  For letting mobile robots travel flexibly through complicated environments,
increasing attention has been paid to the whole-body collision evaluation. Most
existing works either opt for the conservative corridor-based methods that
impose strict requirements on the corridor generation, or ESDF-based methods
that suffer from high computational overhead. It is still a great challenge to
achieve fast and accurate whole-body collision evaluation. In this paper, we
propose a Robo-centric ESDF (RC-ESDF) that is pre-built in the robot body frame
and is capable of seamlessly applied to any-shape mobile robots, even for those
with non-convex shapes. RC-ESDF enjoys lazy collision evaluation, which retains
only the minimum information sufficient for whole-body safety constraint and
significantly speeds up trajectory optimization. Based on the analytical
gradients provided by RC-ESDF, we optimize the position and rotation of robot
jointly, with whole-body safety, smoothness, and dynamical feasibility taken
into account. Extensive simulation and real-world experiments verified the
reliability and generalizability of our method.
