  To achieve safe legged locomotion, it is important to generate motion in
real-time considering various constraints in robots and environments. In this
study, we propose a lightweight real-time perspective motion control system for
the newly developed six-wheeled-telescopic-legged robot, Tachyon 3. In the
proposed method, analytically smoothed constraints including Smooth Separating
Axis Theorem (Smooth SAT) as a novel higher order differentiable collision
detection for 3D shapes is applied to the Control Barrier Function (CBF). The
proposed system integrating the CBF achieves online motion generation in a
short control cycle of 1 ms that satisfies joint limitations, environmental
collision avoidance and safe convex foothold constraints. The efficiency of
Smooth SAT is shown from the collision detection time of 1 us or less and the
CBF constraint computation time for Tachyon3 of several us. Furthermore, the
effectiveness of the proposed system is verified through the stair-climbing
motion, integrating online recognition in a simulation and a real machine.
