3D heading¶
Hold a target altitude and turn onto and hold a target heading with the 3D airliner, using throttle, elevator and aileron. The aileron commands a roll rate, not a bank angle, so heading is controlled through a cascade of two integrators, and the turbulence is hidden.
| Action space | Box((3,)), all actions in [-1, 1] |
| Observation space | Box((15,)) |
| Tracked variable(s) | altitude (m) |
| Episode length | 300 steps of 1 s (5 min) |
| Cite as | plane3d_heading-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¶
15 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 | x_dot, velocity along world x (m/s) |
| 1 | y_dot, velocity along world y (m/s) |
| 2 | z, altitude (m) |
| 3 | z_dot, vertical speed (m/s) |
| 4 | theta, pitch angle (rad) |
| 5 | theta_dot, pitch rate (rad/s) |
| 6 | phi, bank angle (rad) |
| 7 | phi_dot, roll rate (rad/s) |
| 8 | gamma, flight-path angle (rad) |
| 9 | psi, heading (rad) |
| 10 | target altitude (m) |
| 11 | target heading (rad) |
| 12 | throttle, 0 to 1 |
| 13 | elevator deflection (rad) |
| 14 | aileron deflection (rad) |
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 300 steps.
Baselines¶
Recorded over 10 seeds of the 300-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 | -1.672e+06 | 5573 |
| MPC | -6.893e+05 | 2298 |
The MPC beats the PID on 9 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_heading", max_steps_in_episode=...).
| parameter | value | unit |
|---|---|---|
delta_t |
1 | s |
max_steps_in_episode |
300 | 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 |
0.344219 | reward |
rho_floor |
0.344219 | 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 |