Absolute Stability of Multi-DOF Multilateral Haptic Systems
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Bibliographic record
Abstract
Multi-degree-of-freedom (DOF) multilateral haptic systems involve teleoperation of several robots in physical environments by several human operators or collaborative interaction of several human operators in a virtual environment. An m-DOF n-lateral haptic system can be modeled as an n-port network where each port (terminal) connects to a termination defined by m inputs and m outputs. The stability analysis of such systems is not trivial due to dynamic coupling across the different DOFs of the robots, the human operators, and the physical/virtual environments, and unknown dynamics of the human operators and the environments exacerbate the problem. Llewellyn's criterion only allows for absolute stability analysis of 1-DOF bilateral haptic systems (m = 1 and n = 2), which can be modeled as two-port networks. The absolute stability of a general m-DOF bilateral haptic system where m >1 cannot be obtained from m applications of Llewellyn's criterion to each DOF of the bilateral system. In addition, if we were to use Llewellyn's criterion for absolute stability analysis of a general 1-DOF n-lateral haptic system where n- 2, we would need to couple n > 2 terminations of the n-port network to (an infinite number of) known impedances to reduce it to an equivalent two-port network; this is a cumbersome process that involves an infinite number of applications of Llewellyn's criterion. In this brief, we present a straightforward and convenient criterion for absolute stability analysis of a class of m-DOF n-lateral haptic systems for any m ≥ 1 and n ≥ 2. As case studies, a 1-DOF trilateral and a 2-DOF bilateral haptic system are studied for absolute stability with simulations and experiments confirming the theoretical stability conditions.
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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 | 0.000 | 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 | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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