Enabling mobile robots to follow complex natural language instructions is an important yet challenging problem. People want to flexibly express constraints, refer to arbitrary landmarks and verify behavior when instructing robots. Conversely, robots must disambiguate human instructions into specifications and ground instruction referents in the real world. We propose Language Instruction grounding for Motion Planning (LIMP), an approach that enables robots to verifiably follow expressive and complex open-ended instructions in real-world environments without prebuilt semantic maps. LIMP constructs a symbolic instruction representation that reveals the robot's alignment with an instructor's intended motives and affords the synthesis of robot behaviors that are correct-by-construction. We perform a large scale evaluation and demonstrate our approach on 150 instructions in five real-world environments showing the generality of our approach and the ease of deployment in novel unstructured domains. In our experiments, LIMP performs comparably with state-of-the-art LLM task planners and LLM code-writing planners on standard open vocabulary tasks and additionally achieves 79\% success rate on complex spatiotemporal instructions while LLM and Code-writing planners both achieve 38\%. See supplementary materials and demo videos at https://robotlimp.github.io

Within the context of in-field path planning and under the assumption of nonholonomic vehicle models this paper addresses two tasks: smoothing of headland path edges and smoothing of headland-to-mainfield lane transitions. Both tasks are solved by a two-step hierarchical algorithm. The first step differs for the two tasks generating either a piecewise-affine or a Dubins reference path. The second step leverages a transformation of vehicle dynamics from the time domain into the spatial domain and linear programming. Benefits such as a hyperparameter-free objective function and spatial constraints useful for area coverage gaps avoidance and precision path planning are discussed. The method, which is a deterministic optimisation-based method, is evaluated on a real-world field solving 3 instances of the first task and 16 instances of the second task.

In the context of ground robot navigation in unstructured hazardous environments, the coupling of efficient path planning with an adequate environment representation is a crucial topic in order to guarantee the robot safety while ensuring the accomplishment of its mission. This paper discusses the exploitation of an environment representation obtained via Gaussian process regression (GPR) for smooth path planning using gradient descent B\'ezier curve optimisation (BCO). A continuous differentiable GPR of the terrain traversability and obstacle distance is used to plan paths with a weighted A* discrete planner, a T-RRT sampling-based planner and BCO using A* or T-RRT computed paths as prior. Numerical experiments in procedurally generated 2D environments allowed to compare the paths planned by the described methods and highlight the benefits of the joint use of the GPR continuous representation and the BCO smooth path planning with these different priors.

Monte Carlo tree search (MCTS) has been successful in a variety of domains, but faces challenges with long-horizon exploration when compared to sampling-based motion planning algorithms like Rapidly-Exploring Random Trees. To address these limitations of MCTS, we derive a tree search algorithm based on policy optimization with state occupancy measure regularization, which we call {\it Volume-MCTS}. We show that count-based exploration and sampling-based motion planning can be derived as approximate solutions to this state occupancy measure regularized objective. We test our method on several robot navigation problems, and find that Volume-MCTS outperforms AlphaZero and displays significantly better long-horizon exploration properties.

Path planning for a nonholonomic mobile robot is a challenging problem. This paper proposes a novel space adaptive search (SAS) approach that greatly reduces the computation cost of nonholonomic mobile robot path planning. The classic search-based path planning only updates the state on the current location in each step, which is very inefficient, and, therefore, can easily be trapped by local minimum. The SAS updates not only the state of the current location, but also all states in the neighborhood, and the size of the neighborhood is adaptively varied based on the clearance around the current location at each step. Since a great deal of states can be immediately updated, the search can explore the local minimum and get rid of it very fast. As a result, the proposed approach can effectively deal with clustered environments with a large number of local minima. The SAS also utilizes a set of predefined motion primitives, and dynamically scales them into different sizes during the search to create various new primitives with differing sizes and curvatures. This greatly promotes the flexibility of the search of path planning in more complex environments. Unlike the A* family, which uses heuristic to accelerate the search, the experiments shows that the SAS requires much less computation time and memory cost even without heuristic than the weighted A* algorithm, while still preserving the optimality of the produced path. However, the SAS can also be applied together with heuristic or other path planning algorithms.

We consider path planning for a rigid spatial robot with 6 degrees of freedom (6 DOFs), moving amidst polyhedral obstacles. A correct, complete and practical path planner for such a robot has never been achieved, although this is widely recognized as a key challenge in robotics. This paper provides a complete "explicit" design, down to explicit geometric primitives that are easily implementable. Our design is within an algorithmic framework for path planners, called Soft Subdivision Search (SSS). The framework is based on the twin foundations of $\epsilon$-exactness and soft predicates, which are critical for rigorous numerical implementations. The practicality of SSS has been previously demonstrated for various robots including 5-DOF spatial robots. In this paper, we solve several significant technical challenges for SE(3) robots: (1) We first ensure the correct theory by proving a general form of the Fundamental Theorem of the SSS theory. We prove this within an axiomatic framework, thus making it easy for future applications of this theory. (2) One component of $SE(3) = R^3 \times SO(3)$ is the non-Euclidean, non-orientable space SO(3). We design a novel topologically correct data structure for SO(3). Using the concept of subdivision charts and atlases for SO(3), we can now carry out subdivision of SO(3). (3) The geometric problem of collision detection takes place in $R^3$, via the footprint map. Unlike sampling-based approaches, we must reason with the notion of footprints of configuration boxes, which is much harder to characterize. Exploiting the theory of soft predicates, we design suitable approximate footprints which, when combined with the highly effective feature-set technique, lead to soft predicates. (4) Finally, we make the underlying geometric computation "explicit", i.e., avoiding a general solver of polynomial systems, in order to allow a direct implementation.

Data-driven methods such as reinforcement and imitation learning have achieved remarkable success in robot autonomy. However, their data-centric nature still hinders them from generalizing well to ever-changing environments. Moreover, collecting large datasets for robotic tasks is often impractical and expensive. To overcome these challenges, we introduce a new self-supervised neural-symbolic (NeSy) computational framework, imperative learning (IL), for robot autonomy, leveraging the generalization abilities of symbolic reasoning. The framework of IL consists of three primary components: a neural module, a reasoning engine, and a memory system. We formulate IL as a special bilevel optimization (BLO), which enables reciprocal learning over the three modules. This overcomes the label-intensive obstacles associated with data-driven approaches and takes advantage of symbolic reasoning concerning logical reasoning, physical principles, geometric analysis, etc. We discuss several optimization techniques for IL and verify their effectiveness in five distinct robot autonomy tasks including path planning, rule induction, optimal control, visual odometry, and multi-robot routing. Through various experiments, we show that IL can significantly enhance robot autonomy capabilities and we anticipate that it will catalyze further research across diverse domains.

This work presents a fully integrated tree-based combined exploration-planning algorithm: Exploration-RRT (ERRT). The algorithm is focused on providing real-time solutions for local exploration in a fully unknown and unstructured environment while directly incorporating exploratory behavior, robot-safe path planning, and robot actuation into the central problem. ERRT provides a complete sampling and tree-based solution for evaluating "where to go next" by considering a trade-off between maximizing information gain, and minimizing the distances travelled and the robot actuation along the path. The complete scheme is evaluated in extensive simulations, comparisons, as well as real-world field experiments in constrained and narrow subterranean and GPS-denied environments. The framework is fully ROS-integrated, straight-forward to use, and we open-source it at https://github.com/LTU-RAI/ExplorationRRT.

Policy gradient (PG) is a reinforcement learning (RL) approach that optimizes a parameterized policy model for an expected return using gradient ascent. While PG can work well even in non-Markovian environments, it may encounter plateaus or peakiness issues. As another successful RL approach, algorithms based on Monte Carlo Tree Search (MCTS), which include AlphaZero, have obtained groundbreaking results, especially in the game-playing domain. They are also effective when applied to non-Markov decision processes. However, the standard MCTS is a method for decision-time planning, which differs from the online RL setting. In this work, we first introduce Monte Carlo Tree Learning (MCTL), an adaptation of MCTS for online RL setups. We then explore a combined policy approach of PG and MCTL to leverage their strengths. We derive conditions for asymptotic convergence with the results of a two-timescale stochastic approximation and propose an algorithm that satisfies these conditions and converges to a reasonable solution. Our numerical experiments validate the effectiveness of the proposed methods.

Generating diverse samples under hard constraints is a core challenge in many areas. With this work we aim to provide an integrative view and framework to combine methods from the fields of MCMC, constrained optimization, as well as robotics, and gain insights in their strengths from empirical evaluations. We propose NLP Sampling as a general problem formulation, propose a family of restarting two-phase methods as a framework to integrated methods from across the fields, and evaluate them on analytical and robotic manipulation planning problems. Complementary to this, we provide several conceptual discussions, e.g. on the role of Lagrange parameters, global sampling, and the idea of a Diffused NLP and a corresponding model-based denoising sampler.