Stability analysis of trilateral haptic collaboration
Bibliographic record
Abstract
This paper presents a criterion for absolute stability of a general class of three-port networks. Trilateral haptic systems, which have recently found many interesting applications, can be modeled as three-port networks. Traditionally, existing criteria (Llewellyn‘s criterion) have facilitated the stability analysis of bilateral haptic systems modeled as two-port networks. If the same criteria were to be used for stability analysis of a three-port network, its third port would need to be assumed known for it to reduce to a two-port network. However, this is restrictive because, according to the definition of absolute stability, all three terminations of the three-port network must be allowed to be arbitrary (while passive). In this paper, extending Llewellyn's criterion, we present closed-form necessary and sufficient conditions for absolute stability of a general class of three-port networks — the three terminations need to be passive but are otherwise arbitrary. To this end, we first find a symmetrization condition under which a general asymmetric impedance (or admittance) matrix Z <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3×3</inf> has an equivalent symmetric counterpart Zeq; this Zeq models a reciprocal three-port network with the same stability characterization as the general nonreciprocal three-port network modeled by Z. Then, based on the equivalence of passivity and absolute stability for the equivalent reciprocal network, an absolute stability condition for the original nonreciprocal network is derived. To show how the resulting absolute stability criterion can be utilized at the system design stage, we have applied it to the problem of designing controllers for triple-user collaborative haptic virtual environment systems. The validity of the resulting absolute stability conditions have been verified via simulations.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
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) | 0.000 | 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) | 0.003 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".