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Planning for real world problems with explicit temporal constraints is a challenging problem. Among several approaches, the use of flexible timelines in Planning and Scheduling (P&S) has demonstrated to be successful in a number of concrete applications, such as, for instance, autonomous space systems. A flexible timeline describes an envelope of possible solutions which can be exploited by an executive system for robust on-line execution. A remarkable research effort has been dedicated to design, build and deploy software environments, like EUROPA, ASPEN, and APSI-TRF, for the synthesis of timeline-based P&S applications. Several attempts have also been made to characterize the concept of timelines. Nevertheless, a formal characterization of flexible timelines and plans is still missing.\ud \ud This paper presents a formal account of flexible timelines aiming at providing a general semantics for related planning concepts such as domains, goals, problems, constraints and flexible plans. Some basic properties of the defined concepts are also stated and proved. A simple running example inspired by a real world planning domain is exploited to illustrate the proposed formal notions. Finally, a planning tool, called Extensible Planning and Scheduling Library (EPSL), is briefly presented, which is able to generate flexible plans that are compliant with the given semantics

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Combining task and motion planning efficiently in human-robot collaboration (HRC) entails several challenges because of the uncertainty conveyed by the human behavior. Tasks plan execution should be continuously monitored and updated based on the actual behavior of the human and the robot to maintain productivity and safety. We propose control-based approach based on two layers, i.e., task planning and action planning. Each layer reasons at a different level of abstraction: task planning considers high-level operations without taking into account their motion properties; action planning optimizes the execution of high-level operations based on current human state and geometric reasoning. The result is a hierarchical framework where the bottom layer gives feedback to top layer about the feasibility of each task, and the top layer uses this feedback to (re)optimize the process plan. The method is applied to an industrial case study in which a robot and a human worker cooperate to assemble a mosaic.

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