  Ground robots navigating in complex, dynamic environments must compute
collision-free trajectories to avoid obstacles safely and efficiently.
Nonconvex optimization is a popular method to compute a trajectory in
real-time. However, these methods often converge to locally optimal solutions
and frequently switch between different local minima, leading to inefficient
and unsafe robot motion. In this work, We propose a novel topology-driven
trajectory optimization strategy for dynamic environments that plans multiple
distinct evasive trajectories to enhance the robot's behavior and efficiency. A
global planner iteratively generates trajectories in distinct homotopy classes.
These trajectories are then optimized by local planners working in parallel.
While each planner shares the same navigation objectives, they are locally
constrained to a specific homotopy class, meaning each local planner attempts a
different evasive maneuver. The robot then executes the feasible trajectory
with the lowest cost in a receding horizon manner. We demonstrate, on a mobile
robot navigating among pedestrians, that our approach leads to faster and safer
trajectories than existing planners.
