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Passive velocity field control with discontinuous desired fields: Non-smooth potential gradient vector field

机译：具有不连续所需字段的被动速度场控制：非​​平滑电位梯度矢量字段

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摘要

A wide variety of robot tasks cannot be achieved by a smooth velocity field. This paper considers discontinuous desired velocity fields that represent robot tasks. We propose passive velocity field control (PVFC) with discontinuous desired velocity fields. The method deals with a discontinuous field produced by a generalized differential of a non-smooth potential function. The PVFC requires the calculation of a derivative of desired velocity fields. Therefore, we introduce a novel generalized differential of discontinuous vector fields, called disassembled Hessian matrix, which is a second derivative of a non-smooth potential function. Theoretical analysis shows that a closed-loop system with the method satisfies passivity in the sense of the sample-and-hold solution. The simulation result illustrates that the proposed method achieves the same properties of the conventional PVFC, even though the desired velocity field is discontinuous.
机译：通过光滑的速度场无法实现各种机器人任务。本文考虑了代表机器人任务的不连续所需的速度字段。我们提出了具有不连续所需速度场的被动速度场控制（PVFC）。该方法涉及由非平滑电位功能的广义差分产生的不连续的场。 PVFC要求计算所需速度场的衍生物。因此，我们介绍了一种名为拆卸Hessian矩阵的小型广义差分，称为拆卸Hessian矩阵，其是非平滑电位功能的第二导数。理论分析表明，具有该方法的闭环系统满足样品和保持溶液的感觉中的被动。仿真结果表明，即使所需的速度场是不连续的，所提出的方法也可以实现传统PVFC的相同性质。

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