A path is a static line; a trajectory is a living movement. To move a robot through the real world, you must master the physics of time, velocity, and acceleration.
1Adding the Dimension of Time
Trajectory Planning takes a geometric Path (a series of x,y,z coordinates) and assigns a Time to each point. This allows the robot to know not just *where* it should be, but *when* it should be there. This is critical for coordinating multiple robots (e.g., in an automated warehouse) and for ensuring that the robot's movements are predictable and safe for human bystanders.
2The Trapezoidal Velocity Profile
The most common way to move a motor is the Trapezoidal Profile. It consists of three phases: Acceleration (speeding up at a constant rate), Cruise (moving at the target speed), and Deceleration (slowing down to reach the goal at exactly zero speed). While efficient, the sudden changes in acceleration at the corners of the trapezoid can cause 'Jerky' motion. Advanced systems use S-Curves (Polynomial profiles), which smooth out these transitions to protect the robot's gears and motors from mechanical stress.
3Respecting the Physics
Every robot has physical limits. A motor can only spin so fast, and a battery can only provide so much current. Kinodynamic Planning ensures that the planned trajectory never asks the robot to do something it physically can't—like accelerating faster than gravity allows or turning tighter than its steering allows (Non-holonomic constraints). We use Splines (smooth mathematical curves) to connect waypoints, ensuring the trajectory is 'Continuous' and respects the maximum velocity and acceleration limits of the hardware.
