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Trac-IK Paper Review

1. Goal

In the paper, author compared some common open-source project address the kinematics problem. I want to know

  • Which optimization method is used behind these popular project
  • How these project compared to each other

2. Introduciton

The main purpose if trac_ik is to improve the popular KDL

Issue with KDL

  • convergence failure

  • stuck in local minima

  • loop for maximum time rather than iteration

  • Detect by $q_{next}-q_{prev}\approx 0$

  • Change to a random seed

  • Failure with joint limit

  • solved with SQP sequential quadratic programming

  • no utilization of tolerance

3. Candidate IK Algorithm

  • KDL-RR

  • Random Restart

  • maximum time

  • SQP: SLSQP with BFGS
    $$
    \arg \min {q \in \mathbf{R}^n}\left(q{\text {seed }}-q\right)^T\left(q_{\text {seed }}-q\right),
    $$

  • SQP-DQ: dual quaternion

  • combine the translation and orientation

  • $$
    \phi_{D Q}=4\left((\log \hat{e}) \cdot(\log \hat{e})^T\right)
    $$

  • SQP-SS and SQP-L2, $p$ as simple 6-element vector

  • SS: $\phi_{S S}=p_{e r r} \cdot p_{e r r}^T$

  • L2: $\phi_{L 2}=\sqrt{p_{e r r} \cdot p_{e r r}^T} .$

  • Trac-ik

  • Run two algorithm at once

  • SQP-SS

  • KDL-RR

  • Use the fastest one