multirotor.simulation

Module Contents

Classes

Propeller	Models the thrust and aerodynamics of the propeller blades spinning at a
Motor	Models the electronic and mechanical characterists of the rotation of the
Battery	Models the state of charge of the battery of the Multirotor.
Multirotor	The multirotor class models dynamics and control allocation of a vehicle.

class multirotor.simulation.Propeller(params: multirotor.vehicle.PropellerParams, simulation: multirotor.vehicle.SimulationParams)

Models the thrust and aerodynamics of the propeller blades spinning at a certain rate.

property state: float

property rpm: float

speed: float = 0.0

Radians per second

reset()

apply_speed(u: float, **kwargs) → float

Calculate the actual speed of the propeller after the speed signal is given. This method is pure and does not change the state of the propeller. It is used by the multirotor’s dxdt_* methods to calculate derivatives.

Parameters

ufloat

Radians per second speed command

Returns

float

The actual speed

step(u: float, **kwargs) → float

Step through the speed command. This method changes the state of the propeller.

Parameters

ufloat

Speed command in radians per second.

Returns

float

The actual speed achieved.

_thrust_constant(speed, airstream_velocity: numpy.ndarray = np.zeros(3)) → float

_thrust_physics(speed, airstream_velocity: numpy.ndarray = np.zeros(3)) → float

class multirotor.simulation.Motor(params: multirotor.vehicle.MotorParams, simulation: multirotor.vehicle.SimulationParams)

Models the electronic and mechanical characterists of the rotation of the propeller shaft.

speed: float = 0.0

Radians per second

reset() → float

current_average(max_voltage: float) → float

Average current consumption given the duty cycle of the speed controller. Duty cycle depends on max voltage which causes 100% duty cycle.

Parameters

max_voltagefloat

The peak voltage corresponding to 100% duty cycle.

Returns

float

Current consumption

apply_speed(u: float, max_voltage: float = np.inf) → float

Apply a voltage speed signal to the motor. This method is pure and doesn’t change the state of the motor.

Parameters

ufloat

Voltage signal.

max_voltagefloat, optional

The maximum voltage supply from power source. By default infinite.

Returns

float

The speed of the motor (rad /s)

step(u: float, max_voltage: float = np.inf) → float

Apply a voltage speed signal to the motor. This method changes the state of the motor.

Parameters

ufloat

Speed signal (rad/s).

max_voltagefloat, optional

The maximum voltage supply from power source. By default infinite.

Returns

float

The speed of the motor (rad /s)

class multirotor.simulation.Battery(params: multirotor.vehicle.BatteryParams, simulation: multirotor.vehicle.SimulationParams)

Models the state of charge of the battery of the Multirotor.

property state: float

reset()

step()

class multirotor.simulation.Multirotor(params: multirotor.vehicle.VehicleParams, simulation: multirotor.vehicle.SimulationParams)

The multirotor class models dynamics and control allocation of a vehicle.

property position

Position in the inertial frame.

property velocity: numpy.ndarray

Body-frame velocity

property inertial_velocity: numpy.ndarray

Velocity in the intertial frame.

property acceleration: numpy.ndarray

Body-frame acceleration

property inertial_acceleration: numpy.ndarray

Acceleration in the intertial frame.

property orientation: numpy.ndarray

Euler rotations (roll, pitch, yaw)

property angular_rate: numpy.ndarray

Angular rate of body frame axes (not same as rate of roll, pitch, yaw)

property euler_rate: numpy.ndarray

Euler rate of vehicle d(roll, pitch, yaw)/dt

property weight: float

property current_average: float

Duty-cycle adjusted currrent draw from battery.

property speeds: numpy.ndarray

reset() → numpy.ndarray

Reset the state of the vehicle. This includes resetting each propeller and re-calculating inertia and allocation matrices.

Can simulate dynamics with propellers with/out motors.

Returns

np.ndarray

The state of the vehicle.

get_forces_torques(speeds: numpy.ndarray, state: numpy.ndarray) → Tuple[numpy.ndarray, numpy.ndarray]

Calculate the forces and torques acting on the vehicle’s center of gravity given its current state and speed of propellers.

Parameters

speedsnp.ndarray

Propeller speeds (rad/s)

statenp.ndarray

State of the vehicle (position, velocity, orientation, angular rate)

Returns

Tuple[np.ndarray, np.ndarray]

The forces and torques acting on the body.

dxdt_dynamics(t: float, x: numpy.ndarray, u: numpy.ndarray, params=None)

Calculate the rate of change of state given the dynamics (forces, torques) acting on the system.

Parameters

tfloat

Time. Currently this function is time invariant.

xnp.ndarray

State of the vehicle.

unp.ndarray

A 6-vector of forces and torques.

Returns

np.ndarray

The rate of change of state.

dxdt_speeds(t: float, x: numpy.ndarray, u: numpy.ndarray, disturb_forces: numpy.ndarray = 0.0, disturb_torques: numpy.ndarray = 0.0, params=None)

Calculate the rate of change of state given the propeller speeds on the system (rad/s).

Parameters

tfloat

Time. Currently this function is time invariant.

xnp.ndarray

State of the vehicle.

unp.ndarray

A p-vector of propeller speeds (rad/s), where p=number of propellers.

disturb_forcesnp.ndarray, optional

Disturbinng x,y,z forces in the vehicle’s local frame, by default 0.

disturb_torquesnp.ndarray, optional

Disturbing x,y,z torques in the vehicle’s local frame, by default 0.

Returns

np.ndarray

The rate of change of state.

step_dynamics(u: numpy.ndarray) → numpy.ndarray

Given the 6-vector of x,y,z-forces and roll,pitch,yaw-torques, calculate the next state of the vehicle.

Parameters

unp.ndarray

The 6-vector, where the first 3 elements are forces (N) and the next 3 elements are the torques (Nm)

Returns

np.ndarray

The new state of the vehicle.

step_speeds(u: numpy.ndarray, disturb_forces: numpy.ndarray = 0.0, disturb_torques: numpy.ndarray = 0.0) → numpy.ndarray

Given the n-vector of propeller speed signals, calculate the next state of the vehicle. Where n is number of propellers.

Parameters

unp.ndarray

The speed signals to be sent to each propeller’s step() method. Can be the actual speed (rad/s) or the voltage signal (V) if a motor is used and MotorParams.speed_voltage_scaling constant is set.

disturb_forcesnp.ndarray, optional

Disturbinng x,y,z forces in the vehicle’s local frame, by default 0.

disturb_torquesnp.ndarray, optional

Disturbing x,y,z torques in the vehicle’s local frame, by default 0.

Returns

np.ndarray

The new state of the vehicle.

allocate_control(thrust: float, torques: numpy.ndarray) → numpy.ndarray

Allocate control to propellers by converting prescribed forces and torqes into propeller speeds. Uses the control allocation matrix.

Parameters

thrustfloat

The thrust in the body z-direction.

torquesnp.ndarray

The roll, pitch, yaw torques required about (x, y, z) axes.

Returns

np.ndarray

The prescribed propeller speeds (rad /s)

nonlinear_dynamics_controls_system(linearize: bool = False, perturbation: float = 0.1, about_state: numpy.ndarray = 0, about_action: numpy.ndarray = 0)

Create a system representation using the python controls library. The system takes net forces and torques as input.

Parameters

linearizebool, optional

Whether to linearize the system about a state/action, by default False

perturbationfloat, optional

The change in time to use to calculate dx/dt, by default 1e-1

about_statenp.ndarray, optional

The state about which to linearize, by default 0

about_actionnp.ndarray, optional

The action about which to linearize, by default 0

Returns

Union[control.LinearIOSystem, control.NonlinearIOSystem]

The system object

nonlinear_speeds_controls_system(linearize: bool = False, perturbation: float = 0.1, about_state: numpy.ndarray = 0, about_action: numpy.ndarray = 0)

Create a system representation using the python controls library. The system takes propeller speed signals as input.

Parameters

linearizebool, optional

Whether to linearize the system about a state/action, by default False

perturbationfloat, optional

The change in time to use to calculate dx/dt, by default 1e-1

about_statenp.ndarray, optional

The state about which to linearize, by default 0

about_actionnp.ndarray, optional

The action about which to linearize, by default 0

Returns

Union[control.LinearIOSystem, control.NonlinearIOSystem]

The system object