Papers

Relaxed IK

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year: 2018 authors: Daniel Rakita, Bilge Mutlu, Michael Gleicher

Data

Abstract

We present a real-time motion-synthesis method forrobot 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.

https://graphics.cs.wisc.edu/Papers/2018/RMG18a/p43.pdf

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Notes

Goal: achieve smooth feasible motions. Done with weighted-sum non-linear optimization problem.

  • Problem Formulation
    • Match the end-effector pose goal corresponding to goal positon and goal orientation as precisely and quickly as possible without sacrificing robot configuration feasibility
    • feasibility defined by not breaking velocity limits upon consecutive solutions (no joint space discontinuities), no self collisions, and no singularities.
    • Expectation: solving discrete IK problems at each update with this goal, will yield continuous and feasible motions in a sequence.
      • Not sure why I should believe this without look ahead, but maybe there is lookahead?
    • the end-effector constraint is not a hard constraint, pose goals can be relaxed in favor of feasibility or other important properties.
    • you can statically or dynamically weight each term to determine how important each feature is relative to each other.
  • Optimization
    • I get the gist, but I lack the mathematical optimization context to really grok this.
      • good reason to read more textbooks :)
    • A NN estimates some important quantity - but I once again did not really grok it on the once over. I want to read some more optimization/kinematics content and return to this paper. and

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