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.

@Article{RMG20a,
  author       = "Rakita, Daniel and Mutlu, Bilge and Gleicher, Michael",
  title        = "An Analysis of RelaxedIK: An Optimization-based Framework for Generating Accurate and Feasible Robot Arm Motions",
  journal      = "Autonomous Robots",
  number       = "7",
  volume       = "44",
  pages        = "1341--1358",
  month        = "jul",
  year         = "2020",
  doi          = "10.1007/s10514-020-09918-9",
  url          = "http://graphics.cs.wisc.edu/Papers/2020/RMG20a"
}