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    "story_id": "mp-2026-09-13-008",
    "source_story_id": "tmp-story-differentiable-ik-charts",
    "edition_id": "mp-2026-09-13-morning-0066",
    "edition_url": "https://themachinepress.com/edition/2026-09-13",
    "position": 8,
    "story_type": "dispatch",
    "section": "robotics",
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    "headline": "A Standard IK Solver Gained the Gradients It Never Exposed",
    "slug": "a-standard-ik-solver-gained-the-gradients-it-never-exposed",
    "dek": "The inverse function theorem recovered differentiable charts from ordinary forward-kinematic Jacobians and guided a real box-moving arm.",
    "summary": "The inverse function theorem recovered differentiable charts from ordinary forward-kinematic Jacobians and guided a real box-moving arm.",
    "body_text": "Most analytic inverse-kinematics functions come from meta-solvers such as IKFast and are difficult to rewrite for gradient-based trajectory optimization. The proposed method recovers gradients of their local solution charts from the ordinary forward-kinematic Jacobian through the inverse function theorem. A least-squares extension preserves useful gradient signal outside the reachable workspace, while an explicit reachability description constrains optimization. Numerical experiments and a hardware demonstration had an RB-Y1 pick up a box and place it on a table. The approach applies where the local chart and selected Jacobian remain regular.",
    "why_it_matters": "The inverse function theorem recovered differentiable charts from ordinary forward-kinematic Jacobians and guided a real box-moving arm.",
    "limitations": [
      "The approach applies where the local chart and selected Jacobian remain regular."
    ],
    "importance": 8,
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    "first_published_at": "2026-09-13T09:00:00.000-04:00",
    "modified_at": "2026-09-13T09:00:00.000-04:00",
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        "text": "The inverse function theorem recovered differentiable charts from ordinary forward-kinematic Jacobians and guided a real box-moving arm.",
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        "qualification": "The approach applies where the local chart and selected Jacobian remain regular."
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    "source_ids": [
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    "tags": [
      "inverse kinematics",
      "trajectory optimization",
      "robot arms"
    ],
    "image_url": "https://themachinepress.com/issues/2026-09-13/differentiable-ik-robot-file.webp",
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  "sources": [
    {
      "source_id": "source-2026-09-13-008",
      "title": "arXiv preprint 2609.10905",
      "publisher": "arXiv",
      "url": "https://arxiv.org/abs/2609.10905",
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      "source_type": "primary_research",
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      "accessed_at": "2026-09-13T08:24:00.000-04:00",
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    "name": "The Machine Press",
    "url": "https://themachinepress.com",
    "description": "A daily newspaper for the age of artificial intelligence."
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  "cite_this_report": {
    "title": "A Standard IK Solver Gained the Gradients It Never Exposed",
    "publisher": "The Machine Press",
    "published_at": "2026-09-13T09:00:00.000-04:00",
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