Core Concepts
Linear output feedback controllers are synthesized to guide agents along predefined polynomial trajectories while ensuring safety within a polygonal environment.
Abstract
The content introduces a novel technique for trajectory planning and obstacle avoidance using convex optimization. It discusses path planning algorithms, control synthesis, stability constraints, safety constraints, and controller switching. Simulations demonstrate the effectiveness of the proposed method in both noise-free and noisy environments.
I. Introduction
- Path planning is crucial for autonomous systems.
- Various algorithms aim to find feasible paths.
- Traditional methods like Potential Field Algorithms attract agents towards goals.
- A∗and RRT∗algorithms avoid local minima effectively.
- Sample-based techniques may not produce smooth trajectories.
II. Preliminaries
- Linear Time Invariant system dynamics are modeled.
- Polynomial trajectories are represented using Bernstein basis polynomials.
- Bernstein polynomials and their derivatives are bounded.
- The polygonal environment is decomposed into convex cells.
III. Proposed Solution
- Polynomial trajectories are written as outputs of reference dynamical systems.
- Stability constraints ensure agent convergence to reference trajectories.
- Safety constraints based on Control Barrier Functions prevent collisions with walls.
- Controllers are synthesized through convex optimization.
IV. Simulations
- Simulation results without noise show successful trajectory tracking in a polygonal environment.
- Simulation results with noise demonstrate robustness to Gaussian noise.
V. Conclusion
The proposed technique synthesizes linear output feedback controllers for trajectory tracking and obstacle avoidance in complex environments.
Stats
Extensive simulations test motion planning under different conditions.
Quadratic programs with Control Barrier Functions ensure safety critical systems' stability.
Quotes
"We propose an output feedback control-based motion planning technique."
"Our approach combines elements of many path-planning techniques."