  For the cascaded planning and control modules implemented for robot
navigation, the frequency gap between the planner and controller has received
limited attention. In this study, we introduce a novel B-spline parameterized
optimization-based planner (BSPOP) designed to address the frequency gap
challenge with limited onboard computational power in robots. The proposed
planner generates continuous-time control inputs for low-level controllers
running at arbitrary frequencies to track. Furthermore, when considering the
convex control action sets, BSPOP uses the convex hull property to
automatically constrain the continuous-time control inputs within the convex
set. Consequently, compared with the discrete-time optimization-based planners,
BSPOP reduces the number of decision variables and inequality constraints,
which improves computational efficiency as a byproduct. Simulation results
demonstrate that our approach can achieve a comparable planning performance to
the high-frequency baseline optimization-based planners while demanding less
computational power. Both simulation and experiment results show that the
proposed method performs better in planning compared with baseline planners in
the same frequency.
