h?( S /r SSKJr SSKrSSKrSSKJr SSKJ r SSK
J r \R r
Sr " S S \R 5 rS
rg) z Carlos Luis )pathN)spaces)utils)DependencyNotInstalled ?c ^ \ rS rSrSrSS/SS.rSS\S- 4S jjrS
rSSS .S \ S- S
\
S- 4U 4S jjjr S r S r
S rSrU =r$ ) PendulumEnv a
## Description
The inverted pendulum swingup problem is based on the classic problem in control theory.
The system consists of a pendulum attached at one end to a fixed point, and the other end being free.
The pendulum starts in a random position and the goal is to apply torque on the free end to swing it
into an upright position, with its center of gravity right above the fixed point.
The diagram below specifies the coordinate system used for the implementation of the pendulum's
dynamic equations.
- `x-y`: cartesian coordinates of the pendulum's end in meters.
- `theta` : angle in radians.
- `tau`: torque in `N m`. Defined as positive _counter-clockwise_.
## Action Space
The action is a `ndarray` with shape `(1,)` representing the torque applied to free end of the pendulum.
| Num | Action | Min | Max |
|-----|--------|------|-----|
| 0 | Torque | -2.0 | 2.0 |
## Observation Space
The observation is a `ndarray` with shape `(3,)` representing the x-y coordinates of the pendulum's free
end and its angular velocity.
| Num | Observation | Min | Max |
|-----|------------------|------|-----|
| 0 | x = cos(theta) | -1.0 | 1.0 |
| 1 | y = sin(theta) | -1.0 | 1.0 |
| 2 | Angular Velocity | -8.0 | 8.0 |
## Rewards
The reward function is defined as:
*r = -(theta2 + 0.1 * theta_dt2 + 0.001 * torque2)*
where `theta` is the pendulum's angle normalized between *[-pi, pi]* (with 0 being in the upright position).
Based on the above equation, the minimum reward that can be obtained is
*-(pi2 + 0.1 * 82 + 0.001 * 22) = -16.2736044*,
while the maximum reward is zero (pendulum is upright with zero velocity and no torque applied).
## Starting State
The starting state is a random angle in *[-pi, pi]* and a random angular velocity in *[-1,1]*.
## Episode Truncation
The episode truncates at 200 time steps.
## Arguments
- `g`: .
Pendulum has two parameters for `gymnasium.make` with `render_mode` and `g` representing
the acceleration of gravity measured in *(m s-2)* used to calculate the pendulum dynamics.
The default value is `g = 10.0`.
On reset, the `options` parameter allows the user to change the bounds used to determine the new random state.
```python
>>> import gymnasium as gym
>>> env = gym.make("Pendulum-v1", render_mode="rgb_array", g=9.81) # default g=10.0
>>> env
>>>>
>>> env.reset(seed=123, options={"low": -0.7, "high": 0.5}) # default low=-0.6, high=-0.5
(array([ 0.4123625 , 0.91101986, -0.89235795], dtype=float32), {})
```
## Version History
* v1: Simplify the math equations, no difference in behavior.
* v0: Initial versions release
human rgb_array ) render_modes
render_fpsN render_modec SU l SU l SU l X l SU l SU l Xl SU l S U l S U l SU l
[ R " SSU R /[ R S9n[ R " U R * U R S[ R S 9U l [ R " U* U[ R S
9U l g ) N g @皙?r i Tdtype) )lowhighshaper )r r r ) max_speed
max_torquedtgmlr
screen_dimscreenclockisopennparrayfloat32r Box action_spaceobservation_space)selfr r r s a/home/james-whalen/.local/lib/python3.13/site-packages/gymnasium/envs/classic_control/pendulum.py__init__PendulumEnv.__init__g s &
xxc4>>2"**E #JJ td"**
"(D
!S c U R u p#U R nU R nU R nU R n[
R " XR * U R 5 S nXl [ U5 S- SUS- - - SUS- - - nUSU- SU- - [
R " U5 - SXVS- - - U- - U- - n [
R " XR * U R 5 n X)U- - n
[
R " X/5 U l U R S:X a U R 5 U R 5 U* SS0 4$ ) Nr g?gMbP? g @r F)stater r r r r$ clipr last_uangle_normalizesinr r% r render_get_obs) r* uththdotr r r r costsnewthdotnewths r+ stepPendulumEnv.step s& JJ FF FF FF
WW GGA' 9! < #q(3>9EQTNJAEQUObffRj 83!d(;Ka;O OSUUU778nn_dnnE]"XXu /0
w & KKM}}ub88r. )seedoptionsrA rB c > [ TU ] US9 Uc! [ R " [ [
/5 nO}SU; a UR
S5 O[ nSU; a UR
S5 O[
n[ R " U5 n[ R " U5 n[ R " XE/5 nU* nU R R XcS9U l S U l U R S:X a U R 5 U R 5 0 4$ )N)rA x_inity_init)r r r )superresetr$ r% DEFAULT_X DEFAULT_Ygetr verify_number_and_cast np_randomuniformr2 r4 r r7 r8 )r* rA rB r xyr __class__s r+ rG PendulumEnv.reset s
4
?88Y 23D *2W)< H%)A)1W)< H%)A,,Q/A,,Q/A88QF#De^^+++?
w & KKM}}""r. c U R u p[ R " [ R " U5 [ R " U5 U/[ R
S9$ )Nr )r2 r$ r% cosr6 r& )r* thetathetadots r+ r8 PendulumEnv._get_obs s9 **xx u
x@
SSr. c
U R cG U R c e[ R R SU R R
S35 g SS KnSSKJn U R c UR 5 U R S:X aQ UR R 5 UR R U R U R 45 U l
O,UR U R U R 45 U l
U R c UR" R% 5 U l UR U R U R 45 U l U R& R) S5 SnU R US - - nU R S - nS
U- nS U- nSXxS - U* S - 4u ppX4X4X4X4/n
/ nU
Ho nUR* R- U5 R/ U R0 S [2 R4 S - - 5 nUS U- US
U- 4nUR7 U5 Mq UR9 U R& US 5 UR; U R& US 5 UR= U R& Xf[? US - 5 S 5 URA U R& Xf[? US - 5 S 5 US4nUR* R- U5 R/ U R0 S [2 R4 S - - 5 n[? US U- 5 [? US
U- 5 4nUR= U R& US US
[? US - 5 S 5 URA U R& US US
[? US - 5 S 5 [B RD " [B RF " [H 5 S
5 nURJ RM U5 nU RN Gb URP RS U[U U[2 RV " U RN 5 - S - 5 [U U[2 RV " U RN 5 - S - 5 45 n[Y U RN S: 5 nURP R[ UUS5 nU R& R] UUUR_ 5 R` -
UUR_ 5 Rb -
45 UR= U R& Xf[? SU- 5 S5 URA U R& Xf[? SU- 5 S5 URP R[ U R& SS5 U l U R R] U R& S5 U R S:X a] URd Rg 5 U R Ri U Rj S 5 UR R[ 5 g [2 Rl " [2 Rn " URp Rs U R 5 5 SS9$ ! [ a n[ S5 UeS nAff = f)NzYou are calling render method without specifying any render mode. You can specify the render_mode at initialization, e.g. gym.make("z", render_mode="rgb_array")r )gfxdrawzGpygame is not installed, run `pip install "gymnasium[classic_control]"`r ) rY rY g@r0 r g?) M r[ zassets/clockwise.pngTr )r r r F)r r r )r r r0 )axes):r specgymloggerwarnidpygamerX ImportErrorr r! initdisplayset_moder Surfacer" timeClocksurffillmathVector2
rotate_radr2 r$ piappend aapolygonfilled_polygonaacircleint
filled_circler joindirname__file__imageloadr4 transform smoothscalefloatabsboolflipblitget_rectcenterxcenteryeventpumptickmetadata transposer% surfarraypixels3d)r* rb rX eboundscaleoffset
rod_length rod_widthr rtbcoordstransformed_coordscrod_endfnameimg scale_imgis_flips r+ r7 PendulumEnv.render sQ #99( (( JJOO""&)),, /JL
& ;; KKM 7*##% $nn 5 5__doo6 %nndoot-O P :: **,DJNNDOOT__#EF '519- A%Y
%K
MI:>A
a&1&1&1&1 A ##A&11$**Q-"%%!)2KLA1 !v
.A % %a ( $))%7 G tyy*