Project 1 - Phase 2: Trajectory Planning and Generation

• Keywords: Trajectory Planning, Optimization-based Trajectory Generation, Minimum Snap Trajectory, (un)constrained Quadratic Programming
• Coding language: MATLAB
• Detailed code implementation can be found in the Github code repo

Trajectory Generation Method

Design the trajectory for quadrotor given the path (waypoints), and calculate desired states given time. Try to make the trajectory smooth and feasible.

• The trajectory is generated using an optimization-based method (minimum snap trajectory generation). In the actual coding implementation, the built-in function quadprog from MATLAB is used to solve the constrained Quadratic Programming problem.
• The time allocation is proportional to the length of each segment of the trajectory (weighted average).
• At the end of the trajectory, the Quadrotor will hover with the final state if the experiment is still ongoing.

Simulation Figures

Path1

Path2

Path3 (self-designed)

Path4 (self-designed)

Controller Statistics

The Controller’s parameters have been optimized based on Project1-Phase1. Currently, the parameters’ values are:

	X_pos	Y_pos	Z_pos	Roll_att	Pitch_att	Yaw_att
Kp	10	10	10	3000	3000	3000
Kd	8	8	8	100	100	100
Ki	1	1	1	1	1	1

The performances on different paths based on RMSE values:

RMSE	Path1	Path2	Path3	Path4
RMSE Position (m)	0.077445	0.070551	0.084609	0.12952
RMSE Velocity (m/s)	0.13065	0.10243	0.12858	0.16033
RMSE Yaw (deg)	1.3341	1.3232	1.3302	1.3326

Result Analysis

After the optimization of the Controller, the path following becomes smoother and more stable. The trajectory generation is also acceptable.

Reference

Some implementations are adapted from this code repository. - GitHub @ Garyandtang - ELEC5660-2021