Improved Approximation Accuracy for Nonconvex Trajectory Optimization via Trajectory Sensitivities
Bibliographic record
Abstract
Trajectory optimization is valuable for a wide range of applications, from motion planning for mobile robots, to aircraft flight planning. However, nonlinear dynamic models lead to challenging nonconvex trajectory optimization problems. Many existing approaches formulate them as multistage programs and rely on derivatives of each stage to obtain a local approximation at each iteration, in which case quality of approximation when solving the optimization program has significant impact on convergence behavior. In this work, we develop a novel approach for obtaining improved local approximations when solving nonconvex trajectory optimization problems. By performing an input-to-state reformulation of system dynamics, we use trajectory sensitivities, which are derivatives of the entire system trajectory with respect to control inputs, to form local approximations. Local convergence guarantees for the proposed method are presented. The method is applied to generate trajectories for an autonomous vehicle, and is extended to include scenario with static obstacles. Simulation on a variety of reference paths show that the proposed method outperforms the traditional Sequential Quadratic Programming (SQP) in terms of local approximation accuracy, allowable trust-region radius, iterations to converge, and total solver time, and is less prone to failure when handling multiple obstacles with a complex reference.
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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 | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".