Using large language models (LLMs) to solve complex robotics problems requires understanding their planning capabilities. Yet while we know that LLMs can plan on some problems, the extent to which these planning capabilities cover the space of robotics tasks is unclear. One promising direction is to integrate the semantic knowledge of LLMs with the formal reasoning of task and motion planning (TAMP). However, the myriad of choices for how to integrate LLMs within TAMP complicates the design of such systems. We develop 16 algorithms that use Gemini 2.5 Flash to substitute key TAMP components. Our zero-shot experiments across 4,950 problems and three domains reveal that the Gemini-based planners exhibit lower success rates and higher planning times than their engineered counterparts. We show that providing geometric details increases the number of task-planning errors compared to pure PDDL descriptions, and that (faster) non-reasoning LLM variants outperform (slower) reasoning variants in most cases, since the TAMP system can direct the LLM to correct its mistakes.

We consider a bilevel learning framework for learning linear operators. In this framework, the learnable parameters are optimized via a loss function that also depends on the minimizer of a convex optimization problem (denoted lower-level problem). We utilize an iterative algorithm called `piggyback' to compute the gradient of the loss and minimizer of the lower-level problem. Given that the lower-level problem is solved numerically, the loss function and thus its gradient can only be computed inexactly. To estimate the accuracy of the computed hypergradient, we derive an a-posteriori error bound, which provides guides for setting the tolerance for the lower-level problem, as well as the piggyback algorithm. To efficiently solve the upper-level optimization, we also propose an adaptive method for choosing a suitable step-size. To illustrate the proposed method, we consider a few learned regularizer problems, such as training an input-convex neural network.

Generating stable and robust grasps on arbitrary objects is critical for dexterous robotic hands, marking a significant step towards advanced dexterous manipulation. Previous studies have mostly focused on improving differentiable grasping metrics with the assumption of precisely known object geometry. However, shape uncertainty is ubiquitous due to noisy and partial shape observations, which introduce challenges in grasp planning. We propose, SpringGrasp planner, a planner that considers uncertain observations of the object surface for synthesizing compliant dexterous grasps. A compliant dexterous grasp could minimize the effect of unexpected contact with the object, leading to more stable grasp with shape-uncertain objects. We introduce an analytical and differentiable metric, SpringGrasp metric, that evaluates the dynamic behavior of the entire compliant grasping process. Planning with SpringGrasp planner, our method achieves a grasp success rate of 89% from two viewpoints and 84% from a single viewpoints in experiment with a real robot on 14 common objects. Compared with a force-closure based planner, our method achieves at least 18% higher grasp success rate.

Variational regularization is commonly used to solve linear inverse problems, and involves augmenting a data fidelity by a regularizer. The regularizer is used to promote a priori information and is weighted by a regularization parameter. Selection of an appropriate regularization parameter is critical, with various choices leading to very different reconstructions. Classical strategies used to determine a suitable parameter value include the discrepancy principle and the L-curve criterion, and in recent years a supervised machine learning approach called bilevel learning has been employed. Bilevel learning is a powerful framework to determine optimal parameters and involves solving a nested optimization problem. While previous strategies enjoy various theoretical results, the well-posedness of bilevel learning in this setting is still an open question. In particular, a necessary property is positivity of the determined regularization parameter. In this work, we provide a new condition that better characterizes positivity of optimal regularization parameters than the existing theory. Numerical results verify and explore this new condition for both small and high-dimensional problems.