Dynamics of biped robots during a complete gait cycle: Euler-Lagrange vs. Newton-Euler formulations
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Bibliographic record
Abstract
The aim of this report is to derive the equations of motion for biped robot during different walking phases using two well-known formulations: Euler-Lagrange (E-L) and Newton-Euler (N-E) equations. The modeling problems of biped robots lie in their varying configurations during locomotion. They could be fully actuated during the single support phase (SSP) and overactuated during the double support phase (DSP). Therefore, first, the E-L equations of 6-link biped robot are described in some details for dynamic modeling during different walking phases with concentration on the DSP. Second, the detailed description of modified recursive Newton-Euler (N-E) formulation (which is very useful for modeling complex robotic system) is illustrated with a novel strategy for solution of the over-actuation/discontinuity problem. The derived equations of motion of the target biped for both formulations are suitable for control laws if the analyzer needs to deal with control problems. As expected, the N-E formulation is superior to the E-L concerning dealing with high degrees-of freedom (DOFs) robotic systems (larger than six DOFs).
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it