In this paper, we investigate a multi-robot task allocation problem where a team of heterogeneous robots operates in a discrete workspace to achieve a set of tasks expressed by linear temporal logic formulas. In contrast to existing works, we further consider inter-task-time-order constraints, which are imposed on the start or end times of each task. Solving such problems generally requires combinatorial search, which is not scalable. Inspired by the efficiency of max-plus algebra in handling time constraints, we propose a novel approach called MaxAuc, which integrates Auction-based task allocation with Max-plus algebra in a novel manner. Specifically, max-plus computations are performed to approximate task priorities in the auction without explicitly solving the constraint optimization problem. Our numerical results demonstrate that MaxAuc is highly scalable with respect to both the number of robots and the number of tasks, while maintaining a tolerable performance trade-off compared to the baseline’s optimal yet exhaustive solution.

Control Barrier Functions (CBFs) have emerged as an effective and non-invasive safety filter for ensuring the safety of autonomous systems in dynamic environments with formal guarantees. However, most existing works on CBF synthesis focus on fully known settings. Synthesizing CBFs online based on perception data in unknown environments poses particular challenges. Specifically, this requires the construction of CBFs from high-dimensional data efficiently in real time. This paper proposes a new approach for online synthesis of CBFs directly from local Occupancy Grid Maps (OGMs). Inspired by steady-state thermal fields, we show that the smoothness requirement of CBFs corresponds to the solution of the steady-state heat conduction equation with suitably chosen boundary conditions. By leveraging the sparsity of the coefficient matrix in Laplace’s equation, our approach allows for efficient computation of safety values for each grid cell in the map. Simulation and real-world experiments demonstrate the effectiveness of our approach. Specifically, the results show that our CBFs can be synthesized in an average of milliseconds on a 200×200 grid map, highlighting its real-time applicability.

Emergent-scene safety is the key milestone for fully autonomous driving, and reliable on-time prediction is essential to maintain safety in emergency scenarios. However, these emergency scenarios are long-tailed and hard to collect, which restricts the system from getting reliable predictions. In this paper, we build a new dataset, which aims at the longterm prediction with the inconspicuous state variation in history for the emergency event, named the Extro-Spective Prediction (ESP) problem. Based on the proposed dataset, a flexible feature encoder for ESP is introduced to various prediction methods as a seamless plug-in, and its consistent performance improvement underscores its efficacy. Furthermore, a new metric named clamped temporal error (CTE) is proposed to give a more comprehensive evaluation of prediction performance, especially in time-sensitive emergency events of subseconds. Interestingly, as our ESP features can be described in human-readable language naturally, the application of integrating into ChatGPT also shows huge potential. The ESP-dataset and all benchmarks are released at https://dingrui-wang.github.io/ESP-Dataset/.