Signal temporal logic (STL) has gained popularity in robotics for expressing
complex specifications that may involve timing requirements or deadlines. While
the control synthesis for STL specifications without nested temporal operators
has been studied in the literature, the case of nested temporal operators is
substantially more challenging and requires new theoretical advancements. In
this work, we propose an efficient continuous-time control synthesis framework
for nonlinear systems under nested STL specifications. The framework is based
on the notions of signal temporal logic tree (sTLT) and control barrier
function (CBF). In particular, we detail the construction of an sTLT from a
given STL formula and a continuous-time dynamical system, the sTLT semantics
(i.e., satisfaction condition), and the equivalence or under-approximation
relation between sTLT and STL. Leveraging the fact that the satisfaction
condition of an sTLT is essentially keeping the state within certain sets
during certain time intervals, it provides explicit guidelines for the CBF
design. The resulting controller is obtained through the utilization of an
online CBF-based program coupled with an event-triggered scheme for online
updating the activation time interval of each CBF, with which the correctness
of the system behavior can be established by construction. We demonstrate the
efficacy of the proposed method for single-integrator and unicycle models under
nested STL formulas.Comment: Link to accompanying code: https://github.com/xiaotanKTH/sTL