear optimization problem is formulated to solve the joint motion and grasp planning problem. The advantage of our method is that the point-cloud representation is general to be used with any robot in any environment. We demonstrate the effectiveness of our method by performing experiments on a tabletop scene and a shelf scene for grasping with a Fetch mobile manipulator and a Franka Panda arm. 1 1 Code and videos for the project are available at https://irvlutd.github.io/GraspTrajOpt

This letter presents a novel optimization-based fullpose trajectory tracking method to control overactuated multirotor aerial vehicles with limited actuation abilities. The proposed method allocates feasible control inputs to track a reference trajectory, while ensuring the tracking of the reference position, and while tracking the closest feasible attitude. The optimization simultaneously searches for a feasible trajectory and corresponding feasible control inputs from the infinite possible solutions, while ensuring smooth control inputs. The proposed real-time algorithm is tested in extensive simulation on multiple platforms with fixed and actuated propellers. The simulation experiments show the ability of the proposed approach to exploit the complex set of feasible forces and moments of overactuated platforms while allocating smooth feasible control inputs.

Rehabilitation of post stroke patients with upper extremity motor deficits is typically focused on relearning of motor abilities and functionalities requiring interaction with physiotherapists and/or rehabilitation robots. In a point-to-point movement training, the trajectories are usually arbitrarily determined without considering the motor impairment of the individual. In this paper, we used an optimal control model based on arm dynamics enabling also incorporation of muscle functioning constraints (i.e. simulation of muscle tightness) to find the optimal trajectories for planar arm reaching movements. First, we tested ability of the minimum joint torque cost function to replicate the trajectories obtained in previously published experimental trials done by neurologically intact subjects, and second, we predicted the optimal trajectories when muscle constraints were modeled. The resulting optimal trajectories show considerable similarity as compared to the experimental data, while on the other hand, the muscle constraints play a major role in determination of the optimal trajectories for stroke rehabilitation.

This paper discusses and presents an overview of the proportional navigation (PN) guidance law as well as the differential geometry (DG) guidance algorithm that are used to develop the intercept course of a certain target. The intent of this study is to illustrate the advantages of the guidance algorithm generated based on the concepts of differential geometry against the well-known PN guidance law. The basic principles behind the both algorithms are mentioned. Moreover, the different versions of the PN approach is briefly clarified to show the essential improvement from one version to the other. The paper terminated with numerous two-dimension simulation figures to give a great value of visual aids, illustrating the significant relations and main features and properties of both algorithms.

Part of the challenge of charting a human exploration space architecture is finding locations to stage missions to multiple destinations. To that end, a specific subset of Earth-Moon halo orbits, known as Near Rectilinear Halo Orbits (NRHOs) are evaluated. In this paper, a systematic process for generating full ephemeris based ballistic NRHOs is outlined, different size NRHOs are examined for their favorability to avoid eclipses, the performance requirements for missions to and from NRHOs are calculated, and disposal options are evaluated. Combined, these studies confirm the feasibility of cislunar NRHOs to enable human exploration in the cislunar proving ground.

This article presents a detailed examination of projectile motion, exploring its various types and their fundamental role within the broader framework of classical mechanics. Projectile motion, characterized by the curved trajectories of objects under the influence of gravity, is a fundamental concept in classical mechanics and objects in free flight. This study delves into both human-propelled and mechanically-launched projectiles—such as thrown objects, arrows, bullets, and artillery shells—exploring how kinematic equations, air resistance, and gravitational forces govern their behavior. By integrating the analysis of motion with key theoretical physics principles, including energy conservation, Newton’s laws, and the influence of external forces, this article highlights the interdependence of projectile motion with notable physics problems. The discussion extends to the applications of these principles in diverse fields such as engineering, military technology, and sports, offering a holistic view of how the theoretical framework of physics guides real-world problem-solving. This comprehensive examination illustrates the broad relevance of projectile motion in both academic and practical contexts, positioning it as a cornerstone for understanding complex systems in physics.

This paper introduces a novel trajectory generation and optimization algorithm (TGO) that enables agile and aggressive flight of quadrotor UAVs while considering various constraints associated with robot dynamics, actuator inputs, and flight environment. The TGO algorithm employs time-parametrized polynomial trajectories based on a predetermined sequence of waypoints to produce dynamically feasible and collision-free trajectories. This approach extends previous work that utilized differential flatness property and polynomial based trajectories by eliminating the need for iterative searching and computationally intensive sampling. One of the significant advantages of the TGO algorithm is its numerical stability for large number of waypoints and highorder polynomials. To address the ill-conditioned problem of Quadratic Programming (QP) based methods, the TGO algorithm reformulates the trajectory generation and optimization problem into an unconstrained quadratic programming (UCP) using the numerically stable null-space factorization method. The TGO algorithm produces minimum derivative trajectories and minimum waypoints arrival times, generating a wide range of aggressive trajectories that can leverage the full maneuvering capabilities of quadrotor robots. The proposed algorithm's numerical stability and computational advantages are demonstrated through various scenarios and comparisons. An animated simulation of the TGO algorithm is available at: https://youtu.be/MvvhBG14iIg.

This paper presents the preliminary design of the descent and landing trajectory and guidance algorithms of the ESA Argonaut lunar lander. The mission scenario and driving system constraints are presented and accounted for in the design of a fuel-optimal trajectory that includes divert capabilities, as required to achieve a safe landing. A sub-optimal descent and landing trajectory is then presented and computed from the optimal one, and the related onboard guidance algorithms are derived. The proposed end-to-end guidance solution represents an easily implementable alternative to on-board optimization, minimizing the verification & validation effort, computational footprint, and programmatic risk in the development of the related GN&C capabilities. A dedicated off-line optimization process is also outlined, and exploited to optimize the propellant consumption of the sub-optimal trajectory and to ensure the fulfilment of system constraints despite the use of simple algorithms on-board. The sub-optimal trajectory is compared to the optimal baseline, and conclusions are drawn on the applicability of the proposed approach to the Argonaut mission.

This paper focuses on the time integration of the nonlinear EOM associated with a very flexible aircraft in flight. Various integration methods exist for linear structural dynamics problems. However, a review of the literature indicates little material associated with the integration of nonlinear structural EOM of relatively large order. Moreover, for the problem of simulation of very flexible aircraft, a combination of flight dynamics and aeroelastic degrees of freedom must be solved. A modified first and second order Generalized-α Method along with an implicit sub-iteration scheme were developed. It has shown good agreement with predictor/corrector integration schemes for a reduced set of linear EOM. The method is also seen to be numerically stable when compared to non-dissipative time marching integration schemes and requires less computational time compared to predictor/corrector methods for the full set of nonlinear EOM. Recent advances in airborne sensors and communication pac...

A predictive control scheme for a permanent-magnet synchronous machine (PMSM) is presented. It is based on a suboptimal method for computationally efficient trajectory generation based on continuous parameterization and linear programming. The torque controller optimizes a quadratic cost consisting of control error and machine losses in real-time respecting voltage and current limitations. The multivariable controller decouples the two current components and exploits cross-coupling effects in the long-range constrained predictive control strategy. The optimization results in fast and smooth torque dynamics while inherently using field-weakening to improve the power efficiency and the current dynamics in high speed operation. The performance of the scheme is demonstrated by experimental results.