Conceptos Básicos
Dynamic safety margins can be used to systematically design control barrier functions that guarantee safety and recursive feasibility for constrained nonlinear systems.
Resumen
The paper presents an approach to design control barrier functions (CBFs) using the notion of dynamic safety margins (DSMs). It is shown that DSMs are CBFs for an augmented system that includes the reference of a prestabilizing controller as a state. This allows leveraging established tools from the explicit reference governor (ERG) framework to synthesize CBFs.
The key highlights are:
- DSMs are shown to be CBFs for an augmented system, enabling the design of CBFs using the ERG framework.
- The proposed DSM-based CBF approach can handle multiple state and input constraints using the control-sharing property of CBFs.
- The method makes no assumption on the relative degree of the constraints.
- Numerical simulations demonstrate that the DSM-based CBFs outperform existing DSM-based approaches, while guaranteeing safety and recursive feasibility.
- Lyapunov-based DSMs are presented, which trivially satisfy the conditions for the control-sharing property.
- The overhead crane example illustrates the effectiveness of the proposed approach in enforcing various state and input constraints.