Control Synthesis using Signal Temporal Logic Specifications with Integral and Derivative Predicates

In many applications, the integrals and derivatives of signals carry valuable information (e.g., cumulative success over a time window, the rate of change) regarding the behavior of the underlying system. In this paper, we extend the expressiveness of Signal Temporal Logic (STL) by introducing predicates that can define rich properties related to the integral and derivative of a signal. For control synthesis, the new predicates are encoded into mixed-integer linear inequalities and are used in the formulation of a mixed-integer linear program to find a trajectory that satisfies an STL specification. We discuss the benefits of using the new predicates and illustrate them in a case study showing the influence of the new predicates on the trajectories of an autonomous robot.

Decentralized Safe Reactive Planning under TWTL Specifications

We investigate a multi-agent planning problem, where each agent aims to achieve an individual task while avoiding collisions with others. We assume that each agent's task is expressed as a Time-Window Temporal Logic (TWTL) specification defined over a 3D environment. We propose a decentralized receding horizon algorithm for online planning of trajectories. We show that when the environment is sufficiently connected, the resulting agent trajectories are always safe (collision-free) and lead to the satisfaction of the TWTL specifications or their finite temporal relaxations. Accordingly, deadlocks are always avoided and each agent is guaranteed to safely achieve its task with a finite time-delay in the worst case. Performance of the proposed algorithm is demonstrated via numerical simulations and experiments with quadrotors.