We present a real-time motion-synthesis method for robot manipulators, called RelaxedIK, that is able to not only accurately match end-effector pose goals as done by traditional IK solvers, but also create smooth, feasible motions that avoid joint-space discontinuities, self-collisions, and kinematic singularities. To achieve these objectives on-the-fly, we cast the standard IK formulation as a weighted-sum non-linear optimization problem, such that motion goals in addition to end-effector pose matching can be encoded as terms in the sum. We present a normalization procedure such that our method is able to effectively make trade-offs to simultaneously reconcile many, and potentially competing, objectives. Using these trade-offs, our formulation allows features to be relaxed when in conflict with other features deemed more important at a given time. We compare performance against a state-of-the-art IK solver and a real-time motion-planning approach in several geometric and real-world tasks on seven robot platforms ranging from 5-DOF to 8-DOF. We show that our method achieves motions that effectively follow position and orientation end-effector goals without sacrificing motion feasibility, resulting in more successful execution of tasks compared to the baseline approaches. We also empirically evaluate how our solver performs with different optimization solvers, gradient calculation methods, and choice of loss function in the objective function.

中文翻译：

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对RelaxedIK的分析：一个基于优化的框架，用于生成准确且可行的机器人手臂运动

我们提出了一种用于机器人操纵器的实时运动合成方法，称为RelaxedIK，该方法不仅可以像传统IK解算器一样精确匹配末端执行器姿势目标，而且还可以创建平滑，可行的运动，从而避免关节空间不连续，自碰撞和运动学奇点。为了即时实现这些目标，我们将标准IK公式转换为加权总和非线性优化问题，以便可以将除末端执行器姿势匹配之外的运动目标编码为总和项。我们提出了一种标准化程序，以使我们的方法能够有效地权衡取舍，以同时调和许多并可能相互竞争的目标。利用这些权衡，我们的公式允许放松特征与在给定时间被认为更重要的其他功能冲突时。我们将性能与最先进的IK解算器和实时运动计划方法进行了比较，这些方法在从5自由度到8自由度的七个机器人平台上的几个几何和实际任务中进行。我们表明，我们的方法实现的运动可以有效地遵循位置和方向末端执行器的目标，而不会牺牲运动的可行性，与基线方法相比，可以更成功地执行任务。我们还根据经验评估求解器在不同的优化求解器，梯度计算方法以及目标函数中损耗函数的选择下的性能。