Abstract
This paper presents a scalable procedure for time-constrained planning of a class of uncertain nonlinear multi-robot systems. In particular, we consider N robotic agents operating in a workspace which contains regions of interest (RoI), in which atomic propositions for each robot are assigned. The main goal is to design decentralized and robust control laws so that each robot meets an individual high-level specification given as a metric interval temporal logic (MITL), while using only local information based on a limited sensing radius. Furthermore, the robots need to fulfill certain desired transient constraints such as collision avoidance between them. The controllers, which guarantee the transition between regions, consist of two terms: a nominal control input, which is computed online and is the solution of a decentralized finite-horizon optimal control problem (DFHOCP); and an additive state feedback law which is computed offline and guarantees that the real trajectories of the system will belong to a hyper-tube centered along the nominal trajectory. The controllers serve as actions for the individual weighted transition system (WTS) of each robot, and the time duration required for the transition between regions is modeled by a weight. The DFHOCP is solved at every sampling time by each robot and then necessary information is exchanged between neighboring robots. The proposed approach is scalable since it does not require a product computation among the WTS of the robots. The proposed framework is experimentally tested and the results show that the proposed framework is promising for solving real-life robotic as well as industrial applications.
Highlights
Over the last few years, the field of control of multi-robot systems under high-level specifications has been gaining significant attention (Wongpiromsarn et al 2009; Nikou 2019; Kantaros and Zavlanos 2016; Hasanbeig et al 2019; Pant et al 2018, 2019; Raman et al 2014)
Given a robot dynamics and an metric interval temporal logic (MITL) formula, the control design procedure is the following: first, the robot dynamics are abstracted into a weighted transition system (WTS), in which the time duration for navigating between states is modeled by a weight in the WTS; second, an offline product between the WTS and an automaton that accepts the runs that satisfy the given formula is computed; and third, once an accepting run in the product is found, it maps into a sequence of feedback control laws of the robot dynamics
The MITL formulas are interpreted over timed words like the ones produced by a WTS which is given in Definition 8
Summary
Over the last few years, the field of control of multi-robot systems under high-level specifications has been gaining significant attention (Wongpiromsarn et al 2009; Nikou 2019; Kantaros and Zavlanos 2016; Hasanbeig et al 2019; Pant et al 2018, 2019; Raman et al 2014). Controller synthesis for multi-robot systems under MITL specifications has been investigated in Nikou et al (2017, 2018, 2017), Karaman and Frazzoli (2008). The dynamics of the agents were not taken into consideration Issues such as control input saturation and robustness against disturbances were not considered. An algorithm that computes the runs of each agent that in turn map into continuous control laws and provably satisfy the MITL formulas is provided. These control laws correspond to the transitions indicated above.
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