3D holding pattern¶

Fly a holding pattern, two straight legs joined by half circles, at a target altitude with the 3D airliner. The observation gives the signed cross-track error, the tangent heading and the curvature at the nearest point of the pattern, so the work is in the transitions between straight and turning flight.

import target_gym as tg

env, params = tg.make("plane3d_racetrack")


Action space	`Box((3,))`, all actions in [-1, 1]
Observation space	`Box((21,))`
Tracked variable(s)	altitude (m)
Episode length	650 steps of 1 s (10.8 min)
Cite as	`plane3d_racetrack-v4`
Physics	contract

Action space¶

Actions are normalised to [-1, 1] and mapped onto the plant's real actuator range inside the environment.

#	meaning	min	max
0	power	-1	1
1	stick	-1	1
2	aileron	-1	1

Observation space¶

21 values in the plant's own units. The space declares no bounds (it spans the float32 range), so scale them before training. The reward scores obs[2] against obs[10].

#	meaning
0-9	the aircraft's state, as in `plane3d_heading`
10	target altitude (m)
11	x offset from the pattern's centre (m)
12	y offset from the pattern's centre (m)
13	turn radius of the pattern (m)
14	direction of the legs (rad)
15	throttle, 0 to 1
16	elevator deflection (rad)
17	aileron deflection (rad)
18	cross-track error to the nearest point, positive outside the pattern (m)
19	heading of the pattern at the nearest point (rad)
20	signed curvature at the nearest point, 0 on the legs (1/m)

Rewards¶

See the environment's compute_reward.

Every environment in this suite scores on one contract. The reward is minus the sum of three non-negative costs, -(tracking_cost + running_cost + failure_cost). The running cost charges consumption and the failure cost charges trips out of the operating envelope. The reward is never positive, and its scale differs by orders of magnitude between plants. Some plants are priced in dollars or euros and the rest are dimensionless; the per-plant summary says which. See Reward shaping for how each cost is built.

Starting state¶

reset samples the initial condition and the target; state has 27 fields.

Episode end¶

Termination. None by default. Leaving the operating envelope trips the plant: the step that leaves it is charged the trip cost and sets info["tripped"] and info["trip_cost"], and the plant restarts as reset_env would while the episode clock keeps running. Episodic use is optional: with continuing = False the plant is lost and terminated is raised on that step instead. See Reward shaping.

Truncation. After 650 steps.

Baselines¶

Recorded over 10 seeds of the 650-step episode (see Baseline results). The reward is a cost, so a return closer to zero is better.

controller	mean return	cost per step
PID	-1.064e+06	1637
MPC	-3.219e+05	495.2

The MPC beats the PID on 10 of 10 seeds and does not trip the plant on any of them.

Arguments¶

The scored configuration, which tg.make returns. A keyword argument changes one field, as in tg.make("plane3d_racetrack", max_steps_in_episode=...).

parameter	value	unit
`delta_t`	1	s
`max_steps_in_episode`	650	steps
`gravity`	9.81	m/s^2
`initial_mass`	73500	kg
`thrust_output_at_sea_level`	240000	N
`air_density_at_sea_level`	1.225	kg/m^3
`frontal_surface`	12.6	m^2
`wings_surface`	122.6	m^2
`C_x0`	0.095	-
`C_z0`	0.9	-
`initial_fuel_quantity`	19088	kg
`specific_fuel_consumption`	0.0175	kg/(kN.s)
`power_response_rate`	0.05	1/s
`stick_response_rate`	0.9	1/s
`aileron_response_rate`	0.9	1/s
`aspect_ratio`	9.48	-
`aileron_effectiveness`	0.4	-
`cl_alpha`	0.08786	1/deg
`cl0`	0.2	-
`cd0`	0.02	-
`k`	0.045	-
`aoa_stall`	15	deg
`CL_max`	1.5	-
`CL_min`	-1	-
`aoa_stall_width`	3	deg
`M_crit`	0.8	-
`k_shock_stall`	4	-
`shock_stall_floor`	0.25	-
`k_drag`	5	-
`I`	9000000	kg.m^2
`I_x`	2500000	kg.m^2
`moment_arm_stabilizer`	15	m
`moment_arm_wings`	1.5	m
`stabilizer_surface`	27	m^2
`elevator_surface`	10	m^2
`wingspan`	35.8	m
`aileron_surface`	6	m^2
`moment_arm_aileron`	14	m
`C_lp`	-0.4	-
`min_alt`	0	m
`max_alt`	12191.4	m
`precision_floor`	1	m
`heading_precision_floor`	0.0087	rad
`position_precision_floor`	3	m
`reward_version`	2	-
`e_floor_altitude`	1	m
`e_tol_altitude`	0	m
`e_floor_heading`	0.0087	rad
`e_floor_path`	3	m
`tracking_exponent`	2	-
`failure_cost`	2.9729e+08	reward
`restart_steps`	3600	steps
`rho_floor_tracking`	0.486937	reward
`rho_floor`	0.486937	reward
`figure8_altitude_amplitude`	200	m
`initial_z_dot`	0	m/s
`initial_x_dot`	200	m/s
`initial_y_dot`	0	m/s
`initial_theta_dot`	0	deg/s
`initial_theta`	0	deg
`initial_phi`	0	deg
`initial_phi_dot`	0	deg/s
`initial_heading`	0	rad
`initial_power`	1	-
`initial_stick`	0	deg
`initial_aileron`	0	deg
`wind_x`	0	m/s
`wind_y`	0	m/s
`wind_z`	0	m/s
`turbulence_sigma`	1.2	m/s
`turbulence_theta`	0.2	1/s
`wind_shear_x`	0	1/s
`wind_shear_y`	0	1/s
`shear_ref_alt`	0	m