Optimal Trajectory Planning for Rotorcraft With Underslung Payload

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

In the past few years, an important increase in the small satellites market has been noticed by the space community. Following this boost on the small satellites business, the need for dedicated launch services arises and designing an efficient and competitive small launcher is a challenge. Together with an innovative design for a small launcher comes the need for the optimization of the trajectory. A trajectory optimization approach has a lot to bring in terms of launcher performances such as achievable payload mass or a higher altitude of the target orbit. This paper is focused on an in-house 3 degree-of-freedom (3DOF) tool for trajectory computation and optimization using a genetic algorithm approach. The cost function is built in such a way to maximize the payload mass of the launcher while achieving the target orbit. The tool is also used for performing sensitivity analyses considering structural mass uncertainties, that can play an important role in the design phase of the vehicle, in order to check their impact on the launcher's performances.

A method for determining optimal trajectories for tethered systems is presented based on a parameterization of the tension control input. Three separate models of the tether system are used to compare the effects of different cost functions on optimal trajectories. The parameterization of the control is based on a rigid tether model, while the optimal trajectories are determined using a model that discretizes the tether into 4 point masses connected by massless inextensible strings. The effect of various cost functions and terminal times are compared for deployment and retrieval. The effect of various cost functions are also studied for a tether-assisted sample return problem. It is shown that a cost function that minimizes the tether reel acceleration maintains the tether essentially straight when simulated in a fully flexible model of the system, whereas several other cost functions result in significant bending of the tether.

The authors present research results on a method to perform waypoint rendezvous in conjunction with multiple-threat avoidance with the horizontal plane trajectory optimization algorithm. A 737-300 aircraft performance model was used to study trajectory optimization with SP/HTO (singular perturbation/horizontal trajectory optimization). The cost function used by J.L. Vian and J.R. Moore (1989) was modified to include the cost of line-of-sight angle to the destination in order to generate more flyable trajectories through regions of multiple threat envelopes. Results are presented for several scenarios in which there are multiple threats and rendezvous points. The surface-to-air threat effectiveness envelope developed and used in these mission scenarios to generate optimal trajectories is discussed. It is shown that the addition of a cost of line-of-sight angle to the destination avoids a tendency of the trajectory to immediately return to the x-axis when no threats are present in the direct path to the target; instead the trajectory leads directly to the target and is a more desirable solution. The local approach to trajectory optimization is shown to be useful in short-range scenarios or in cases where there may be pop-up threats. >

Spoke pulses improve excitation homogeneity in parallel-transmit MRI. We propose an efficient global optimization algorithm, Bayesian optimization of gradient trajectory (BOGAT), for single-slice and simultaneous multislice imaging. BOGAT adds an outer loop to optimize kT-space positions. For each position, the RF coefficients are optimized (e.g., with magnitude least squares) and the cost function evaluated. Bayesian optimization progressively estimates the cost function. It automatically chooses the kT-space positions to sample, to achieve fast convergence, often coming close to the globally optimal spoke positions. We investigated the typical features of spokes cost functions by a grid search with field maps comprising 85 slabs from 14 volunteers. We tested BOGAT in this database, and prospectively in a phantom and in vivo. We compared the vendor-provided Fourier transform approach with the same magnitude least squares RF optimizer. The cost function is nonconvex and seen empirically to be piecewise smooth with discontinuities where the underlying RF optimum changes sharply. BOGAT converged to within 10% of the global minimum cost within 30 iterations in 93% of slices in our database. BOGAT achieved up to 56% lower flip angle RMS error (RMSE) or 55% lower pulse energy in phantoms versus the Fourier transform approach, and up to 30% lower RMSE and 29% lower energy in vivo with 7.8 s extra computation. BOGAT efficiently estimated near-global optimum spoke positions for the two-spoke tests, reducing flip-angle RMSE and/or pulse energy in a computation time (˜10 s), which is suitable for online optimization.

This dissertation advances the field of autonomous vehicle motion planning in various challenging environments, ranging from flows and planetary atmospheres to cluttered real-world scenarios. By addressing the challenge of navigating environmental flows, this work introduces the Flow-Aware Fast Marching Tree algorithm (FlowFMT*). This algorithm optimizes motion planning for unmanned vehicles, such as UAVs and AUVs, navigating in tridimensional static flows. By considering reachability constraints caused by vehicle and flow dynamics, flow-aware neighborhood sets are found and used to reduce the number of calls to the cost function. The method computes feasible and optimal trajectories from start to goal in challenging environments that may contain obstacles or prohibited regions (e.g., no-fly zones). The method is extended to generate a vector field-based policy that optimally guides the vehicle to a given goal. Numerical comparisons with state-of-the-art control solvers demonstrate the method's simplicity and accuracy. In this dissertation, the proposed sampling-based approach is used to compute trajectories for an autonomous semi-buoyant solar-powered airship in the challenging Venusian atmosphere, which is characterized by super-rotation winds. A cost function that incorporates the energetic balance of the airship is proposed to find energy-efficient trajectories. This cost function combines the main forces acting on the vehicle: weight, buoyancy, aerodynamic lift and drag, and thrust. The FlowFMT* method is also extended to consider the possibility of battery depletion due to thrust or battery charging due to solar energy and tested in this Venus atmosphere scenario. Simulations showcase how the airship selects high-altitude paths to minimize energy consumption and maximize battery recharge. They also show the airship sinking down and drifting with the wind at the altitudes where it is fully buoyant. For terrestrial applications, this dissertation finally introduces the Sensor-Space Lattice (SSLAT) motion planner, a real-time obstacle avoidance algorithm for autonomous vehicles and mobile robots equipped with planar range finders. This planner uses a lattice to tessellate the area covered by the sensor and to rapidly compute collision-free paths in the robot surroundings by optimizing a cost function. The cost function guides the vehicle to follow an artificial vector field that encodes the desired vehicle path. This planner is evaluated in challenging, cluttered static environments, such as warehouses and forests, and in the presence of moving obstacles, both in simulations and real experiments. Our results show that our algorithm performs collision checking and path planning faster than baseline methods. Since the method can have sequential or parallel implementations,

Trajectory optimization for lunar rover performing vertical takeoff vertical landing maneuvers in the presence of terrain

This paper investigates dynamic modeling, trajectory optimization, and control of a flexible kiteplane used for wind energy harvesting. The individual components of the kiteplane, including flexible wings and a rigid fuselage, are modeled separately and then constrained together using the null-space method. The flexible wings of the kiteplane are modeled as flexible plates, and the Rayleigh–Ritz method is used to discretize the partial differential equation that describes the strain energy stored in the wing. The attitude of the kiteplane is described by the direction cosine matrix (DCM) directly and a proportional-integral-derivative control law that makes use of the DCM is implemented for attitude control. An unsteady aerodynamic model based on Theodorsen’s lift model is used in simulation to allow for an accurate model under transient conditions. An optimal trajectory is found using a simplified dynamic model and solving a finite-dimensional constrained optimization problem. Numerical simulations of the optimal trajectories are performed to demonstrate the kiteplane’s energy-harvesting capability.

State-of-charge-constraint-based energy management strategy of plug-in hybrid electric vehicle with bus route

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

Learning-based spacecraft multi-constraint rapid trajectory planning for emergency collision avoidance

Despite their well-known advantages in terms of higher intrinsic rigidity, larger payload-to-weight ratio, and higher velocity and acceleration capacities, parallel robots have drawbacks. Among them, the most important one is surely the presence of singularities in the workspace, which divide the workspace into different aspects (each aspect corresponding to one or more assembly modes) and near which the performance is considerably reduced. In order to increase the reachable workspace of parallel robots, a promising solution consists in the definition of optimal trajectories passing through the singularities to change either the leg working modes or the robot assembly modes. Previous works on the field have shown that it is possible to define optimal trajectories that allow the passing through the robot type 2 singularities. Such trajectories must respect a physical criterion that can be obtained through the analysis of the degeneracy conditions of the parallel robot inverse dynamic model. However, the mentioned works were not complete: they lacked a degeneracy condition of the parallel robot inverse dynamic model, which is not due to type 2 singularity anymore, but to a serial singularity. Crossing a serial singularity is appealing as in that case we can change the robot leg working mode and then potentially access to other workspace zones. This absence is due to the fact that the authors used a reduced dynamic model, which was not taking into account all link dynamic parameters. The present paper aims to fill this gap by providing a complete study of the degeneracy conditions of the parallel robot dynamic model and by demonstrating that it is possible to cross the type 2, but also serial singularity, by defining trajectories that respect some given criteria obtained from the analysis of the degeneracy of the robot dynamic model. It also aims to demonstrate that the serial singularities have impacts on the robot effort transmission, which is a point that is usually bypassed in the literature. All theoretical developments are validated through simulations and experiments.

Solar-powered Unmanned Aerial Vehicles (SUAV) designed for Low-Altitude Long-Endurance (LALE) applications provide potential multi-day continuous flight capability, but are generally prone to local meteorological impediments such as rain, strong winds or reduced solar irradiance. This paper therefore presents METPASS, the Meteorology-aware Trajectory Planning and Analysis Software for Solar-powered UAVs. METPASS optimizes large-scale solar-powered UAV missions using a detailed consideration of meteorological effects: An optimal trajectory is found on a 3-D grid for given departure and arrival points by applying a Dynamic Programming approach and a cost function that considers environmental hazards, winds, solar radiation, aircraft parameters and flight time. The cost function is evaluated based on a kinematic and energetic UAV system model and forecast data from the European Centre for Medium-Range Weather Forecasts (ECMWF). The trajectory-planning environment is applied to an envisioned fully autonomous and solar-powered crossing of the North Atlantic Ocean by AtlantikSolar, a 5.6m-wingspan SUAV developed at ETH Zurich. Results based on historical ECMWF weather data from 2012 and 2013 show that properly pre-optimized routes allow the Atlantic crossing even in case of significant global cloud coverage and that optimal routes can reduce the required flight time by up to 50% (from 106h to 52h) by exploiting wind conditions.

Trajectory optimization for lunar soft landing with a Hamiltonian-based adaptive mesh refinement strategy

The global warming and the environmental destruction are caused from the mass consumption of energy in a factory in which robotic manipulators are used. It is necessary to take the trajectory planning into considerations in order to save the consumption energy of the manipulator controlled with Point-to-Point (PTP) motion. An optimal trajectory that minimizes the consumption energy can be obtained by solving a two-point boundary value problem. The optimal trajectory can be analyzed easily if the system is linear. However, the dynamical equation of the multi-link manipulator with Coulomb friction has a strong non-linearity. Then the Genetic Algorithm (GA) is applied to obtain the solution of two-point boundary value problem with the strong non-linearity. The GA is the method for searching discrete solution space by genes. However, the trajectory function is continuous with respect to time. In this paper, the coefficients of the approximation functions are determined as the gene’s phenotype. This method has disadvantages that are long computation time and increase the possibility of lapsing into the local optimal solution. So, a new method is proposed in order to shorten the computation time and to lessen the possibility of lapsing into the local optimal solution. It is seen from application to the minimization of the consumption energy of a manipulator with Coulomb friction that a proposed method is effective.