This paper introduces Bidirectional Lazy Informed Trees (BLIT*), the first algorithm to incorporate anytime incremental lazy bidirectional heuristic search (Bi-HS) into batch-wise sampling-based motion planning (Bw-SBMP). BLIT* operates on batches of informed states (states that can potentially improve the cost of the incumbent solution) structured as an implicit random geometric graph (RGG). The computational cost of collision detection is mitigated via a new lazy edge-evaluation strategy by focusing on states near obstacles. Experimental results, especially in high dimensions, show that BLIT* outperforms existing Bw-SBMP planners by efficiently finding an initial solution and effectively improving the quality as more computational resources are available.

In bidirectional heuristic search, the meeting-in-the-middle property (MMP) and the theory of must-expand pairs (MEP) have driven significant recent developments in search efficiency. However, these methodologies typically terminate the search based on minimal priority metrics in the forward and backward open lists, requiring exploration of all potentially better solutions and potentially incurring substantial computational burden. In this paper, we investigate the reasons that contribute to the potential inefficiency in MM , and introduce a tighter termination condition that enables earlier termination without exhaustive exploration while still ensuring both MMP and optimality. This results in a highly efficient bidirectional search algorithm. Experimental comparisons demonstrate that our algorithm outperforms MM in terms of running time by at least two orders of magnitude and is on par or better compared to A*, highlighting its potential in a wide range of applications.

In this paper, we propose an event-triggered rendezvous control method for multiple two-wheeled mobile robots (2WMRs) subject to time-varying communication delays. By checking the integral-type event-triggering conditions asynchronously and periodically, each 2WMR determines whether or not to sample and broadcast its states. When the information used in an agent's controller is updated, the 2WMR calculates its x (or y ) control input, and then a Rotate&Compensate&Run Rendezvous Scheme is provided for 2WMRs to update their states. We present a sufficient condition for 2WMRs to asymptotically reach rendezvous, and the convergence analysis is conducted using the Lyapunov functional approach. Experiments are further presented to validate the effectiveness of the proposed control method.