Homotopy-based Motion Planning for Car-like Robots

Abstract

Path planning for car-like robots in
environments with obstacles constitutes a complex
problem, as it requires simultaneously satisfying
geometric and kinematic (non-holonomic) constraints.
Although there are planners available in the literature
that address this setting, this work proposes an
alternative two-stage planning methodology based on
algebraic and geometric methods. In the first stage,
the homotopy continuation method is used to solve
the system of nonlinear equations that incorporates
the geometric constraints of the vehicle and the
environment, obtaining an initial collision-free trajectory
in the configuration space of the rigid chassis. In
the second stage, a post-processing step applies
Reeds-Shepp curves to connect and smooth the
trajectory, followed by a randomized shortcutting pass
that reduces total path length while preserving kinematic
feasibility. To validate the proposed approach, simulation
results are presented comparing the performance of
the methodology against geometric sampling-based
planners from the OMPL library, all operating in the
same Reeds-Shepp configuration space. The evaluation
metrics focus on computation time and total path length,
demonstrating the feasibility and competitiveness of the
homotopic method for autonomous navigation problems.