A convex polynomial model for planar sliding mechanics: theory, application, and experimental validation
A convex polynomial model for planar sliding mechanics: theory, application, and experimental validation
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DOI：
10.1177/0278364918755536
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发表时间：
2018-03
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影响因子：
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通讯作者：
Jiaji Zhou;M. T. Mason;R. Paolini;J. Bagnell
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文献类型：
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作者：
Jiaji Zhou;M. T. Mason;R. Paolini;J. Bagnell
提出了平面滑动力学的多项式模型。对于力-运动映射，我们将广义摩擦载荷集视为多项式的1-子级集，其梯度方向对应于广义速度。为了满足最大功不等式、对称性、尺度形状不变性和快速可逆性，该多项式被限定为凸偶次齐次多项式。我们提出了一个简单的和统计上有效的模型识别过程中使用的平方和凸松弛。然后，我们推导出的运动学接触模型，解决了接触模式和瞬时物体运动给定的位置控制的机械手的行动。固有的随机物体表面摩擦分布的采样多项式参数保持平方和凸分布建模。由于模型的平滑性，贴片接触的力学被捕获，同时在支撑点处没有模式选择的情况下计算效率高。仿真和机器人实验的推动和抓取验证了我们的方法的准确性和效率。
We propose a polynomial model for planar sliding mechanics. For the force–motion mapping, we treat the set of generalized friction loads as the 1-sublevel set of a polynomial whose gradient directions correspond to generalized velocities. The polynomial is confined to be convex even-degree homogeneous in order to obey the maximum work inequality, symmetry, shape invariance in scale, and fast invertibility. We present a simple and statistically efficient model identification procedure using a sum-of-squares convex relaxation. We then derive the kinematic contact model that resolves the contact modes and instantaneous object motion given a position controlled manipulator action. The inherently stochastic object-to-surface friction distributions are modeled by sampling polynomial parameters from distributions that preserve sum-of-squares convexity. Thanks to the model smoothness, the mechanics of patch contact is captured while being computationally efficient without mode selection at support points. Simulation and robotic experiments on pushing and grasping validate the accuracy and efficiency of our approach.