Online conformal prediction (OCP) wraps around any pre-trained predictor to produce prediction sets with coverage guarantees that hold irrespective of temporal dependencies or distribution shifts. However, standard OCP faces two key limitations: it operates in the output space using simple nonconformity (NC) scores, and it treats all historical observations uniformly when estimating quantiles. This paper introduces attention-based feature OCP (AFOCP), which addresses both limitations through two key innovations. First, AFOCP operates in the feature space of pre-trained neural networks, leveraging learned representations to construct more compact prediction sets by concentrating on task-relevant information while suppressing nuisance variation. Second, AFOCP incorporates an attention mechanism that adaptively weights historical observations based on their relevance to the current test point, effectively handling non-stationarity and distribution shifts. We provide theoretical guarantees showing that AFOCP maintains long-term coverage while provably achieving smaller prediction intervals than standard OCP under mild regularity conditions. Extensive experiments on synthetic and real-world time series datasets demonstrate that AFOCP consistently reduces the size of prediction intervals by as much as $88\%$ as compared to OCP, while maintaining target coverage levels, validating the benefits of both feature-space calibration and attention-based adaptive weighting.

We present FilterDDP, a differential dynamic programming algorithm for solving discrete-time, optimal control problems (OCPs) with nonlinear equality constraints. Unlike prior methods based on merit functions or the augmented Lagrangian class of algorithms, FilterDDP uses a step filter in conjunction with a line search to handle equality constraints. We identify two important design choices for the step filter criteria which lead to robust numerical performance: 1) we use the Lagrangian instead of the cost as one of the filter criterion and, 2) for the stopping criteria and backward pass Hessians, we replace the value function gradient with an estimated dual variable of the dynamics constraints. Both choices are rigorously justified, for 2) in particular by a formal proof of local quadratic convergence. We validate FilterDDP on three contact implicit trajectory optimisation problems which arise in robotics.

--Scene understanding and risk-aware attentions are crucial for human drivers to make safe and effective driving decisions. T o imitate this cognitive ability in urban autonomous driving while ensuring the transparency and interpretability, we propose a vision-language model (VLM)-enhanced unified decision-making and motion control framework, named VLM-UDMC. This framework incorporates scene reasoning and risk-aware insights into an upper-level slow system, which dynamically reconfigures the optimal motion planning for the downstream fast system. The reconfiguration is based on real-time environmental changes, which are encoded through context-aware potential functions. More specifically, the upper-level slow system employs a two-step reasoning policy with Retrieval-Augmented Generation (RAG), leveraging foundation models to process mul-timodal inputs and retrieve contextual knowledge, thereby generating risk-aware insights. Meanwhile, a lightweight multi-kernel decomposed LSTM provides real-time trajectory predictions for heterogeneous traffic participants by extracting smoother trend representations for short-horizon trajectory prediction. The effectiveness of the proposed VLM-UDMC framework is verified via both simulations and real-world experiments with a full-size autonomous vehicle. It is demonstrated that the presented VLM-UDMC effectively leverages scene understanding and attention decomposition for rational driving decisions, thus improving the overall urban driving performance. Urban autonomous driving has emerged as a critical technology to address the escalating challenges of traffic congestion, safety risks, and operational inefficiency in populated cities [1]. Haichao Liu is with the Robotics and Autonomous Systems Thrust, The Hong Kong University of Science and Technology (Guangzhou), Guangzhou 511453, China, and also with the Department of Electrical and Computer Engineering, National University of Singapore, Singapore (e-mail: haichao.liu@u.nus.edu).

This research introduces MP-RBFN, a novel formulation leveraging Radial Basis Function Networks for efficiently learning Motion Primitives derived from optimal control problems for autonomous driving. While traditional motion planning approaches based on optimization are highly accurate, they are often computationally prohibitive. In contrast, sampling-based methods demonstrate high performance but impose constraints on the geometric shape of trajectories. MP-RBFN combines the strengths of both by coupling the high-fidelity trajectory generation of sampling-based methods with an accurate description of vehicle dynamics. Empirical results show compelling performance compared to previous methods, achieving a precise description of motion primitives at low inference times. MP-RBFN yields a seven times higher accuracy in generating optimized motion primitives compared to existing semi-analytic approaches. We demonstrate the practical applicability of MP-RBFN for motion planning by integrating the method into a sampling-based trajectory planner. MP-RBFN is available as open-source software at https://github.com/TUM-AVS/RBFN-Motion-Primitives.

In many applications, including underwater robotics, the coverage problem requires an autonomous vehicle to systematically explore a defined area while minimizing redundancy and avoiding obstacles. This paper investigates coverage path planning strategies to enhance the efficiency of underwater gliders, particularly in maximizing the probability of detecting a radioactive source while ensuring safe navigation. We evaluate three path-planning approaches: the Traveling Salesman Problem (TSP), Minimum Spanning Tree (MST), and Optimal Control Problem (OCP). Simulations were conducted in MATLAB, comparing processing time, uncovered areas, path length, and traversal time. Results indicate that OCP is preferable when traversal time is constrained, although it incurs significantly higher computational costs. Conversely, MST-based approaches provide faster but less optimal solutions. These findings offer insights into selecting appropriate algorithms based on mission priorities, balancing efficiency and computational feasibility.

In this work, we propose an optimization-based trajectory planner for tractor-trailer vehicles on curvy roads. The lack of analytical expression for the trailer's errors to the center line pose a great challenge to the trajectory planning for tractor-trailer vehicles. To address this issue, we first use geometric representations to characterize the lateral and orientation errors in Cartesian frame, where the errors would serve as the components of the cost function and the road edge constraints within our optimization process. Next, we generate a coarse trajectory to warm-start the subsequent optimization problems. On the other hand, to achieve a good approximation of the continuous-time kinematics, optimization-based methods usually discretize the kinematics with a large sampling number. This leads to an increase in the number of the variables and constraints, thus making the optimization problem difficult to solve. To address this issue, we design a Progressively Increasing Sampling Number Optimization (PISNO) framework. More specifically, we first find a nearly feasible trajectory with a small sampling number to warm-start the optimization process. Then, the sampling number is progressively increased, and the corresponding intermediate Optimal Control Problem (OCP) is solved in each iteration. Next, we further resample the obtained solution into a finer sampling period, and then use it to warm-start the intermediate OCP in next iteration. This process is repeated until reaching a threshold sampling number. Simulation and experiment results show the proposed method exhibits a good performance and less computational consumption over the benchmarks.

-- This paper details an approach to linearise differentiable but non-convex collision avoidance constraints tailored to convex shapes. It revisits introducing differential collision avoidance constraints for convex objects into an optimal control problem (OCP) using the separating hyperplane theorem. By framing this theorem as a classification problem, the hyper-planes are eliminated as optimisation variables from the OCP . This effectively transforms non-convex constraints into linear constraints. A bi-level algorithm computes the hyperplanes between the iterations of an optimisation solver and subsequently embeds them as parameters into the OCP . Experiments demonstrate the approach's favourable scalability towards cluttered environments and its applicability to various motion planning approaches. It decreases trajectory computation times between 50% and 90% compared to a state-of-the-art approach that directly includes the hyperplanes as variables in the optimal control problem. Deploying autonomous robots in practical and real-life settings, e.g., a warehouse, industrial production cell, homes, etc. is a complex problem with many interesting challenges that remain.

Exploration algorithms for reinforcement learning typically replace or augment the reward function with an additional "intrinsic" reward that trains the agent to seek previously unseen states of the environment. Here, we consider an exploration algorithm that exploits meta-learning, or learning to learn, such that the agent learns to maximize its exploration progress within a single episode, even between epochs of training. The agent learns a policy that aims to minimize the probability density of new observations with respect to all of its memories. In addition, it receives as feedback evaluations of the current observation density and retains that feedback in a recurrent network. By remembering trajectories of density, the agent learns to navigate a complex and growing landscape of familiarity in real-time, allowing it to maximize its exploration progress even in completely novel states of the environment for which its policy has not been trained. Introduction In reinforcement learning (RL), exploration refers to algorithms that induce an agent to observe as much of a given task as possible. All RL algorithms include some form of random exploration, such as the epsilon-greedy policy or by additionally training to maximize the policy's entropy. These algorithms are necessary for the agent to find rewarding states and expand its policy, but often fall short when rewards are sparsely distributed, that is, requiring non-obvious and improbable sequences of action.

This paper proposes a novel approach to formulate time-optimal point-to-point motion planning and control under uncertainty. The approach defines a robustified two-stage Optimal Control Problem (OCP), in which stage 1, with a fixed time grid, is seamlessly stitched with stage 2, which features a variable time grid. Stage 1 optimizes not only the nominal trajectory, but also feedback gains and corresponding state covariances, which robustify constraints in both stages. The outcome is a minimized uncertainty in stage 1 and a minimized total motion time for stage 2, both contributing to the time optimality and safety of the total motion. A timely replanning strategy is employed to handle changes in constraints and maintain feasibility, while a tailored iterative algorithm is proposed for efficient, real-time OCP execution.

Optimal control problems (OCPs) involve finding a control function for a dynamical system such that a cost functional is optimized. It is central to physical systems in both academia and industry. In this paper, we propose a novel instance-solution control operator perspective, which solves OCPs in a one-shot manner without direct dependence on the explicit expression of dynamics or iterative optimization processes. The control operator is implemented by a new neural operator architecture named Neural Adaptive Spectral Method (NASM), a generalization of classical spectral methods. We theoretically validate the perspective and architecture by presenting the approximation error bounds of NASM for the control operator. Experiments on synthetic environments and a real-world dataset verify the effectiveness and efficiency of our approach, including substantial speedup in running time, and high-quality in- and out-of-distribution generalization.