  Safe autonomy is important in many application domains, especially for
applications involving interactions with humans. Existing safe control
algorithms are similar to one another in the sense that: they all provide
control inputs to maintain a low value of an energy function that measures
safety. In different methods, the energy function is called a potential
function, a safety index, or a barrier function. The connections and relative
advantages among these methods remain unclear. This paper introduces a unified
framework to derive safe control laws using energy functions. We demonstrate
how to integrate existing controllers based on potential field method, safe set
algorithm, barrier function method, and sliding mode algorithm into this
unified framework. In addition to theoretical comparison, this paper also
introduces a benchmark which implements and compares existing methods on a
variety of problems with different system dynamics and interaction modes. Based
on the comparison results, a new method, called the sublevel safe set
algorithm, is derived under the unified framework by optimizing the
hyperparameters. The proposed algorithm achieves the best performance in terms
of safety and efficiency on the vast majority of benchmark tests.
