Mobile Robot Control 2024 Ultron:Solution 2
Methodology
1. Artificial Potential Field
2. Dynamic Window Approach
The Dynamic Window Approach (DWA) algorithm simulates motion trajectories in velocity space [math]\displaystyle{ (v, \omega) }[/math] for a certain period of time. It evaluates these trajectories using an evaluation function and selects the optimal trajectory corresponding to [math]\displaystyle{ (v, \omega) }[/math] to drive the robot's motion.
Consider velocities which have to be
- Possible: velocities are limited by robot’s dynamics
[math]\displaystyle{ V_s = \{(v, \omega) \mid v \in [v_{\min}, v_{\max}] \land \omega \in [\omega_{\min}, \omega_{\max}]\} }[/math]
- Admissible: robot can stop before reaching the closest obstacle
[math]\displaystyle{ V_a = \{(v, \omega) \mid v \leq \sqrt{2 d(v, \omega) \dot{v_b}} \land \omega \leq \sqrt{2 d(v, \omega) \dot{\omega_b}}\} }[/math]
where \( \dot{v_b} \) and \( \dot{\omega_b} \) are maximum deceleration values, and \( d(v, \omega) \) is the distance to the closest object.
- Reachable: velocity and acceleration constraints (dynamic window)
[math]\displaystyle{ V_d = \{(v, \omega) \mid v \in [v_a - \dot{v} t, v_a + \dot{v} t] \land \omega \in [\omega_a - \dot{\omega} t, \omega_a + \dot{\omega} t]\} }[/math]
where \( v_a \) and \( \omega_a \) are actual velocities, and \( \dot{v} \) and \( \dot{\omega} \) are acceleration values.