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"""
Top-down car dynamics simulation.
Some ideas are taken from this great tutorial http://www.iforce2d.net/b2dtut/top-down-car by Chris Campbell.
This simulation is a bit more detailed, with wheels rotation.
Created by Oleg Klimov
"""
import math
import Box2D
import numpy as np
from gym.error import DependencyNotInstalled
try:
from Box2D.b2 import fixtureDef, polygonShape, revoluteJointDef
except ImportError:
raise DependencyNotInstalled("box2D is not installed, run `pip install gym[box2d]`")
SIZE = 0.02
ENGINE_POWER = 100000000 * SIZE * SIZE
WHEEL_MOMENT_OF_INERTIA = 4000 * SIZE * SIZE
FRICTION_LIMIT = (
1000000 * SIZE * SIZE
) # friction ~= mass ~= size^2 (calculated implicitly using density)
WHEEL_R = 27
WHEEL_W = 14
WHEELPOS = [(-55, +80), (+55, +80), (-55, -82), (+55, -82)]
HULL_POLY1 = [(-60, +130), (+60, +130), (+60, +110), (-60, +110)]
HULL_POLY2 = [(-15, +120), (+15, +120), (+20, +20), (-20, 20)]
HULL_POLY3 = [
(+25, +20),
(+50, -10),
(+50, -40),
(+20, -90),
(-20, -90),
(-50, -40),
(-50, -10),
(-25, +20),
]
HULL_POLY4 = [(-50, -120), (+50, -120), (+50, -90), (-50, -90)]
WHEEL_COLOR = (0, 0, 0)
WHEEL_WHITE = (77, 77, 77)
MUD_COLOR = (102, 102, 0)
class Car:
def __init__(self, world, init_angle, init_x, init_y):
self.world: Box2D.b2World = world
self.hull: Box2D.b2Body = self.world.CreateDynamicBody(
position=(init_x, init_y),
angle=init_angle,
fixtures=[
fixtureDef(
shape=polygonShape(
vertices=[(x * SIZE, y * SIZE) for x, y in HULL_POLY1]
),
density=1.0,
),
fixtureDef(
shape=polygonShape(
vertices=[(x * SIZE, y * SIZE) for x, y in HULL_POLY2]
),
density=1.0,
),
fixtureDef(
shape=polygonShape(
vertices=[(x * SIZE, y * SIZE) for x, y in HULL_POLY3]
),
density=1.0,
),
fixtureDef(
shape=polygonShape(
vertices=[(x * SIZE, y * SIZE) for x, y in HULL_POLY4]
),
density=1.0,
),
],
)
self.hull.color = (0.8, 0.0, 0.0)
self.wheels = []
self.fuel_spent = 0.0
WHEEL_POLY = [
(-WHEEL_W, +WHEEL_R),
(+WHEEL_W, +WHEEL_R),
(+WHEEL_W, -WHEEL_R),
(-WHEEL_W, -WHEEL_R),
]
for wx, wy in WHEELPOS:
front_k = 1.0 if wy > 0 else 1.0
w = self.world.CreateDynamicBody(
position=(init_x + wx * SIZE, init_y + wy * SIZE),
angle=init_angle,
fixtures=fixtureDef(
shape=polygonShape(
vertices=[
(x * front_k * SIZE, y * front_k * SIZE)
for x, y in WHEEL_POLY
]
),
density=0.1,
categoryBits=0x0020,
maskBits=0x001,
restitution=0.0,
),
)
w.wheel_rad = front_k * WHEEL_R * SIZE
w.color = WHEEL_COLOR
w.gas = 0.0
w.brake = 0.0
w.steer = 0.0
w.phase = 0.0 # wheel angle
w.omega = 0.0 # angular velocity
w.skid_start = None
w.skid_particle = None
rjd = revoluteJointDef(
bodyA=self.hull,
bodyB=w,
localAnchorA=(wx * SIZE, wy * SIZE),
localAnchorB=(0, 0),
enableMotor=True,
enableLimit=True,
maxMotorTorque=180 * 900 * SIZE * SIZE,
motorSpeed=0,
lowerAngle=-0.4,
upperAngle=+0.4,
)
w.joint = self.world.CreateJoint(rjd)
w.tiles = set()
w.userData = w
self.wheels.append(w)
self.drawlist = self.wheels + [self.hull]
self.particles = []
def gas(self, gas):
"""control: rear wheel drive
Args:
gas (float): How much gas gets applied. Gets clipped between 0 and 1.
"""
gas = np.clip(gas, 0, 1)
for w in self.wheels[2:4]:
diff = gas - w.gas
if diff > 0.1:
diff = 0.1 # gradually increase, but stop immediately
w.gas += diff
def brake(self, b):
"""control: brake
Args:
b (0..1): Degree to which the brakes are applied. More than 0.9 blocks the wheels to zero rotation"""
for w in self.wheels:
w.brake = b
def steer(self, s):
"""control: steer
Args:
s (-1..1): target position, it takes time to rotate steering wheel from side-to-side"""
self.wheels[0].steer = s
self.wheels[1].steer = s
def step(self, dt):
for w in self.wheels:
# Steer each wheel
dir = np.sign(w.steer - w.joint.angle)
val = abs(w.steer - w.joint.angle)
w.joint.motorSpeed = dir * min(50.0 * val, 3.0)
# Position => friction_limit
grass = True
friction_limit = FRICTION_LIMIT * 0.6 # Grass friction if no tile
for tile in w.tiles:
friction_limit = max(
friction_limit, FRICTION_LIMIT * tile.road_friction
)
grass = False
# Force
forw = w.GetWorldVector((0, 1))
side = w.GetWorldVector((1, 0))
v = w.linearVelocity
vf = forw[0] * v[0] + forw[1] * v[1] # forward speed
vs = side[0] * v[0] + side[1] * v[1] # side speed
# WHEEL_MOMENT_OF_INERTIA*np.square(w.omega)/2 = E -- energy
# WHEEL_MOMENT_OF_INERTIA*w.omega * domega/dt = dE/dt = W -- power
# domega = dt*W/WHEEL_MOMENT_OF_INERTIA/w.omega
# add small coef not to divide by zero
w.omega += (
dt
* ENGINE_POWER
* w.gas
/ WHEEL_MOMENT_OF_INERTIA
/ (abs(w.omega) + 5.0)
)
self.fuel_spent += dt * ENGINE_POWER * w.gas
if w.brake >= 0.9:
w.omega = 0
elif w.brake > 0:
BRAKE_FORCE = 15 # radians per second
dir = -np.sign(w.omega)
val = BRAKE_FORCE * w.brake
if abs(val) > abs(w.omega):
val = abs(w.omega) # low speed => same as = 0
w.omega += dir * val
w.phase += w.omega * dt
vr = w.omega * w.wheel_rad # rotating wheel speed
f_force = -vf + vr # force direction is direction of speed difference
p_force = -vs
# Physically correct is to always apply friction_limit until speed is equal.
# But dt is finite, that will lead to oscillations if difference is already near zero.
# Random coefficient to cut oscillations in few steps (have no effect on friction_limit)
f_force *= 205000 * SIZE * SIZE
p_force *= 205000 * SIZE * SIZE
force = np.sqrt(np.square(f_force) + np.square(p_force))
# Skid trace
if abs(force) > 2.0 * friction_limit:
if (
w.skid_particle
and w.skid_particle.grass == grass
and len(w.skid_particle.poly) < 30
):
w.skid_particle.poly.append((w.position[0], w.position[1]))
elif w.skid_start is None:
w.skid_start = w.position
else:
w.skid_particle = self._create_particle(
w.skid_start, w.position, grass
)
w.skid_start = None
else:
w.skid_start = None
w.skid_particle = None
if abs(force) > friction_limit:
f_force /= force
p_force /= force
force = friction_limit # Correct physics here
f_force *= force
p_force *= force
w.omega -= dt * f_force * w.wheel_rad / WHEEL_MOMENT_OF_INERTIA
w.ApplyForceToCenter(
(
p_force * side[0] + f_force * forw[0],
p_force * side[1] + f_force * forw[1],
),
True,
)
def draw(self, surface, zoom, translation, angle, draw_particles=True):
import pygame.draw
if draw_particles:
for p in self.particles:
poly = [pygame.math.Vector2(c).rotate_rad(angle) for c in p.poly]
poly = [
(
coords[0] * zoom + translation[0],
coords[1] * zoom + translation[1],
)
for coords in poly
]
pygame.draw.lines(
surface, color=p.color, points=poly, width=2, closed=False
)
for obj in self.drawlist:
for f in obj.fixtures:
trans = f.body.transform
path = [trans * v for v in f.shape.vertices]
path = [(coords[0], coords[1]) for coords in path]
path = [pygame.math.Vector2(c).rotate_rad(angle) for c in path]
path = [
(
coords[0] * zoom + translation[0],
coords[1] * zoom + translation[1],
)
for coords in path
]
color = [int(c * 255) for c in obj.color]
pygame.draw.polygon(surface, color=color, points=path)
if "phase" not in obj.__dict__:
continue
a1 = obj.phase
a2 = obj.phase + 1.2 # radians
s1 = math.sin(a1)
s2 = math.sin(a2)
c1 = math.cos(a1)
c2 = math.cos(a2)
if s1 > 0 and s2 > 0:
continue
if s1 > 0:
c1 = np.sign(c1)
if s2 > 0:
c2 = np.sign(c2)
white_poly = [
(-WHEEL_W * SIZE, +WHEEL_R * c1 * SIZE),
(+WHEEL_W * SIZE, +WHEEL_R * c1 * SIZE),
(+WHEEL_W * SIZE, +WHEEL_R * c2 * SIZE),
(-WHEEL_W * SIZE, +WHEEL_R * c2 * SIZE),
]
white_poly = [trans * v for v in white_poly]
white_poly = [(coords[0], coords[1]) for coords in white_poly]
white_poly = [
pygame.math.Vector2(c).rotate_rad(angle) for c in white_poly
]
white_poly = [
(
coords[0] * zoom + translation[0],
coords[1] * zoom + translation[1],
)
for coords in white_poly
]
pygame.draw.polygon(surface, color=WHEEL_WHITE, points=white_poly)
def _create_particle(self, point1, point2, grass):
class Particle:
pass
p = Particle()
p.color = WHEEL_COLOR if not grass else MUD_COLOR
p.ttl = 1
p.poly = [(point1[0], point1[1]), (point2[0], point2[1])]
p.grass = grass
self.particles.append(p)
while len(self.particles) > 30:
self.particles.pop(0)
return p
def destroy(self):
self.world.DestroyBody(self.hull)
self.hull = None
for w in self.wheels:
self.world.DestroyBody(w)
self.wheels = []
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