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This study focuses on addressing the problem of motion planning within workspaces cluttered with obstacles while considering temporal and input constraints. These specifications can encapsulate intricate high-level objectives involving both temporal and spatial constraints. The existing literature lacks the ability to fulfill time specifications while simultaneously managing input-saturation constraints. The proposed approach introduces a hybrid three-component control algorithm designed to learn the safe execution of a high-level specification expressed as a timed temporal logic formula across predefined regions of interest in the workspace. The first component encompasses a motion controller enabling secure navigation within the minimum allowable time interval dictated by input constraints, facilitating the abstraction of the robot's motion as a timed transition system between regions of interest. The second component utilizes formal verification and convex optimization techniques to derive an optimal high-level timed plan over the mentioned transition system, ensuring adherence to the agent's specification. However, the necessary navigation times and associated costs among regions are initially unknown. Consequently, the algorithm's third component iteratively adjusts the transition system and computes new plans as the agent navigates, acquiring updated information about required time intervals and associated navigation costs. The effectiveness of the proposed scheme is demonstrated through both simulation and experimental studies. [ABSTRACT FROM AUTHOR]

Abstract This paper presents a novel control protocol for distance and orientation formation control of rigid bodies, whose sensing graph is a static and undirected tree, in the special Euclidean group SE (3). The proposed control laws are decentralized, in the sense that each agent uses only local relative information from its neighbors to calculate its control signal, as well as robust with respect to modeling (parametric and structural) uncertainties and external disturbances. The proposed methodology guarantees the satisfaction of inter-agent distance constraints that resemble collision avoidance and connectivity maintenance properties. Moreover, certain predefined functions characterize the transient and steady state performance of the closed loop system. Finally, simulation results verify the validity and efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]