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Bottom-up hybrid control and planning synthesis with application to multi-robot multi-human coordination

Periodic Reporting for period 4 - BUCOPHSYS (Bottom-up hybrid control and planning synthesis with application to multi-robot multi-human coordination)

Reporting period: 2019-09-01 to 2020-08-31

Motivated by a large subset of today’s control engineering applications, which necessitate the treatment of systems with multiple components that are interconnected with each other, rather than the traditional single plant paradigm, this project is focused on the decentralized coordination of interconnected systems under complex specifications. The individual subsystems, also called agents, may need to fulfil different and possibly conflicting tasks in a real-time manner. An example of this situation is the case of heterogeneous robotic teams, where robots are deployed by different users in the same environment and need to fulfil individual and thus potentially conflicting specifications. At the same time, the individual subsystems may need to fulfill certain coupled state constraints, such as maximum relative distances in mobile sensor networks and minimum safety distances which ensure collision avoidance in robotics and transportation applications.

The deployment of multi-robot teams has various important applications including search and rescue missions in hazardous environments, high precision assembly tasks, collaborative load transportation, inspection and repair of infrastructures, assistance for healthcare, as well as manufacturing logistics related activities, to name a few. Multi-robot cooperation allows the accomplishment of complex tasks that would otherwise be impossible by one single robot. In addition, through the multi-component paradigm several desired system attributes are enhanced, such as scalability, adaptability to changes in the workspace and new agents being added to the system, fault tolerance, reduction of computational load, reliability and robustness.

The project’s primary goal is to fuse decentralized control at the continuous state level with discrete planning at the task level. Continuous-time control involves both coupled constraints between the agents as well as driving the multi-agent group to a desired configuration in the state space. Multi-agent task planning involves high level specifications such as combinations of surveillance, sequencing, safety, request response, and many others, which are usually modelled through formal languages and their discrete automata representations. Our goal is to elaborate on decentralized planning in both the continuous and discrete domains. Along this line, the project's objectives are summarized in (i) introducing a systematic framework which incorporates coupled constraints in cooperative control at the continuous layer, (ii) addressing the problem of distributed initial task allocation to the agents combined with real-time task planning in a coordinated manner at the discrete layer, and, (iii) introducing unification approaches, involving distributed coordination and planning both at the control and task levels, which have been up to now centralized since they basically treat the multi-agent team as a single entity.
Towards the project’s objectives, we have elaborated on cooperative multi-agent control under coupled constraints and collaborative planning under local, possibly conflicting, discrete specifications, as well as the development of hybrid control schemes which take into account both aforementioned aspects in a unified way. Furthermore, we have presented results on the systematic fusion between continuous control and discrete planning in a framework which incorporates dynamical system properties of the agents’ hybrid behavior.
More specifically, novel results have been obtained in the direction of cooperative multi-agent control under coupled constraints. In particular, we have developed robust network connectivity maintenance control protocols, and have addressed distance and orientation based formation control for nonlinear dynamic agents. We have also addressed the problem of cooperative object transportation and developed Nonlinear Model Predictive Control schemes for uncertain nonlinear agent navigation in workspaces with obstacles. Furthermore, we developed an aperiodic model predictive control framework for nonlinear continuous-time systems, in order to take into account the restrictions on the agents’ individual computational and energy resources. We have further derived results on time-varying feedback control laws such as funnel controller or time varying control barrier functions for multi-agent systems that are coupled by local and possibly conflicting spatiotemporal constraints
Towards cooperative task planning under local agent specifications, we have proposed efficient procedures for discrete plan synthesis under complex temporal tasks. In order to further reduce the computational complexity, we also decomposed the plan synthesis problem into finite horizon planning problems that are solved iteratively, upon the run of the agents. Furthermore, we have provided results on cooperative multi-agent task planning under timing constraints using timed logics and introduced quantifiable mission guarantees in the presence of uncertainties via probabilistic model checking techniques. Furthermore, decompositions of a finite time global specifications into sets of independently executable tasks have been addressed and bottom-up coordination strategies for heterogeneous agent groups have been derived. Beyond these qualitative temporal specifications, we have proposed an efficient planning framework for fully quantitative temporal specifications, such as signal temporal logic, by creating a timed signal transducer that is equivalent to the specification while simulating the controlled system according to control laws from the first objective.
In order to provide a correct by design and distributed solution to the hybrid coordination of coupled multi-agent systems under high level specifications, we have derived distributed symbolic models for the agents which can be utilized by leveraging tools from formal verification. These symbolic models have been leveraged in order to build an automated controller synthesis framework for coupled multi-agent systems under timed MITL specifications. We also obtained distributed abstractions through a cell partition of the agents’ workspace and a time quantization for general invariant domains and allows each agent to perform multiple transitions from each discrete state. With respect to symbolic abstraction-based methods, we have derived a new framework based on over- and under-approximating the event-triggering mechanism for periodic event-triggering systems. We also derived new abstraction methods via feedback refinement by using static and dynamic quantizers for nonlinear systems with time delay. In addition, to compensate for potential mission unsatisfaction due to insufficient detail of the discrete representations, we introduced an automated abstraction refinement scheme, which iteratively refines an initial coarse abstraction until the specification is satisfied on the refined discretization. We have made further progress in the direction of abstraction-free control under quantitative temporal specifications by effectively combining results from the first and second objective for purely quantitative specifications using decentralised feedback control laws from the first objective.
In addition, dynamical system properties of the multi-agent hybrid systems were considered in a framework where satisfiability of a high level plan which can be decomposed into a sequence of simple control objectives is proven by leveraging hybrid stability tools. Furthermore, appropriate barrier certificates were exploited to guarantee existence of a finite hybrid time where all solutions of the system will reach a desired subset of the continuous-specification domain. Complementary to this approach, we also we incorporated the metric robustness property of continuous control systems into the hybrid agent-specification domain, by leveraging tools from the quantitative Signal Temporal Logic formalism.
Finally, we developed a practical hybrid control strategy for motion planning of a multi-agent teams under both qualitative and quantitative specifications based on decentralized funnel and control barrier function type controllers while ensuring collision avoidance based on local agent information. These results have been experimentally validated in the Smart Mobility Lab (SML) of the KTH Electrical Engineering School.
The obtained results so far in the project contain several novel and interdisciplinary approaches which were required in order to address the objectives at hand. In particular, the outcome of the results includes a successful merging of techniques and concepts from robust multi-agent control, robotics, computer science, and hybrid systems. In addition, new concepts and techniques have been developed in order to address the needs of the corresponding problem formulations and approaches. Among the main novelties of the results we summarize the following:
Applying receding horizon approaches in order to address multi-agent high level planning in a bottom up manner with guaranteed computational complexity reduction is new since previous results were focused on the single plant case.
Incorporating quantifiable robustness in the design of cooperative multi-agent protocols and leveraging these results for the derivation of distributed abstractions is also new. In particular, there exist no prior results which capture the coupled agents’ motion capabilities through discrete representations in a purely decentralized manner. Furthermore, the derivation of such models in an online manner has been successfully formulated.
Another novel direction is the consideration of time constraints in temporal logic-based multi-agent control synthesis. These results have also been fused with multi-agent planning under continuous coupled constraints for the first time, by leveraging the agents’ distributed symbolic models.
A novelty of the project is the introduction of time-varying feedback control laws such as control barrier functions for multi-agent systems that are coupled by local and possibly conflicting spatiotemporal constraints. This approach is in particular unconventional since the use of spatiotemporal constraints has not been considered before, requiring new design methodologies and novel ways of thinking.
Combining both abstraction refinement and specification revision in a standalone framework constitutes another novel direction which provides solutions to potential plan infeasibility both at the discrete layer and at the interface between the continuous system and its discrete representations. Furthermore, compositional abstraction refinement algorithms have been proposed which provide the desired scalability of the methodology.
The consideration of new robust Signal Temporal Logic (STL) semantics provides a novel and convenient framework for control synthesis, due to their linearity with respect to the temporal operators. In addition, the robust semantics of STL allowed for a new discretization free approach in the context of formal methods-based multi-agent control with guaranteed computational complexity reduction.
Finally, incorporating dynamical systems notions in the hybrid continuous-specification domain has paved the way to leverage hybrid analysis tools for the multi-agent task planning and provides a promising solid theoretical framework for the qualitative study of such systems’ behavior.
The outcome of the project is summarized in successful results towards all of the project’s objectives.