  The design process and complexity of existing safety controls are heavily
determined by the geometrical properties of the environment, which affects the
proof of convergence, design scalability, performance robustness, and numerical
efficiency of the control. Hence, this paper proposes a variable structure
control to isolate the environment's geometrical complexity from the control
structure. A super-twisting algorithm is used to achieve accurate trajectory
tracking and robust safety control. The safety control is designed solely based
on distance measurement. First, a nominal safety model for obstacle avoidance
is derived, where realistic system constraints are considered. The nominal
model is well-suited for safety control design for obstacle avoidance,
geofencing, and border patrol with analytically proven stability results. The
safety control utilizes distance measurement to maintain a safe distance by
compensating the robot's angular velocity. A supervisory logic is constructed
to guarantee the overall stability and safety of the system. Operational safety
and precision tracking are proven under parametric uncertainty and
environmental uncertainty. The proposed design is modular with minimal tuning
parameters, which reduces the computational burden and improves the control
scalability. The effectiveness of the proposed method is verified against
various case studies.
