{
  "schemaVersion": 1,
  "assumptions": {
    "lengthM": 1.1779260039329529,
    "massKg": 44.298666240233715,
    "densityKgM3": 1000,
    "scaleMetersPerUnit": 1,
    "volumeM3": 0.044298666240233715,
    "centerOfMassM": [
      -0.033683354376165195,
      -0.0016793824703048197,
      0.24173852321860162
    ],
    "inertiaKgM2": [
      [
        0.5776080884500744,
        -0.033266547745268556,
        -0.04938965552303185
      ],
      [
        -0.033266547745268556,
        2.5022194703403087,
        -0.000668960945965471
      ],
      [
        -0.04938965552303185,
        -0.000668960945965471,
        2.4773743055489055
      ]
    ],
    "distanceM": 1.1741478859239904,
    "durationSeconds": 8,
    "speedMs": 0.1467684857404988,
    "strideSeconds": 2,
    "dutyFactor": 0.8,
    "frictionCoefficient": 0.7,
    "gravityMs2": 9.81,
    "swingClearanceM": 0.038,
    "maxLegExtensionFraction": 0.975
  },
  "results": {
    "balanced": {
      "workJ": 352.9609454891661,
      "positiveWorkJ": 179.12853352940078,
      "negativeWorkJ": 173.8324119597653,
      "costOfTransport": 0.6917420804407466
    },
    "optimized": {
      "workJ": 328.9518455274967,
      "positiveWorkJ": 167.28683864647036,
      "negativeWorkJ": 161.66500688102627,
      "costOfTransport": 0.6446884192092526
    }
  },
  "workReductionPercent": 6.80219731630517,
  "search": {
    "gridSamples": 1836,
    "feasibleSamples": 643,
    "spacingM": 0.001,
    "heightOffsetM": 0.011000000000000027,
    "forwardFootOffsetM": 0.015000000000000034,
    "heightRangeM": [
      -0.02,
      0.015
    ],
    "forwardRangeM": [
      -0.025,
      0.025
    ]
  },
  "interpretation": "The best sampled posture raises the body by 11 mm and moves each foot placement 15 mm forward. It reduces both positive and negative joint work while keeping the same weight-shift path, speed, step timing and recorded secondary motion.",
  "optimalityScope": "Lowest verified work among the sampled postures and common foot offsets. Body weight-shift path, cadence and contact sequence are held fixed. No global or metabolic optimality claim.",
  "modes": [
    {
      "id": "video",
      "label": "Video reference",
      "clip": "Walk from video",
      "summary": "Back height follows the video markers, with the original fitted footfalls."
    },
    {
      "id": "balanced",
      "label": "Balanced start",
      "clip": "Balanced starting gait",
      "summary": "353 J of modeled joint work \u00b7 supported crawl at the reference\u2019s average speed."
    },
    {
      "id": "optimized",
      "label": "Less joint work",
      "clip": "Lower joint work",
      "summary": "6.8% less modeled joint work \u00b7 same speed, step timing and recorded secondary motion."
    }
  ],
  "validation": {
    "balanced": {
      "force_balance_max_bodyweights": 3.330849780364482e-16,
      "moment_balance_max_bw_m": 5.898062309593993e-17,
      "friction_cone_max_violation_bw": 0.0,
      "minimum_normal_force_bw": 0.0,
      "swing_force_max_bw": 0.0,
      "max_leg_extension_fraction": 0.9697743374081297,
      "bone_length_error_m": 2.0816681711721685e-16,
      "stance_foot_drift_m": 0.0,
      "joint_power_recompute_max_error_w": 0.0,
      "absolute_joint_work_j": 352.9609454891661,
      "positive_joint_work_j": 179.12853352940078,
      "negative_joint_work_j": 173.8324119597653,
      "forward_integration_max_position_error_m": 1.021405182655144e-14,
      "support_samples": 769,
      "support_hz": 96,
      "quadrature_24_vs_96_hz_difference_percent": 1.4933680099030053,
      "peak_horizontal_acceleration_m_s2": 0.46532128432009556,
      "peak_vertical_acceleration_m_s2": 0.029887261292014945,
      "peak_foot_load_bodyweights": 0.5514659732212034,
      "body_height_offset_range_m": [
        -0.040701642572326155,
        -0.039856648114099114
      ]
    },
    "optimized": {
      "force_balance_max_bodyweights": 3.33402798339899e-16,
      "moment_balance_max_bw_m": 7.473425314851612e-17,
      "friction_cone_max_violation_bw": 0.0,
      "minimum_normal_force_bw": 0.0,
      "swing_force_max_bw": 0.0,
      "max_leg_extension_fraction": 0.9723927674728934,
      "bone_length_error_m": 2.498001805406602e-16,
      "stance_foot_drift_m": 0.0,
      "joint_power_recompute_max_error_w": 1.6261765267699957e-08,
      "absolute_joint_work_j": 328.9518455274967,
      "positive_joint_work_j": 167.28683864647036,
      "negative_joint_work_j": 161.66500688102627,
      "forward_integration_max_position_error_m": 1.021405182655144e-14,
      "support_samples": 769,
      "support_hz": 96,
      "quadrature_24_vs_96_hz_difference_percent": 1.6522405181398883,
      "peak_horizontal_acceleration_m_s2": 0.46532128432009556,
      "peak_vertical_acceleration_m_s2": 0.029887261292014945,
      "peak_foot_load_bodyweights": 0.5776175877334847,
      "body_height_offset_range_m": [
        -0.029701642572326128,
        -0.028856648114099083
      ]
    },
    "work_reduction_percent": 6.80219731630517,
    "scope": "Independent NumPy recomputation of joint work and 769 samples of force, moment, contact and friction constraints, plus forward integration of the prescribed force schedule. A reduced model, not a full musculoskeletal simulation or a global optimum."
  },
  "rigValidation": {
    "Balanced starting gait": {
      "max_ik_error_m": 4.45125186801712e-07,
      "max_stance_drift_m": 5.352504567999187e-07,
      "lowest_sampled_mesh_z_m": -0.0007551210001111031,
      "secondary_local_transform_max_error": 0.0,
      "hip_attachment_max_error_m": 4.973500717788212e-07
    },
    "Lower joint work": {
      "max_ik_error_m": 4.864639587714261e-07,
      "max_stance_drift_m": 6.753469451354779e-07,
      "lowest_sampled_mesh_z_m": -0.0004794010892510414,
      "secondary_local_transform_max_error": 0.0,
      "hip_attachment_max_error_m": 4.927605729150236e-07
    }
  },
  "exportValidation": {
    "mesh_reimport_comparisons": {
      "Walk from video": [
        {
          "seconds": 0.0,
          "max_vertex_error_m": 6.5073091130957756e-06,
          "mean_vertex_error_m": 2.0029895543966673e-07
        },
        {
          "seconds": 1.0,
          "max_vertex_error_m": 1.295625117720575e-05,
          "mean_vertex_error_m": 2.4654196992020254e-07
        },
        {
          "seconds": 2.6666666666666665,
          "max_vertex_error_m": 1.1069637281325572e-05,
          "mean_vertex_error_m": 3.856573730645647e-07
        },
        {
          "seconds": 4.0,
          "max_vertex_error_m": 1.4374276759360944e-05,
          "mean_vertex_error_m": 5.7096489833419e-07
        },
        {
          "seconds": 6.0,
          "max_vertex_error_m": 8.747489311717398e-06,
          "mean_vertex_error_m": 8.025704687160469e-07
        },
        {
          "seconds": 8.0,
          "max_vertex_error_m": 6.4262413017971344e-06,
          "mean_vertex_error_m": 9.577521072121404e-07
        }
      ],
      "Balanced starting gait": [
        {
          "seconds": 0.0,
          "max_vertex_error_m": 9.35897616756973e-06,
          "mean_vertex_error_m": 1.7738316012464182e-07
        },
        {
          "seconds": 1.0,
          "max_vertex_error_m": 9.228307293611161e-06,
          "mean_vertex_error_m": 2.4052546041300786e-07
        },
        {
          "seconds": 2.6666666666666665,
          "max_vertex_error_m": 1.5417921205309956e-05,
          "mean_vertex_error_m": 4.325481905951393e-07
        },
        {
          "seconds": 4.0,
          "max_vertex_error_m": 1.4761864122905773e-05,
          "mean_vertex_error_m": 5.967748861303133e-07
        },
        {
          "seconds": 6.0,
          "max_vertex_error_m": 1.7517992947415905e-05,
          "mean_vertex_error_m": 7.164618383309544e-07
        },
        {
          "seconds": 8.0,
          "max_vertex_error_m": 1.418569414648584e-05,
          "mean_vertex_error_m": 9.410992290366232e-07
        }
      ],
      "Lower joint work": [
        {
          "seconds": 0.0,
          "max_vertex_error_m": 8.725825961957079e-06,
          "mean_vertex_error_m": 1.7142816851341205e-07
        },
        {
          "seconds": 1.0,
          "max_vertex_error_m": 1.0401130597185114e-05,
          "mean_vertex_error_m": 2.580215312227792e-07
        },
        {
          "seconds": 2.6666666666666665,
          "max_vertex_error_m": 1.764998669670812e-05,
          "mean_vertex_error_m": 4.0260305951903606e-07
        },
        {
          "seconds": 4.0,
          "max_vertex_error_m": 1.433094532782347e-05,
          "mean_vertex_error_m": 5.653865823474827e-07
        },
        {
          "seconds": 6.0,
          "max_vertex_error_m": 1.7182113115223916e-05,
          "mean_vertex_error_m": 7.007520733450756e-07
        },
        {
          "seconds": 8.0,
          "max_vertex_error_m": 1.3640171666483993e-05,
          "mean_vertex_error_m": 8.890064303334964e-07
        }
      ]
    },
    "actual_rig_vs_model_max_knee_error_m": {
      "Balanced starting gait": 4.819183084925143e-07,
      "Lower joint work": 5.611998632477411e-07
    },
    "sampled_render_review": "Physical clips preserve their previously inspected mesh poses. The corrected video clip has separate render and body-height validation."
  },
  "sourceModelSha256": "6e5ec15aafdc6068f407aa0d5efa0b39a7f1567017a6ce659b34e5ef0cdf4150",
  "sourceMotionSha256": "7130539a8aca310d46a30049b156d07a15385cfbc6fa1bcff70c6b8df883e101",
  "sources": [
    {
      "title": "Competing Models of Work in Quadrupedal Walking",
      "url": "https://www.frontiersin.org/journals/bioengineering-and-biotechnology/articles/10.3389/fbioe.2022.826336/full"
    },
    {
      "title": "CasADi documentation",
      "url": "https://web.casadi.org/docs/"
    }
  ],
  "videoReferenceRevision": "Body height corrected against dorsal video markers; visible skin residuals refitted. The physical comparison clips retain their original numerical trajectories and secondary channels."
}