Trajectory Flow in AI & Artificial Intelligence

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.

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.

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.

A path is just a line on a map, but a Trajectory is a 'Time-stamped' plan for motion. It describes exactly where the robot should be, and how fast it should be moving, at every millisecond.

Path Planning gives you the 'Waypoints' (A to B to C). Trajectory Planning calculates the velocity and acceleration between them to ensure a smooth ride.

We use 'S-Curves' or 'Trapezoidal Velocity Profiles' to avoid jerky movements that could damage the robot's motors or spill its cargo.

Checkpoint: What is the difference between a 'Path' and a 'Trajectory'?

• →A trajectory has more points
• →A path is just a set of coordinates; a trajectory adds 'Time' and 'Velocity' to those coordinates

For drones or cars, we must also consider 'Kinodynamic' constraints—the physics of the vehicle. A car can't move sideways, and a drone can't stop instantly.

By mastering Trajectory Planning, you create robotic motion that is not just functional, but elegant, safe, and physically realistic.

Checkpoint: Why do we use a 'Deceleration' phase at the end of a trajectory?

• →To save battery
• →To ensure the robot reaches the final position at zero speed without 'Slamming' into the target or overshooting

Trajectory Planning mastered! You've learned the flow of motion. Ready to see in 3D depth with Stereo Vision?

Compute a Real Velocity Profile. Finish computing velocity along a trapezoidal profile, capped at the robot's maximum speed.