Path Following of a Wheeled Mobile Robot Combining Piecewise-Affine Synthesis and Backstepping Approaches
Bibliographic record
Abstract
This paper presents a novel controller synthesis method for the path following problem of a wheeled mobile robot (WMR). The controller synthesis consists of a three- step procedure mixing piecewise-afflne (PWA) techniques with backstepping ideas. In the first step, a PWA controller is designed for the steering torque while assuming the forward velocity is constant. In the second step, a backstepping-type approach is used to include the forward velocity dynamics and design the forward input force. Finally, in the third step, the actuator dynamics are included using backstepping and the input voltage laws are designed. There are three primary advantages to the synthesis method proposed here. First, it includes both the actuator dynamics and a general, non-singular path parameterization. Second, it is a first step toward including hard nonlinearities in the actuator dynamics, which are PWA characteristics. Third, this technique does not require higher-order derivatives of the states as previously suggested techniques that rely solely on backstepping do. This is of fundamental importance given that those derivatives are typically not measured. The proposed method is demonstrated through a numerical example for the case of a circular path.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 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 | 0.001 |
| Research integrity | 0.001 | 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".