Control of Redundant Mechanical Systems Under Equality and Inequality Constraints on Both Input and Constraint Forces
Bibliographic record
Abstract
The equality and inequality constraints on constraint force and/or the actuator force/torque arise in several robotic applications, for which different controllers have been specifically developed. This paper presents a unified approach to control a rather general class of robotic systems with closed loops under a set of linear equality and inequality constraints using the notion of projection operator. The controller does not require the kinematic constraints to be independent, i.e., systems with time-varying topology can be dealt with, while demanding minimum-norm actuation force or torque in the case that the system becomes redundant. The orthogonal decomposition of the control input force yields the null-space component and its orthogonal complement. The null-space component is obtained using the projected inverse dynamics control law, while the orthogonal complement component is found through solving a quadratic programming problem, in which the equality and inequality constraints are derived to be equivalent to the originally specified ones. Finally, a case study is presented to demonstrate how the control technique can be applied to multi-arms manipulation of an object.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 source (direct Gemma or distilled Codex), 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".