This paper reviews the large spectrum of methods for generating robot motion proposed over the 50 years of robotics research culminating in recent developments. It crosses the boundaries of methodologies, typically not surveyed together, from those that operate over explicit models to those that learn implicit ones.

The ability of a robot to plan complex behaviors with real-time computation, rather than adhering to predesigned or offline-learned routines, alleviates the need for specialized algorithms or training for each problem instance. Monte Carlo Tree Search is a powerful planning algorithm that strategically explores simulated future possibilities, but it requires a discrete problem representation that is irreconcilable with the continuous dynamics of the physical world. We present Spectral Expansion Tree Search (SETS), a real-time, tree-based planner that uses the spectrum of the locally linearized system to construct a low-complexity and approximately equivalent discrete representation of the continuous world. We prove SETS converges to a bound of the globally optimal solution for continuous, deterministic and differentiable Markov Decision Processes, a broad class of problems that includes underactuated nonlinear dynamics, non-convex reward functions, and unstructured environments. We experimentally validate SETS on drone, spacecraft, and ground vehicle robots and one numerical experiment, each of which is not directly solvable with existing methods. We successfully show SETS automatically discovers a diverse set of optimal behaviors and motion trajectories in real time.

In recent years, computing diverse sets of high quality solutions for combinatorial optimisation problems has gained significant attention in the area of artificial intelligence from both theoretical (Baste et al., 2022, 2019; Fomin et al., 2024; Hanaka et al., 2023) and experimental (Vonásek and Saska, 2018; Ingmar et al., 2020) perspectives. Prominent examples where diverse sets of high quality solutions are sought come from the area of path planning (Hanaka et al., 2021; Gao et al., 2022). Particularly, quality diversity (QD) algorithms have shown to produce excellent results for challenging problems in the areas such as robotics (Miao et al., 2022; Shen et al., 2020), games (Cully and Demiris, 2018) and combinatorial optimisation (Nikfarjam et al., 2024a). This work contributes to the theoretical understanding of QD algorithms. Such algorithms compute several solutions that occupy different areas of a so-called behavioural space. Approaches that use a multidimensional archive of phenotypic elites, called Map-Elites (Mouret and Clune, 2015), are among the most commonly used QD algorithms.

This paper introduces a comprehensive planning and navigation framework that address these limitations by integrating semantic mapping, adaptive coverage planning, dynamic obstacle avoidance and precise trajectory tracking. Our framework begins by generating panoptic occupancy local semantic maps and accurate localization information from data aligned between a monocular camera, IMU, and GPS. This information is combined with input terrain point clouds or preloaded terrain information to initialize the planning process. We propose the Radiant Field-Informed Coverage Planning algorithm, which utilizes a diffusion field model to dynamically adjust the robot's coverage trajectory and speed based on environmental attributes such as dirtiness and dryness. By modeling the spatial influence of the robot's actions using a Gaussian field, ensures a speed-optimized, uniform coverage trajectory while adapting to varying environmental conditions.

The Space-Air-Ground Integrated Network (SAGIN) framework is a crucial foundation for future networks, where satellites and aerial nodes assist in computational task offloading. The low-altitude economy, leveraging the flexibility and multifunctionality of Unmanned Aerial Vehicles (UAVs) in SAGIN, holds significant potential for development in areas such as communication and sensing. However, effective coordination is needed to streamline information exchange and enable efficient system resource allocation. In this paper, we propose a Clustering-based Multi-agent Deep Deterministic Policy Gradient (CMADDPG) algorithm to address the multi-UAV cooperative task scheduling challenges in SAGIN. The CMADDPG algorithm leverages dynamic UAV clustering to partition UAVs into clusters, each managed by a Cluster Head (CH) UAV, facilitating a distributed-centralized control approach. Within each cluster, UAVs delegate offloading decisions to the CH UAV, reducing intra-cluster communication costs and decision conflicts, thereby enhancing task scheduling efficiency. Additionally, by employing a multi-agent reinforcement learning framework, the algorithm leverages the extensive coverage of satellites to achieve centralized training and distributed execution of multi-agent tasks, while maximizing overall system profit through optimized task offloading decision-making. Simulation results reveal that the CMADDPG algorithm effectively optimizes resource allocation, minimizes queue delays, maintains balanced load distribution, and surpasses existing methods by achieving at least a 25\% improvement in system profit, showcasing its robustness and adaptability across diverse scenarios.

Nano-drones, with their small, lightweight design, are ideal for confined-space rescue missions and inherently safe for human interaction. However, their limited payload restricts the critical sensing needed for ego-velocity estimation and obstacle detection to single-bean laser-based time-of-flight (ToF) and low-resolution optical sensors. Although those sensors have demonstrated good performance, they fail in some complex real-world scenarios, especially when facing transparent or reflective surfaces (ToFs) or when lacking visual features (optical-flow sensors). Taking inspiration from bats, this paper proposes a novel two-way ranging-based method for ego-velocity estimation and obstacle avoidance based on down-and-forward facing ultra-low-power ultrasonic sensors, which improve the performance when the drone faces reflective materials or navigates in complete darkness. Our results demonstrate that our new sensing system achieves a mean square error of 0.019 m/s on ego-velocity estimation and allows exploration for a flight time of 8 minutes while covering 136 m on average in a challenging environment with transparent and reflective obstacles. We also compare ultrasonic and laser-based ToF sensing techniques for obstacle avoidance, as well as optical flow and ultrasonic-based techniques for ego-velocity estimation, denoting how these systems and methods can be complemented to enhance the robustness of nano-drone operations.

Large Language Models have been shown to fail to create executable and verifiable plans in grounded environments. An emerging line of work shows success in using LLM as a formalizer to generate a formal representation (e.g., PDDL) of the planning domain, which can be deterministically solved to find a plan. We systematically evaluate this methodology while bridging some major gaps. While previous work only generates a partial PDDL representation given templated and thus unrealistic environment descriptions, we generate the complete representation given descriptions of various naturalness levels. Among an array of observations critical to improve LLMs' formal planning ability, we note that large enough models can effectively formalize descriptions as PDDL, outperforming those directly generating plans, while being robust to lexical perturbation. As the descriptions become more natural-sounding, we observe a decrease in performance and provide detailed error analysis.

We study a path planning problem where the possible move actions are represented as a finite set of motion primitives aligned with the grid representation of the environment. That is, each primitive corresponds to a short kinodynamically-feasible motion of an agent and is represented as a sequence of the swept cells of a grid. Typically heuristic search, i.e. A*, is conducted over the lattice induced by these primitives (lattice-based planning) to find a path. However due to the large branching factor such search may be inefficient in practice. To this end we suggest a novel technique rooted in the idea of searching over the grid cells (as in vanilla A*) simultaneously fitting the possible sequences of the motion primitives into these cells. The resultant algorithm, MeshA*, provably preserves the guarantees on completeness and optimality, on the one hand, and is shown to notably outperform conventional lattice-based planning (x1.5 decrease in the runtime), on the other hand. Moreover, we suggest an additional pruning technique that additionally decreases the search space of MeshA*. The resultant planner is combined with the regular A* to retain completeness and is shown to further increase the search performance at the cost of negligible decrease of the solution quality.

Trajectory planning in robotics aims to generate collision-free pose sequences that can be reliably executed. Recently, vision-to-planning systems have garnered increasing attention for their efficiency and ability to interpret and adapt to surrounding environments. However, traditional modular systems suffer from increased latency and error propagation, while purely data-driven approaches often overlook the robot's kinematic constraints. This oversight leads to discrepancies between planned trajectories and those that are executable. To address these challenges, we propose iKap, a novel vision-to-planning system that integrates the robot's kinematic model directly into the learning pipeline. iKap employs a self-supervised learning approach and incorporates the state transition model within a differentiable bi-level optimization framework. This integration ensures the network learns collision-free waypoints while satisfying kinematic constraints, enabling gradient back-propagation for end-to-end training. Our experimental results demonstrate that iKap achieves higher success rates and reduced latency compared to the state-of-the-art methods. Besides the complete system, iKap offers a visual-to-planning network that seamlessly integrates kinematics into various controllers, providing a robust solution for robots navigating complex and dynamic environments.

For safety, autonomous systems must be able to consider sudden changes and enact contingency plans appropriately. State-of-the-art methods currently find trajectories that balance between nominal and contingency behavior, or plan for a singular contingency plan; however, this does not guarantee that the resulting plan is safe for all time. To address this research gap, this paper presents Contingency-MPPI, a data-driven optimization-based strategy that embeds contingency planning inside a nominal planner. By learning to approximate the optimal contingency-constrained control sequence with adaptive importance sampling, the proposed method's sampling efficiency is further improved with initializations from a lightweight path planner and trajectory optimizer.