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.

@InProceedings{RMG18a,
  author       = "Rakita, Daniel and Mutlu, Bilge and Gleicher, Michael",
  title        = "RelaxedIK: Real-time Synthesis of Accurate and Feasible Robot Arm Motion",
  booktitle    = "Proceedings of Robotics: Science and Systems",
  month        = "jul",
  year         = "2018",
  doi          = "10.15607/RSS.2018.XIV.043",
  url          = "http://graphics.cs.wisc.edu/Papers/2018/RMG18a"
}