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Michael Acheson

Publications and source records attributed to Michael Acheson.

11 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2023

On Hermite Interpolation using Bernstein Polynomials for Trajectory Generation

This work presents a solution to the two-point Hermite interpolation problem using Bernstein polynomials. The Hermite interpolation problem is of particular interest in aerospace applications where boundary conditions for trajectories often specify derivative constraints. In the examples shown, a trajectory will be generated between an initial condition and a final condition. For example, a trajectory is generated that connects an aircraft’s current position and velocity with a point on the runway at a desired landing velocity. The numerical stability of the proposed algorithms is analyzed empirically.

Bezier curves↗
NASA NTRSDate not supplied

An L1 Adaptive Control Augmentation for a Lift Plus-Cruise Vehicle

This paper presents anL1adaptive control augmentation for a Lift-Plus-Cruise (L+C)vehicle. This class of vehicles operates in three flight modes with different dynamic behavior: vertical, transition, and forward flight. A robust uniform controller is used as a baseline to stabilize the system throughout these flight modes. The uniform controller is a linear control law designed around trim conditions of the aircraft and includes control allocation to achieve the desired forces and moments on the vehicle. TheL1control augmentation is designed for each of these trim conditions to compensate for the nonlinear time- and state-dependent uncertainties in the vehicle dynamics. The augmented control output is then added to the desired force and moment commands on the vehicle. Simulation results demonstrate the effectiveness of control augmentation for reducing the effects of unmodeled dynamics, reduced actuator effectiveness, and time-dependent disturbances. Effectiveness is demonstrated through tracking error metrics.

Andrew Patterson↗
NASA NTRSDate not supplied

Modified Cascading Generalized Inverse Control Allocation

The current aviation revolution towards electric propulsion aircraft (e.g., electric vertical takeoff-and-landing) brings unique control challenges. These vehicles are typically over-actuated (more effectors than desired control outcomes), may require control strategies for the three phases of flight (hover, transition and cruise), and currently have limited electric power availability. These vehicle challenges bring the need for optimal control allocation to the forefront of research. A leading control allocation algorithm, used in current flight vehicles, is the Cascading Generalized Inverse (CGI). Unfortunately, the Cascading Generalized Inverse algorithm is unable to achieve some desired outcomes, it intermittently provides non-optimal allocations, and it may fail to preserve moment direction near maximal achievable outcomes. In this research, the shortcomings of the Cascading Generalized Inverse algorithm are addressed by augmenting the algorithm with Scalar Difference Quadratic unsaturation identification and location at each iteration. Rigorous theory is shown that the Modified Cascading Generalized Inverse performs better at obtaining optimal allocations for all attainable outcomes. Numerical case studies for over-actuated vehicles demonstrate resolution to the aforementioned deficiencies.

Control Allocation↗
NASA NTRSDate not supplied

Adaptive Optimization for System Performance and Combined Bernstein Polynomial, Optimal Reciprocal Collision Avoidance, Differential Dynamic Programming for Trajectory Replanning and Collision Avoidance for UAM Vehicles

The emerging urban air mobility (UAM) sector in aerospace is driving development of unconventional multi-modal vehicle configurations and autonomous flight. The combination of multi-modal vehicle dynamics, complex environment, requirements to deal with flight contingencies in an efficient and safe manner, as well as necessity for precise trajectory following and performance, are the driving influence behind adaptive optimization for system performance. We are interested in trajectory optimization algorithm that would system parameter estimation and identifying the optimal switching time between modes of hybrid dynamical systems. This presentation discusses a parameterized optimal control trajectory optimization algorithm that is an extended and generalized version of Differential Dynamic Programming (DDP), titled Parameterized Differential Dynamic Programming (PDDP). DDP is an efficient trajectory optimization algorithm relying on second order approximations of a system’s dynamics and cost function and has recently been applied to optimize systems with time invariant parameters. Experiments are presented applying PDDP to solve model predictive control (MPC) and moving horizon estimation (MHE) tasks simultaneously. In particular, PDDP is used to determine the optimal transition point between flight regimes of a complex urban air mobility (UAM) class vehicle exhibiting multiple phases of flight and to identify and compensate for actuation faults.

optimization↗
NASA NTRSDate not supplied

Reference Command Optimization for the Transition Flight Mode of a Lift plus Cruise Vehicle

Advanced air mobility mainly utilizes vehicles that are capable of vertical takeoff and landing (VTOL) for the simplicity of operation and large-scale deployment. However, VTOL vehicles need specialized trajectory and command design for the transition phase, where the vehicles transition between rotor-borne flight and wing-borne flight. Since VTOL vehicles are commonly designed as over-actuated systems for redundancy, one challenge that arises is actuator ambiguity, where it is unclear how to uniquely command actuators for the VTOL vehicle to track a given trajectory. We propose a method to design optimal reference commands for the transition mode. By formulating an 𝑙 1 -norm cost function on the rotor thrusts of the vehicle, we can achieve economical operation of the rotors such that they only operate when necessary and efficiently utilize the aerodynamics to save energy from reduced rotor actuation. We validate our approach in simulations and show its benefit compared to the commonly used differential flatness-based method.

John L Bullock↗
NASA NTRSDate not supplied

Off-Nominal Event Analysis in Autonomous Flights Based on Explainable Artificial Intelligence

A key objective in the Urban Air Mobility program at NASA is to intelligently perform an autonomous flight in a complex urban environment under all weather conditions with guaranteed levels of safety. To accomplish this, the mission manager (central decision-making module) of the vehicle needs to make informed decisions between various Courses of Action (CoA) based on its' interpretation of the inputs it receives. If an off-nominal event is detected either based on the amalgamation of sensor data or the use of machine learning models, the mission manager may greatly benefit from identification of the input features that most likely contributed to that specific event. Such an understanding is usually not possible to obtain from the classical machine learning models (deep learning) due to the inherent black box like structure. However, this understanding is achieved using eXplainable Artificial Intelligence (XAI) models that provide a human interpretable rationale for the predictions made. This work presents a game theory inspired XAI model for the off-nominal assessment of autonomous flights. The proposed approach based on Shapley values is model agnostic, provides local as well as global explanation and satisfies the four axioms (efficiency, symmetry, dummy, additivity) to achieve fair contribution. The versatility of the approach is first demonstrated on a simulated dataset in which the significance of each input to flight phase prediction is clearly identified. Subsequently, data from simulated flight trajectories are fed into the model which reveal the input features that most likely contributed to a rotor failure event thereby empowering the mission manager to take the appropriate CoA.

autonomy↗
NASA NTRSDate not supplied

Optimal Control using Composite Bernstein Approximants

In this work, we present composite Bernstein polynomials as a direct collocation method for approximating optimal control problems. An analysis of the convergence properties of composite Bernstein polynomials is provided, and beneficial properties of composite Bernstein polynomials for the solution of optimal control problems are discussed. The efficacy of the proposed approximation method is demonstrated through a bang-bang example. Lastly, we apply this method to a motion planning problem, offering a practical solution that emphasizes the ability of this method to solve complex optimal control problems.

Gage MacLin↗