  Optimization-based approaches are widely employed to generate optimal robot
motions while considering various constraints, such as robot dynamics,
collision avoidance, and physical limitations. It is crucial to efficiently
solve the optimization problems in practice, yet achieving rapid computations
remains a great challenge for optimization-based approaches with nonlinear
constraints. In this paper, we propose a geometric projector for dynamic
obstacle avoidance based on velocity obstacle (GeoPro-VO) by leveraging the
projection feature of the velocity cone set represented by VO. Furthermore,
with the proposed GeoPro-VO and the augmented Lagrangian spectral projected
gradient descent (ALSPG) algorithm, we transform an initial mixed integer
nonlinear programming problem (MINLP) in the form of constrained model
predictive control (MPC) into a sub-optimization problem and solve it
efficiently. Numerical simulations are conducted to validate the fast computing
speed of our approach and its capability for reliable dynamic obstacle
avoidance.
