This paper presents a method for optimal motion planning of continuum robots by employing Bernstein surfaces to approximate the system's dynamics and impose complex constraints, including collision avoidance. The main contribution is the approximation of infinite-dimensional continuous problems into their discrete counterparts, facilitating their solution using standard optimization solvers. This discretization leverages the unique properties of Bernstein surface, providing a framework that extends previous works which focused on ODEs approximated by Bernstein polynomials. Numerical validations are conducted through several numerical scenarios. The presented methodology offers a promising direction for solving complex optimal control problems in the realm of soft robotics.

In this paper, an integrated path planning and tube-following control scheme is proposed for collision-free navigation of a wheeled mobile robot (WMR) in a compact convex workspace cluttered with sufficiently separated spherical obstacles. An analytical path planning algorithm is developed based on Bouligand's tangent cones and Nagumo's invariance theorem, which enables the WMR to navigate towards a designated goal location from almost all initial positions in the free space, without entering into augmented obstacle regions with safety margins. We further construct a virtual "safe tube" around the reference trajectory, ensuring that its radius does not exceed the size of the safety margin. Subsequently, a saturated adaptive controller is designed to achieve safe trajectory tracking in the presence of disturbances. It is shown that this tube-following controller guarantees that the WMR tracks the reference trajectory within the predefined tube, while achieving uniform ultimate boundedness of both the position tracking and parameter estimation errors. This indicates that the WMR will not collide with any obstacles along the way. Finally, we report simulation and experimental results to validate the effectiveness of the proposed method.

This paper addresses a new motion planning problem for mobile robots tasked with accomplishing multiple high-level sub-tasks, expressed using natural language (NL). These sub-tasks should be accomplished in a temporal and logical order. To formally define the overarching mission, we leverage Linear Temporal Logic (LTL) defined over atomic predicates modeling these NL-based sub-tasks. This is in contrast to related planning approaches that define LTL tasks over atomic predicates capturing desired low-level system configurations. Our goal is to design robot plans that satisfy LTL tasks defined over NL-based atomic propositions. A novel technical challenge arising in this setup lies in reasoning about correctness of a robot plan with respect to such LTL-encoded tasks. To address this problem, we propose HERACLEs, a hierarchical conformal natural language planner, that relies on (i) automata theory to determine what NL-specified sub-tasks should be accomplished next to make mission progress; (ii) Large Language Models to design robot plans satisfying these sub-tasks; and (iii) conformal prediction to reason probabilistically about correctness of the designed plans and to determine if external assistance is required. We provide theoretical probabilistic mission satisfaction guarantees as well as extensive comparative experiments on mobile manipulation tasks.

Monte Carlo Tree Search (MCTS) is an immensely popular search-based framework used for decision making. It is traditionally applied to domains where a perfect simulation model of the environment is available. We study and improve MCTS in the context where the environment model is given but imperfect. We show that the discrepancy between the model and the actual environment can lead to significant performance degradation with standard MCTS. We therefore develop Uncertainty Adapted MCTS (UA-MCTS), a more robust algorithm within the MCTS framework. We estimate the transition uncertainty in the given model, and direct the search towards more certain transitions in the state space. We modify all four MCTS phases to improve the search behavior by considering these estimates. We prove, in the corrupted bandit case, that adding uncertainty information to adapt UCB leads to tighter regret bound than standard UCB. Empirically, we evaluate UA-MCTS and its individual components on the deterministic domains from the MinAtar test suite. Our results demonstrate that UA-MCTS strongly improves MCTS in the presence of model transition errors.

A continuous motion planning method for connected automated vehicles is considered for generating feasible trajectories in real-time using three consecutive clothoids. The proposed method reduces path planning to a small set of nonlinear algebraic equations such that the generated path can be efficiently checked for feasibility and collision. After path planning, velocity planning is executed while maintaining a parallel simple structure. Key strengths of this framework include its interpretability, shareability, and ability to specify boundary conditions. Its interpretability and shareability stem from the succinct representation of the resulting local motion plan using a handful of physically meaningful parameters. Vehicles may share these parameters via V2X communication so that the recipients can precisely reconstruct the planned trajectory of the senders and respond accordingly. The proposed local planner guarantees the satisfaction of boundary conditions, thus ensuring seamless integration with a wide array of higher-level global motion planners. The tunable nature of the method enables tailoring the local plans to specific maneuvers like turns at intersections, lane changes, and U-turns.

We study graph-based Multi-Robot Coverage Path Planning (MCPP) that aims to compute coverage paths for multiple robots to cover all vertices of a given 2D grid terrain graph $G$. Existing graph-based MCPP algorithms first compute a tree cover on $G$ -- a forest of multiple trees that cover all vertices -- and then employ the Spanning Tree Coverage (STC) paradigm to generate coverage paths on the decomposed graph $D$ of the terrain graph $G$ by circumnavigating the edges of the computed trees, aiming to optimize the makespan (i.e., the maximum coverage path cost among all robots). In this paper, we take a different approach by exploring how to systematically search for good coverage paths directly on $D$. We introduce a new algorithmic framework, called LS-MCPP, which leverages a local search to operate directly on $D$. We propose a novel standalone paradigm, Extended-STC (ESTC), that extends STC to achieve complete coverage for MCPP on any decomposed graphs, even those resulting from incomplete terrain graphs. Furthermore, we demonstrate how to integrate ESTC with three novel types of neighborhood operators into our framework to effectively guide its search process. Our extensive experiments demonstrate the effectiveness of LS-MCPP, consistently improving the initial solution returned by two state-of-the-art baseline algorithms that compute suboptimal tree covers on $G$, with a notable reduction in makespan by up to 35.7\% and 30.3\%, respectively. Moreover, LS-MCPP consistently matches or surpasses the results of optimal tree cover computation, achieving these outcomes with orders of magnitude faster runtime, thereby showcasing its significant benefits for large-scale real-world coverage tasks.

A significant challenge in applying planning technology to real-world problems lies in obtaining a planning model that accurately represents the problem's dynamics. Numeric Safe Action Models Learning (N-SAM) is a recently proposed algorithm that addresses this challenge. It is an algorithm designed to learn the preconditions and effects of actions from observations in domains that may involve both discrete and continuous state variables. N-SAM has several attractive properties. It runs in polynomial time and is guaranteed to output an action model that is safe, in the sense that plans generated by it are applicable and will achieve their intended goals. To preserve this safety guarantee, N-SAM must observe a substantial number of examples for each action before it is included in the learned action model. We address this limitation of N-SAM and propose N-SAM*, an enhanced version of N-SAM that always returns an action model where every observed action is applicable at least in some state, even if it was only observed once. N-SAM* does so without compromising the safety of the returned action model. We prove that N-SAM* is optimal in terms of sample complexity compared to any other algorithm that guarantees safety. An empirical study on a set of benchmark domains shows that the action models returned by N-SAM* enable solving significantly more problems compared to the action models returned by N-SAM.

We present a fast planning architecture called Hamilton-Jacobi-based bidirectional A* (HJBA*) to solve general tight parking scenarios. The algorithm is a two-layer composed of a high-level HJ-based reachability analysis and a lower-level bidirectional A* search algorithm. In high-level reachability analysis, a backward reachable tube (BRT) concerning vehicle dynamics is computed by the HJ analysis and it intersects with a safe set to get a safe reachable set. The safe set is defined by constraints of positive signed distances for obstacles in the environment and computed by solving QP optimization problems offline. For states inside the intersection set, i.e., the safe reachable set, the computed backward reachable tube ensures they are reachable subjected to system dynamics and input bounds, and the safe set guarantees they satisfy parking safety with respect to obstacles in different shapes. For online computation, randomized states are sampled from the safe reachable set, and used as heuristic guide points to be considered in the bidirectional A* search. The bidirectional A* search is paralleled for each randomized state from the safe reachable set. We show that the proposed two-level planning algorithm is able to solve different parking scenarios effectively and computationally fast for typical parking requests. We validate our algorithm through simulations in large-scale randomized parking scenarios and demonstrate it to be able to outperform other state-of-the-art parking planning algorithms.

Automating the assembly of objects from their parts is a complex problem with innumerable applications in manufacturing, maintenance, and recycling. Unlike existing research, which is limited to target segmentation, pose regression, or using fixed target blueprints, our work presents a holistic multi-level framework for part assembly planning consisting of part assembly sequence inference, part motion planning, and robot contact optimization. We present the Part Assembly Sequence Transformer (PAST) -- a sequence-to-sequence neural network -- to infer assembly sequences recursively from a target blueprint. We then use a motion planner and optimization to generate part movements and contacts. To train PAST, we introduce D4PAS: a large-scale Dataset for Part Assembly Sequences (D4PAS) consisting of physically valid sequences for industrial objects. Experimental results show that our approach generalizes better than prior methods while needing significantly less computational time for inference.

Autonomous robots need to be able to handle uncertainties when deployed in the real world. For the robot to be able to robustly work in such an environment, it needs to be able to adapt both its architecture as well as its task plan. Architecture adaptation and task plan adaptation are mutually dependent, and therefore require the system to apply runtime architecture and task plan co-adaptation. This work presents Metaplan, which makes use of models of the robot and its environment, together with a PDDL planner to apply runtime architecture and task plan co-adaptation. Metaplan is designed to be easily reusable across different domains. Metaplan is shown to successfully perform runtime architecture and task plan co-adaptation with a self-adaptive unmanned underwater vehicle exemplar, and its reusability is demonstrated by applying it to an unmanned ground vehicle.