This paper presents a methodology for computation of artificial vector fields that allows a robot to converge to and circulate around generic curves specified in n-dimensional spaces. These vector fields may be directly applied to solve several robotnavigation problems such as border monitoring, surveillance, target tracking, and multirobot pattern generation, with special application to fixed-wing aerial robots, which must keep a positive forward velocity and cannot converge to a single point. Unlike previous solutions found in the literature, the approach is based on fully continuous vector fields and is generalized to time-varying curves defined in n-dimensional spaces. We provide mathematical proofs and present simulation and experimental results that illustrate the applicability of the proposed approach. We also present a methodology for construction of the target curve based on a given set of its samples.

International audienceWhen a robot is highly redundant in comparison to the task to be executed, current control techniques are not " economic " in the sense that they demand, most of the time unnecessarily, all the joints to move. Such behavior can be undesirable for some applications. In this direction, this work proposes a new control paradigm based on linear programming that intrinsically provides a parsimonious control strategy, that is, one in which few joints move. In addition to a formal stability proof, the paper presents simulation and experimental results on the HOAP-3 humanoid robot. Finally, a comparison is made with a least-square method based on the pseudoinverse of the task Jacobian, showing that the proposed method indeed uses fewer joints than the classic one

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This paper addresses the problem of controlling a single mobile robot to converge smoothly to a pre-specified closed curve. Once in the curve, the robot remains circulating along it. The main motivation for this is the control of unmanned airplanes, where the robot cannot converge to a single point. Our control law is based on an artificial vector field that allows for the generalization to time-varying curves defined in n-dimensional spaces. We also present results that may be used to control mobile robots moving with constant speed. We devise convergence proofs and present simulations that verify the proposed approach.

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