Program creates smooth motion paths for robots and drones
Cubic Spline Interpolation for Smooth Trajectory Generation in Autonomous Motion Systems
Robotics
Summary
Following waypoints with simple straight lines can cause robots or drones to jerk abruptly because their speed or acceleration changes instantly. The authors created a program that automatically makes smoother paths using cubic splines, which connect points with gentle curves. These paths keep position, speed, and acceleration continuous and avoid unrealistic sudden changes. They showed it working on drawing curves and digitizing signatures, which are similar challenges to generating smooth robot movements.
What this means in practice
- •For robotics engineers: Generate smooth and physically realistic movement paths from waypoint sequences without manual equation setup.
- •For drone operators: Create continuous acceleration trajectories for drones that avoid abrupt motion changes and improve flight stability.
Authors
Aarush Mandayam, Sriram Aditya Gundla, Elliott Tammaro
Abstract
We presented a program that automates the construction and solution of the cubic spline interpolation problem for a sequence of position-time waypoints, producing trajectories that are continuous in position, velocity, and acceleration and therefore avoid the infinite-acceleration problem inherent to piecewise-linear waypoint following. By assembling the interpolation and continuity conditions into a single linear system and solving directly for the spline coefficients, the program removes the need to manually derive per-segment equations for each new waypoint set. We illustrated the approach on free-form curve drawing and signature digitization, two tasks that use the same underlying machinery required for smooth robot and drone trajectory generation. Future work includes extending the implementation to multi-axis trajectories with explicit velocity and acceleration bounds, adopting the more computationally efficient tridiagonal solution method for larger waypoint sets, and evaluating the approach quantitatively against alternative trajectory generation methods.