Real-time trajectory generation for differentially flat systems

Flight management systems have greatly reduced cockpit workloads, but are not capable of calculating new flight plans in real time when flight characteristics vary or when flight trajectories become nonstationary. This paper presents a real-time flight trajectory generator (R-FTG) applicable to emergency landing approaches. First, the R-FTG calculates a preliminary flight path, which consists of an initial turn, a straight-line flight, and a terminal turn. The R-FTG then optimizes the preliminary flight path by using a direct collocation method. In order to give the direct collocation method real-time performance, an idea called stage division is incorporated. Combining the direct collocation and stage division enables real-time generation of near optimal flight trajectories. Additionally, wind effects are considered in the generating process. The R-FTG is evaluated by numerical simulations; calculation results of the R-FTG are compared with those of an offline optimization method, and the calculation results under different bank angle constraints are examined. The calculations for the wind effects are also studied. These results show the effectiveness of the proposed real-time flight trajectory generator.

Real-time adaptive entry trajectory generation with modular policy and deep reinforcement learning

This paper presents a systematic method for generating optimal helicopter flight trajectories in real time for cockpit display. Helicopter flights in the event of a single engine failure are critical, and display of optimal flight paths on-board is desirable. Due to the large number of states and constraints, however, numerical solutions on a mainframe computer can take a long tune. In this paper, optimal solutions are first obtained off-line using a ground computer. For a given set of initial helicopter states and flight parameters, optimal solutions are fitted by a Fourier series. The coefficients of the Fourier approximations are then interpolated as functions of initial flight states and parameters. The approximate optimal trajectories can be quickly generated on-board using the proposed method. Introduction Engine failure is a major safety issue for all helicopters, especially during takeoff and landing operations. Due to the complexity of the situation and the dependence of safety on many parameters, optimal flight trajectories can provide useful guidance for pilot operation. In particular, on-board display of optimal trajectories is desirable. This paper presents a method for generating optimal flight trajectories in real-tune that can be used for on-board display. Depending on its capability and performance during an engine failure, a transport helicopter can be certified as Category A or Category B. The Federal Aviation Administration (FAA) grants Category B certification to a single or multi-engine helicopter with gross weight less than 20,000 Ib and capable of landing safely in case of one or all engine failures. Category A certification, on the other hand, is granted to multi-engine helicopters with independent engine systems. Category A helicopters must be able to either land safely or continue flight in case of One Engine Inoperation (OEI). This makes Category A helicopters uniquely suited for remote places where emergency landing sites are not available. I Ph.D. Candidate, Center for Control Sciences, Member AIAA * Assistant Professor, Dept. of Aerospace Eng. and Mechanics, Member AIAA + Civil Rotorcraft Group Leader, Rotorcraft and Powered Lift Branch The decision to continue the flight or to land represents an energy management problem. It has been shown''' that this decision depends on initial conditions at the time of failure as well as flight parameters. Due to the numerous initial variables involved in this decision, a method to communicate all this information to the pilot instantaneously, at engine failure, is needed. This method must keep the emergency procedure simple and manageable. In particular, on-board cockpit display of optimal flight trajectories is useful. This requires a reliable real-tune solution of optimal trajectories, on board, with limited time, limited computing power, and limited memory available. If possible, an analytical solution of optimal trajectories is desirable. Unfortunately, this can only be achieved for systems of low order and where the equations of motion and the cost function are simple. Therefore, for a complex system, an open-loop numerical procedure becomes necessary. Research efforts were made to solve optimal control problems in real-time. Schultz et al. used calculus of variation and energy state method to generate optimal trajectories on-board for the National Aerospace Plane (NASP). In his study, the equations of motion of the NASP are less complex than those of the helicopter, and an interval of time of few minutes is allowed. Bryson used neighboring control theory to generate near-optimal solutions that could be used in real-time. This method is elegant but requires a large amount of memory to store the needed perturbation matrices. Also, it is valid on a relatively small neighborhood of the nominal trajectory. Perturbation methods and table lookups are often used if only few parameters are involved. In the current problem, the equations of motion of the helicopter are complex and too many path equality and inequality constraints are present. Also, limitations on tune, computing power, and memory available make all the above methods unsuitable for this problem. This paper proposes a technique of real-time optimal trajectory generation based on approximation and

This thesis will present various methods of trajectory generation for various types of mobile robots. Then it will progress to evaluating Robot Operating Systems (ROS’s) that can be used to control and simulate mobile robots, and it will explain why Player/Stage was chosen as the ROS for this thesis. It will then discuss Nonlinear Trajectory Generation as the main method for producing a path for mobile robots with dynamic and kinematic constraints. Finally, it will combine Player, Stage, and NTG into a system that produces a trajectory in real-time for a mobile robot and simulates a differential drive robot being driven from the initial state to the goal state in the presence of obstacles. Experiments will include the following: Blobfinding for physical and simulated camera systems, position control of physical and simulated differential drive robots, wall following using simulated range sensors, trajectory generation for omnidirectional and differential drive robots, and a combination of blobfinding, position control, and trajectory generation. Each experiment was a success, to varying degrees. The culmination of the thesis will present a real-time trajectory generation and position control method for a differential drive robot in the presence of obstacles.

Guidance algorithms for the return flight of suborbital spaceplanes must generate a variety of guidance trajectories that satisfy terminal conditions even in unexpected abort operations. To tackle this issue, a trajectory optimization method that combines convex quadratic programming and a global derivative-free optimization technique in a nested structure has been recently studied by the authors. This hybrid method efficiently explores the three-dimensional Bezier trajectories and associated guidance commands that exactly fulfill the equality terminal conditions and command continuity. In this paper, Monte-Carlo simulations are performed to investigate the applicability of this guidance method to the realistic scenario of unpowered return flight. Six stochastic evolutionary algorithms, a Bayesian optimization method, and three deterministic search algorithms are implemented and tested as global optimizers. They are compared in terms of computational and implementational complexities, robustness, and diversity of solutions obtained. The results show that reliable and real-time trajectory generation is possible, when an optimizer and its settings are properly chosen. It also reveals that diverse trajectories between initial and terminal conditions are successfully generated.KeywordsGuidanceTrajectory optimizationGlobal optimizationReal-time optimizationSuborbital spaceplane

Real-time dynamic optimization of nonlinear systems: A flatness-based approach

In this note, an extremum-seeking controller is developed to steer a periodic system to orbits that maximize a functional of interest for a class of differentially flat nonlinear systems. The problem is posed as a real-time optimal trajectory generation problem in which the optimal orbit is computed using an extremum-seeking approach. Using the flatness property of the dynamics, the original dynamic optimization problem is transformed to a parameterized optimization problem which can be solved in real-time to approximate the optimal orbit. The control algorithm provides tracking of the optimal orbit. A drug delivery control problem is considered to demonstrate the application of the technique.

Real-Time Four-Dimensional Trajectory Generation Based on Gain-Scheduling Control and a High-Fidelity Aircraft Model

Real-Time Optimal Trajectory Generation for UAV to Rendezvous with an Aerial Orbit

Unmanned aerial vehicles (UAVs), equipped with navigation systems and video capability, are currently being deployed for intelligence, reconnaissance and surveillance mission. In this paper, we present a systematic approach for the generation of UAV trajectory using a video image matching system based on SURF (Speeded up Robust Feature) and Preemptive RANSAC (Random Sample Consensus). Video image matching to find matching points is one of the most important steps for the accurate generation of UAV trajectory (sequence of poses in 3D space). We used the SURF algorithm to find the matching points between video image sequences, and removed mismatching by using the Preemptive RANSAC which divides all matching points to outliers and inliers. The inliers are only used to determine the epipolar geometry for estimating the relative pose (rotation and translation) between image sequences. Experimental results from simulated video image sequences showed that our approach has a good potential to be applied to the automatic geo-localization of the UAVs system

Maritime transportation is vital to the global economy. With the increased operating and labor costs of maritime transportation, autonomous shipping has attracted much attention in both industry and academia. Autonomous shipping can not only reduce the marine accidents caused by human factors but also save labor costs. Path planning is one of the key technologies to enable the autonomy of ships. However, mainstream ship path planning focuses on searching for the shortest path and controlling the vehicle in order to track it. Such path planning methods may lead to a dynamically infeasible trajectory that fails to avoid obstacles or reduces fuel efficiency. This paper presents a data-driven, efficient, and safe path planning (ESP) method that considers ship dynamics to provide a real-time optimal trajectory generation. The optimization objectives include fuel consumption and trajectory smoothness. Furthermore, ESP is capable of fast replanning when encountering obstacles. ESP consists of three components: (1) A path search method that finds an optimal search path with the minimum number of sharp turns from the geographic data collected by the geographic information system (GIS); (2) a minimum-snap trajectory optimization formulation with dynamic ship constraints to provide a smooth and collision-free trajectory with minimal fuel consumption; (3) a local trajectory replanner based on B-spline to avoid unexpected obstacles in real time. We evaluate the performance of ESP by data-driven simulations. The geographical data have been collected and updated from GIS. The results show that ESP can plan a global trajectory with safety, minimal turning points, and minimal fuel consumption based on the maritime information provided by nautical charts. With the long-range perception of onboard radars, the ship can avoid unexpected obstacles in real time on the planned global course.

This paper presents a novel real-time quasi-optimal trajectory generator, based on the inverse dynamics in the virtual domain (IDVD) method, to produce a reliable and efficient guidance system for autonomous underwater vehicle (AUV) docking operations. To this end, a challenging docking scenario is defined in a cluttered operating field, encompassing ocean currents and no-fly zones. Using the IDVD method, a trajectory that takes into consideration the hydrodynamic model of the vehicle is generated and the optimality of this trajectory, in regards to mission time and energy expenditure of the vehicle, is considered. Computer simulations demonstrate that the IDVD-based strategy enables the guiding of a vehicle into the dock by satisfying the final boundary conditions of the dock's position and orientation. Generated trajectories are feasible, smooth and realizable using for the vehicle's low-level auto-pilot module. In terms of computation, the solution is suitable for real-time implementation that incorporates uncertainty handling of the operating environment. For further analysis, the generated trajectory is evaluated on a high fidelity AUV simulator. The result of this latter test also demonstrates applicability of the utilized IDVD method for optimization of docking trajectories.

Multi-robot collaboration and marine robotics constitute key research directions in intelligent autonomous systems. In this context, multi-ROV cooperative operations are increasingly deployed for sunken ship search missions. A central technical challenge in such applications is to ensure efficient, non-redundant coverage while maintaining accurate formation tracking. This scenario confronts two principal difficulties. First, overlapping operational regions among multiple ROVs tend to produce both redundant coverage and search blind zones. Second, trajectory tracking accuracy is significantly degraded by the combined effects of hydrodynamic disturbances and inherent actuator constraints in ROVs. To address these challenges, an improved dynamic window approach (DWA), incorporating a search distance penalty mechanism, is proposed for multi-ROV trajectory planning. Concurrently, a cascaded tracking control architecture is constructed, wherein a model predictive kinematic controller generates constrained velocity references, while an adaptive sliding mode dynamic controller augmented with an extended state observer provides robust disturbance rejection. Collaborative search is conducted using a three-ROV leader–follower formation. Simulation results indicate that regional search coverage is effectively improved and areas of repeated detection are significantly reduced by the proposed planning algorithm. Real-time trajectory tracking is achieved by the designed controller under two typical extreme strong disturbance conditions, namely, time-varying disturbances and abrupt disturbances, on the premise of satisfying thruster thrust constraints. The proposed scheme enables all three ROVs to successfully complete the tracking task under time-varying disturbances while reducing the frequency of thrust saturation events by up to seven times. In contrast, under the conventional MPC–ASMC controller, one ROV deviates from the formation and fails to complete the tracking task. Under abrupt disturbances, the proposed approach reduces the trajectory tracking error by up to six times and decreases the frequency of thrust saturation events by up to four times.

<div>In this dissertation, methods for real-time trajectory generation and autonomous obstacle avoidance for fixed-wing and quad-rotor unmanned aerial vehicles (UAV) are studied. A key challenge for such trajectory generation is the high computation time required to plan a new path to safely maneuver around obstacles instantaneously. Therefore, methods for rapid generation of obstacle avoidance trajectory are explored. The high computation time is a result of the computationally intensive algorithms used to generate trajectories for real-time object avoidance. Recent studies have shown that custom solvers have been developed that are able to solve the problem with a lower computation time however these designs are limited to small sized problems or are proprietary. Additionally, for a swarm problem, which is an area of high interest, as the number of agents increases the problem size increases and in turn creates further computational challenges. A solution to these challenges will allow for UAVs to be used in autonomous missions robust to environmental uncertainties.</div><div><br></div><div>In this study, a trajectory generation problem posed as an optimal control problem is solved using a sequential convex programming approach; a nonlinear programming algorithm, for which custom solver is used. First, a method for feasible trajectory generation for fast-paced obstacle-rich environments is presented for the case of fixed-wing UAVs. Next, a problem of trajectory generation for fixed-wing and quad-rotor UAVs is defined such that starting from an initial state a UAV moves forward along the direction of flight while avoiding obstacles and remaining close to a reference path. The problem is solved within the framework of finite-horizon model predictive control. Finally, the problem of trajectory generation is extended to a swarm of quad-rotors where each UAV in a swarm has a reference path to fly along. Utilizing a centralized approach, a swarm scenario with moving targets is studied in two different cases in an attempt to lower the solution time; the first, solve the entire swarm problem at once, and the second, solve iteratively for a UAV in the swarm while considering trajectories of other UAVs as fixed.</div><div><br></div><div>Results show that a feasible trajectory for a fixed-wing UAV can be obtained within tens of milliseconds. Moreover, the obtained feasible trajectories can be used as initial guesses to the optimal solvers to speed up the solution of optimal trajectories. The methods explored demonstrated the ability for rapid feasible trajectory generation allowing for safe obstacle avoidance, which may be used in the case an optimal trajectory solution is not available. A comparative study between a dynamic and a kinematic model shows that the dynamic model provides better trajectories including aggressive trajectories around obstacles compared to the kinematic counterpart for fixed-wing UAVs, despite having approximately the same computational demands. Whereas, for the case of quad-rotor UAVs, the kinematic model takes almost half the solution time than with a reduced dynamic model, despite having approximately the similar range of values for the cost function. When extended to a swarm, solving the problem for each UAV is four to seven times computationally cheaper than solving the swarm as a whole. With the improved computation time for trajectory generation for a swarm of quad-rotors using centralized approach, the problem is now reasonably scalable, which opens up the possibility to increase the number of agents in a swarm using high-end computing machines for real-time applications. Overall, a custom solver jointly with a sequential convex programming approach solves an optimization problem in a low computation time.</div>

The problem of real-time trajectory generation in the decentralized control of a manipulator is considered. The trajectory generator presented is based on a vector-integration-to-endpoint (VITE) model of neural dynamics in planned human arm movements. In contrast to approaches which require the stipulation of the desired individual joint positions, the trajectory generator operates with desired coordinates of the end effector and generates the individual joint driving functions in real time, using geometric constraints which characterize the manipulator. The resulting manipulator trajectory exhibited VITE model characteristics including synchronous joint operation. An illustrative two-joint manipulator example is given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>