Optimal Control and Avoidance Using HJR

The project focuses on optimizing the control of a Dubins vehicle, which follows a path with constrained curvature. The primary goal is to develop strategies for avoiding obstacles and reaching targets efficiently.

Dubins Dynamics

Dubins vehicles are characterized by their nonholonomic constraints, limiting their turning capabilities. This project utilizes the vehicle's dynamics to compute optimal paths to a target while avoiding obstacles.

Minimum Time Dubins

Four possible paths (LSR, LSL, RSR, RSL) are considered to find the minimum time route.

Minimum Time-Avoid Problem

A distance-based penalty function is introduced to ensure the vehicle avoids obstacles.

Hamilton Jacobi Reachability (HJR)

The approach involves solving a partial differential equation using dynamic programming. The cost function and value function are key components, helping to compute the optimal control strategies.

Results

6 Pillar Simulation

Simulation results with six obstacles.

6 Pillar with YAPPS (MATLAB)

Simulation results with six obstacles using YAPPS.

Conclusion and Future Work

The project highlights challenges such as grid discretization and computational time. Future work aims to extend the approach to 3D Dubins dynamics and explore control barrier functions.