Vehicle Dynamics Simulation
Basic Kinematic Model
For vehicle simulations, use discrete-time kinematic equations.
Speed Update:
pythonnew_speed = current_speed + acceleration * dt new_speed = max(0, new_speed) # Speed cannot be negative
Position Update:
pythonnew_position = current_position + speed * dt
Distance Between Vehicles:
python# When following another vehicle relative_speed = ego_speed - lead_speed new_distance = current_distance - relative_speed * dt
Safe Following Distance
The time headway model calculates safe following distance:
pythondef safe_following_distance(speed, time_headway, min_distance): """ Calculate safe distance based on current speed. Args: speed: Current vehicle speed (m/s) time_headway: Time gap to maintain (seconds) min_distance: Minimum distance at standstill (meters) """ return speed * time_headway + min_distance
Time-to-Collision (TTC)
TTC estimates time until collision at current velocities:
pythondef time_to_collision(distance, ego_speed, lead_speed): """ Calculate time to collision. Returns None if not approaching (ego slower than lead). """ relative_speed = ego_speed - lead_speed if relative_speed <= 0: return None # Not approaching return distance / relative_speed
Acceleration Limits
Real vehicles have physical constraints:
pythondef clamp_acceleration(accel, max_accel, max_decel): """Constrain acceleration to physical limits.""" return max(max_decel, min(accel, max_accel))
State Machine Pattern
Vehicle control often uses mode-based logic:
pythondef determine_mode(lead_present, ttc, ttc_threshold): """ Determine operating mode based on conditions. Returns one of: 'cruise', 'follow', 'emergency' """ if not lead_present: return 'cruise' if ttc is not None and ttc < ttc_threshold: return 'emergency' return 'follow'
