  We consider the problem of navigating a nonlinear dynamical system from some
initial set to some target set while avoiding collision with an unsafe set. We
extend the concept of density function to control density function (CDF) for
solving navigation problems with safety constraints. The occupancy-based
interpretation of the measure associated with the density function is
instrumental in imposing the safety constraints. The navigation problem with
safety constraints is formulated as a quadratic program (QP) using CDF. The
existing approach using the control barrier function (CBF) also formulates the
navigation problem with safety constraints as QP. One of the main advantages of
the proposed QP using CDF compared to QP formulated using CBF is that both the
convergence/stability and safety can be combined and imposed using the CDF.
Simulation results involving the Duffing oscillator and safe navigation of
Dubin car models are provided to verify the main findings of the paper.
