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Adaptively Informed Trees (AIT*) is an algorithm that uses the problem-specific heuristic to avoid unnecessary searches, which significantly improves its performance, especially when collision checking is expensive. However, the heuristic estimation in AIT* consumes lots of computational resources, and its asymmetric bidirectional searching strategy cannot fully exploit the potential of the bidirectional method. In this article, we propose an extension of AIT* called BiAIT*. Unlike AIT*, BiAIT* uses symmetrical bidirectional search for both the heuristic and space searching. The proposed method allows BiAIT* to find the initial solution faster than AIT*, and update the heuristic with less computation when a collision occurs. We evaluated the performance of BiAIT* through simulations and experiments, and the results show that BiAIT* can find the solution faster than state-of-the-art methods. We also analyze the reasons for the different performances between BiAIT* and AIT*. Furthermore, we discuss two simple but effective modifications to fully exploit the potential of the adaptively heuristic method. Note to Practitioners—This work is inspired by the adaptively heuristic method and the symmetrical bidirectional searching method. The article introduces a novel algorithm that uses the symmetrical bidirectional method to calculate the adaptive heuristic and efficiently search the state space. The problem-specific heuristic in BiAIT* is derived from a lazy-forward tree and a lazy-reverse tree, which are constructed without collision checking. The lazy-forward and lazy-reverse trees are enabled to meet in the middle, thus generating the effective and accurate heuristic. In BiAIT*, the lazy-forward and lazy-reverse trees share heuristic information and jointly guide the growth of the forward and reverse trees, which conduct collision checking and guarantee the feasibility of their edges. Compared with state-of-the-art methods, BiAIT* finds the initial heuristic and updates the heuristic more quickly. The proposed algorithm can be applied to industrial robots, medical robots, or service robots to achieve efficient path planning. The implementation of BiAIT* is available at https://github.com/Licmjy-CU/BiAITstar.

Building a general and efficient path planning framework in uncertain nonconvex environments is challenging due to the safety constraints and complex configuration. Traditional avenues usually involve convexifying obstacles and presume Gaussian distribution, which are not universal. Meanwhile, the fast convergence of high-quality solutions is not guaranteed. Therefore, we develop a novel neural risk-bounded path planner to quickly find near-optimal solutions that have an acceptable collision probability in the complex environments. Firstly, we retrieve the nonconvex obstacles with arbitrary probabilistic uncertainties in the form of a deterministic point cloud map. A neural network sampler encodes it into a latent embedding and is trained with sufficient expert demonstrations, predicting states in the potential subspace. We construct a neural cost estimator to select the best informed state from those samples. Then, we recursively use the simple yet effective neural networks to march toward the start and goal bidirectionally. The collision risk of the intermediate connections is verified based on sum-of-squares optimization. Simulation results show that our approach significantly saves time and resources in finding comparable solutions over the state-of-the-art methods in the seen and unseen challenging environments. Note to Practitioners—More and more robots are deployed in unstructured environments, such as forests and subterranean caves. However, uncertainty in the environment situational awareness usually causes accidents. To quickly generate safe paths without over-conservation in uncertain complex environments, we propose a neural risk-bounded sampling-based path planner. Conventional methods consume lots of computation time and resources to generate satisfactory results. Our learning-based risk-bounded path planning framework can efficiently find paths with a guaranteed risk tolerance avoiding uncertain nonconvex static obstacles. It imitates the expert to generate informed states in a subspace that potentially contains the optimal solution. In practice, we need to formulate the observed uncertain obstacle at a grid map into the polynomial containing random variables and determine their probability distributions.

Balancing the trade-off between safety and efficiency is of significant importance for path planning under uncertainty. Many developed risk-aware path planners explicitly limit the probability of collision to an acceptable bound in uncertain environments. However, convex obstacles or Gaussian uncertainties are usually assumed to make the problem tractable in the existing method. These assumptions limit the generalization and application of path planners in real-world implementations. In this article, we propose to apply deep learning methods to the sampling-based planner, developing a novel risk bounded near-optimal path planning algorithm named neural risk-aware RRT (NR-RRT). Specifically, a deterministic risk contours map is maintained by perceiving the probabilistic nonconvex obstacles, and a neural network sampler is proposed to predict the next most-promising safe state. Furthermore, the recursive divide-and-conquer planning and bidirectional search strategies are used to accelerate the convergence to a near-optimal solution with guaranteed bounded risk. Worst-case theoretical guarantees can also be proven owing to a standby safety guaranteed planner utilizing a uniform sampling distribution. Simulation experiments demonstrate that the proposed algorithm outperforms the state-of-the-art for finding risk bounded low-cost paths in uncertain nonconvex environments with seen and unseen scene layouts. Note to Practitioners—This article is motivated by developing an efficient risk-aware path planner that can quickly find risk bounded solutions in uncertain nonconvex environments for practical applications, such as autonomous vehicles and search-and-rescue robots. Sampling-based planning approaches such as rapidly-exploring random tree (RRT) and its variants are popular for their good performance in exploring the state space. However, it is quite time-consuming to look for risk bounded paths in uncertain environments, especially under nonconvex and non-Gaussian constraints. The initial paths are often of poor quality. Therefore, we propose the NR-RRT algorithm to rapidly find near-optimal solutions with guaranteed bounded risk. It utilizes an informed bidirectional search strategy after having past experiences in the challenging environments. It can be applied in not only seen uncertain scenarios but also those have unseen scene layouts different from the training scenarios. However, the algorithm cannot handle the problem in environments that contain entirely unseen obstacles. In future research, we will address the problem of planning under robot model uncertainty.

A 1-D wide-angle scanning phased antenna array with enhanced gain and reduced mutual coupling by using a thin dielectric superstrate (DS) is presented. The DS can enlarge the effective aperture in the ${H}$ -plane and improve the directivity without sacrificing the wide scan range in the ${E}$ -plane. The directly coupled waves between the antenna elements can be cancelled out by the partially reflected waves from the DS, giving reduced mutual coupling. To demonstrate the idea, a $1\times 8$ phased patch antenna array loaded with a 3-D printed DS was designed, fabricated, and measured at 10 GHz. The DS has a small thickness of $0.16~\lambda _{0}$ , where $\lambda _{0}$ is the wavelength in free space. The measured realized gain is enhanced by 1.6–3 dB in the scan range of ±48° with the scan loss being less than 3.2 dB. The measured port isolation is improved by 7.4 dB.