Predictive modeling of aircraft dynamics
A computer-implemented method for predicting behavior of aircraft is provided. The method comprises inputting a current state of a number of aircraft into a number of hidden layers of a neural network, wherein the neural network is fully connected. An action applied to the aircraft is input into the hidden layers concurrently with the current state. The hidden layers, according to the current state and current action, determine a residual output that comprises an incremental difference in the state of the aircraft resulting from the current action. A skip connection feeds forward the current state of the aircraft, and the residual output is added to the current state to determine a next state of the aircraft.
1 . A method for learning aircraft dynamics when a pre-existing model of at least one of a number of aircraft, in a sensor cone of an aircraft that comprises a sensor, is either unavailable or is unsuitable for use in autonomous decision making and predicting behavior of the number of aircraft in the sensor cone, the method comprising using a number of processors performing the steps of:
training a neural network;
applying, for any numerical conditioning challenges encountered during training, a loss function only to a residual output, excluding a skip connection;
subsequently inputting a current state, respectively, of the number of aircraft in the sensor cone into a number of hidden layers of the neural network, wherein the neural network is fully connected and comprises a feedforward skip connection from the current state, respectively, of the number of aircraft in the sensor cone to all outputs of the neural network;
inputting an action applied to the aircraft that comprises the sensor into the hidden layers concurrently with the current state;
determining, by the hidden layers according to the current state and current action, residual output that comprises an incremental difference in the current state of the aircraft that comprises the sensor resulting from the current action;
feeding forward, by the skip connection, the current state of the aircraft that comprises the sensor to all outputs of the neural network;
adding the residual output to the current state to determine a next state of the aircraft that comprises the sensor, wherein the next state defines a trajectory for the aircraft for a next timestep; and
controlling a next action of the aircraft that comprises the sensor with a controller using the next state.
2 . The method of claim 1 , further comprising:
sensing, through a sensor system of the aircraft that comprises the sensor, parameters of the number of aircraft in the sensor cone of the aircraft that comprises the sensor indicating the current state respectively for each of the number of aircraft in the sensor cone;
inputting the residual output into a loss function;
inputting a number of ground truth residual values into the loss function concurrently with the residual output;
inputting an output from the loss function into a gradient descent optimizer that computes gradients for the hidden layers; and
updating connection weights in the hidden layers according to the gradients.
3 . The method of claim 1 , wherein the action is selected randomly from a set of possible actions according to a number of control policies for a controller.
4 . The method of claim 1 , wherein the neural network models the behavior of the number of aircraft.
5 . The method of claim 1 , wherein the current state and next state comprise trajectory data.
6 . The method of claim 1 , wherein the current state and next state comprise a heading angle.
7 . The method of claim 6 , further comprising applying a modulo operation to the residual output after adding the residual output to the current state, wherein the modulo operation ensures the heading angle changes within a specified range.
8 . The method of claim 1 , further comprising clamping the next state to ensure the next state is within predefined maximum and minimum values.
9 . The method of claim 1 , wherein the action is one-hot encoded for input into the hidden layers.
10 . A system configured to predict behavior of a number of aircraft, wherein the system comprises:
a sensor, on an aircraft that comprises a sensor cone, configured to sense parameters that indicate a current state, respectively, for each of a number of aircraft in the sensor cone;
a controller;
a storage device configured to store program instructions; and
one or more processors operably connected to the storage device and configured to execute the program instructions to cause the system to:
train a neural network;
apply, for any numerical conditioning challenges encountered during training, a loss function only to a residual output, excluding a skip connection;
subsequently input a current state, respectively, of the number of aircraft in the sensor cone into a number of hidden layers of the neural network, wherein the neural network is fully connected and comprises a feedforward skip connection from the current state of the number of aircraft in the sensor cone to all outputs of the neural network;
input an action applied to the aircraft that comprises the sensor into the hidden layers concurrently with the current state;
determine, by the hidden layers according to the current state and current action, a residual output that comprises an incremental difference in the current state of the aircraft that comprises the sensor resulting from the current action;
feed forward, by the skip connection, the current state of the aircraft that comprises the sensor to all outputs of the neural network;
add the residual output to the current state to determine a next state of the aircraft that comprises the sensor, wherein the next state defines a trajectory for the aircraft that comprises the sensor for a next timestep; and
control, based upon the next state, a next action of the aircraft that comprises the sensor with the controller.
11 . The system of claim 10 , wherein the system further comprises:
a sensor that comprises a sensor cone configured to sense parameters that indicate a current state, respectively, for each of a number of aircraft in the sensor cone; and
the processors configured to execute program instructions to:
input the residual output into a loss function;
input a number of ground truth residual values into the loss function concurrently with the residual output;
input an output from the loss function into a gradient descent optimizer that computes gradients for the hidden layers; and
update connection weights in the hidden layers according to the gradients.
12 . The system of claim 10 , wherein the action is selected randomly from a set of possible actions according to a number of control policies for a controller.
13 . The system of claim 10 , wherein the current state and next state comprise at least one of:
trajectory data; or
a heading angle.
14 . The system of claim 10 , further comprising clamping the next state to ensure the next state is within predefined maximum and minimum values.
15 . A computer program product configured to predict behavior of a number of aircraft, wherein the computer program product comprises a controller configured to determine a next action of an aircraft that comprises a sensor, wherein the sensor comprises a sensor cone, and a computer-readable storage medium that comprises program instructions configured to:
receive, from the sensor, parameters that indicate a current state, respectively, for each of the number of aircraft in the sensor cone;
train a neural network;
apply, for any numerical conditioning challenges encountered during training, a loss function only to a residual output, excluding a skip connection;
subsequently input the current state of the number of aircraft in the sensor cone into a number of hidden layers of the neural network, wherein the neural network is fully connected and comprises a feedforward skip connection from the current state of the number of aircraft in the sensor cone to all outputs of the neural network;
input an action applied to the aircraft that comprises the sensor into the hidden layers concurrently with the current state;
determine, by the hidden layers according to the current state and current action, a residual output that comprises an incremental difference in a state of the aircraft that comprises the sensor resultant from the current action;
feed forward, by a skip connection, the current state of the aircraft that comprises the sensor to all outputs of the neural network;
add the residual output to the current state to determine a next state of the aircraft that comprises the sensor, wherein the next state defines a trajectory for the aircraft for a next timestep; and
control, with the controller and based upon the next state, a next action of the aircraft that comprises the sensor.
16 . The computer program product of claim 15 , further comprising:
inputting the residual output into a loss function;
inputting a number of ground truth residual values into the loss function concurrently with the residual output;
inputting an output from the loss function into a gradient descent optimizer that computes gradients for the hidden layers; and
updating connection weights in the hidden layers according to the gradients.
17 . The computer program product of claim 15 , wherein the action is selected randomly from a set of possible actions according to a number of control policies for a controller.
18 . The computer program product of claim 15 , wherein the current state and next state comprise at least one of:
trajectory data; or
a heading angle.
19 . The computer program product of claim 18 , further comprising applying, for the heading angle, a modulo operation to the residual output after adding the residual output to the current state, wherein the modulo operation ensures the heading angle changes within a specified range.
20 . The computer program product of claim 15 , further comprising clamping the next state to ensure the next state is within predefined maximum and minimum values.