Abstract-- Motion planning can be cast as a trajectory optimisation problem where a cost is minimised as a function of the trajectory being generated. In complex environments with several obstacles and complicated geometry, this optimisation problem is usually difficult to solve and prone to local minima. However, recent advancements in computing hardware allow for parallel trajectory optimisation where multiple solutions are obtained simultaneously, each initialised from a different starting point. Unfortunately, without a strategy preventing two solutions to collapse on each other, naive parallel optimisation can suffer from mode collapse diminishing the efficiency of the approach and the likelihood of finding a global solution. In this paper we leverage on recent advances in the theory of rough paths to devise an algorithm for parallel trajectory optimisation that promotes diversity over the range of solutions, therefore avoiding mode collapses and achieving better global properties. These can be roughly divided into two main paradigms: sampling-based and trajectory optimisation algorithms. Sampling-based planning [2] is a class of planners with Trajectory optimisation is one of the key tools in robotic probabilistically complete and asymptotically optimal guarantees motion, used to find control signals or paths in obstaclecluttered [3]. These approaches decompose the planning problem environments that allow the robot to perform into a series of sequential decision-making problems with desired tasks. These trajectories can represent a variety of a tree-based [4] or graph-based [5], [6] approach.

Abstract-- Unlike human beings that can employ the entire surface of their limbs as a means to establish contact with their environment, robots are typically programmed to interact with their environments via their end-effectors, in a collision-free fashion, to avoid damaging their environment. In a departure from such a traditional approach, this work presents a contactaware controller for reference tracking that maintains interaction forces on the surface of the robot below a safety threshold in the presence of both rigid and soft contacts. A demo video of our results can be seen here: https://youtu.be/2WeYytauhNg We derive a simple yet effective quasi-static dynamics I. INTRODUCTION Furthermore, we introduce Contact-rich tasks require robots to make contact with a contact-aware planning method that finds near-optimal their environment. A good example of such tasks is the trajectories, minimizing the deformation of the environment stowing task in the Amazon warehouses, where elastic bands and preventing our controller from being stuck in local are mounted on cabinets to prevent objects from falling out, minima, when reaching into the cabinet environment in Fig. and human operators establish contact with the elastic bands 1.

In this paper, we propose a novel end-to-end approach for solving the multi-goal path planning problem in obstacle environments. Our proposed model, called S&Reg, integrates multi-task learning networks with a TSP solver and a path planner to quickly compute a closed and feasible path visiting all goals. Specifically, the model first predicts promising regions that potentially contain the optimal paths connecting two goals as a segmentation task. Simultaneously, estimations for pairwise distances between goals are conducted as a regression task by the neural networks, while the results construct a symmetric weight matrix for the TSP solver. Leveraging the TSP result, the path planner efficiently explores feasible paths guided by promising regions. We extensively evaluate the S&Reg model through simulations and compare it with the other sampling-based algorithms. The results demonstrate that our proposed model achieves superior performance in respect of computation time and solution cost, making it an effective solution for multi-goal path planning in obstacle environments. The proposed approach has the potential to be extended to other sampling-based algorithms for multi-goal path planning.

This paper analyzes finite state Markov Decision Processes (MDPs) with uncertain parameters in compact sets and re-examines results from robust MDP via set-based fixed point theory. To this end, we generalize the Bellman and policy evaluation operators to contracting operators on the value function space and denote them as \emph{value operators}. We lift these value operators to act on \emph{sets} of value functions and denote them as \emph{set-based value operators}. We prove that the set-based value operators are \emph{contractions} in the space of compact value function sets. Leveraging insights from set theory, we generalize the rectangularity condition in classic robust MDP literature to a containment condition for all value operators, which is weaker and can be applied to a larger set of parameter-uncertain MDPs and contracting operators in dynamic programming. We prove that both the rectangularity condition and the containment condition sufficiently ensure that the set-based value operator's fixed point set contains its own extrema elements. For convex and compact sets of uncertain MDP parameters, we show equivalence between the classic robust value function and the supremum of the fixed point set of the set-based Bellman operator. Under dynamically changing MDP parameters in compact sets, we prove a set convergence result for value iteration, which otherwise may not converge to a single value function. Finally, we derive novel guarantees for probabilistic path-planning problems in planet exploration and stratospheric station-keeping.

We consider a chance-constrained multi-robot motion planning problem in the presence of Gaussian motion and sensor noise. Our proposed algorithm, CC-K-CBS, leverages the scalability of kinodynamic conflict-based search (K-CBS) in conjunction with the efficiency of the Gaussian belief trees used in the Belief-A framework, and inherits the completeness guarantees of Belief-A's low-level sampling-based planner. We also develop three different methods for robot-robot probabilistic collision checking, which trade off computation with accuracy. Our algorithm generates motion plans driving each robot from its initial state to its goal while accounting for the evolution of its uncertainty with chance-constrained safety guarantees. Benchmarks compare computation time to conservatism of the collision checkers, in addition to characterizing the performance of the planner as a whole. Results show that CC-K-CBS can scale up to 30 robots.

In many engineering applications it is useful to reason about "negative information". For example, in planning problems, providing an optimal solution is the same as giving a feasible solution (the "positive" information) together with a proof of the fact that there cannot be feasible solutions better than the one given (the "negative" information). We model negative information by introducing the concept of "norphisms", as opposed to the positive information of morphisms. A "nategory" is a category that has "nom"-sets in addition to hom-sets, and specifies the interaction between norphisms and morphisms. In particular, we have composition rules of the form morphism + norphism $\to$ norphism. Norphisms do not compose by themselves; rather, they use morphisms as catalysts. After providing several applied examples, we connect nategories to enriched category theory. Specifically, we prove that categories enriched in de Paiva's dialectica categories GC, in the case C = Set and equipped with a modified monoidal product, define nategories which satisfy additional regularity properties. This formalizes negative information categorically in a way that makes negative and positive morphisms equal citizens.

In this paper, we present a novel method for mobile manipulators to perform multiple contact-rich manipulation tasks. While learning-based methods have the potential to generate actions in an end-to-end manner, they often suffer from insufficient action accuracy and robustness against noise. On the other hand, classical control-based methods can enhance system robustness, but at the cost of extensive parameter tuning. To address these challenges, we present MOMA-Force, a visual-force imitation method that seamlessly combines representation learning for perception, imitation learning for complex motion generation, and admittance whole-body control for system robustness and controllability. MOMA-Force enables a mobile manipulator to learn multiple complex contact-rich tasks with high success rates and small contact forces. In a real household setting, our method outperforms baseline methods in terms of task success rates. Moreover, our method achieves smaller contact forces and smaller force variances compared to baseline methods without force imitation. Overall, we offer a promising approach for efficient and robust mobile manipulation in the real world. Videos and more details can be found on \url{https://visual-force-imitation.github.io}

Robotics and automation are poised to change the landscape of home and work in the near future. Robots are adept at deliberately moving, sensing, and interacting with their environments. The pervasive use of this technology promises societal and economic payoffs due to its capabilities - conversely, the capabilities of robots to move within and sense the world around them is susceptible to abuse. Robots, unlike typical sensors, are inherently autonomous, active, and deliberate. Such automated agents can become AI double agents liable to violate the privacy of coworkers, privileged spaces, and other stakeholders. In this work we highlight the understudied and inevitable threats to privacy that can be posed by the autonomous, deliberate motions and sensing of robots. We frame the problem within broader sociotechnological questions alongside a comprehensive review. The privacy-aware motion planning problem is formulated in terms of cost functions that can be modified to induce privacy-aware behavior - preserving, agnostic, or violating. Simulated case studies in manipulation and navigation, with altered cost functions, are used to demonstrate how privacy-violating threats can be easily injected, sometimes with only small changes in performance (solution path lengths). Such functionality is already widely available. This preliminary work is meant to lay the foundations for near-future, holistic, interdisciplinary investigations that can address questions surrounding privacy in intelligent robotic behaviors determined by planning algorithms.

Earth imaging satellites are a crucial part of our everyday lives that enable global tracking of industrial activities. Use cases span many applications, from weather forecasting to digital maps, carbon footprint tracking, and vegetation monitoring. However, there are limitations; satellites are difficult to manufacture, expensive to maintain, and tricky to launch into orbit. Therefore, satellites must be employed efficiently. This poses a challenge known as the satellite mission planning problem, which could be computationally prohibitive to solve on large scales. However, close-to-optimal algorithms, such as greedy reinforcement learning and optimization algorithms, can often provide satisfactory resolutions. This paper introduces a set of quantum algorithms to solve the mission planning problem and demonstrate an advantage over the classical algorithms implemented thus far. The problem is formulated as maximizing the number of high-priority tasks completed on real datasets containing thousands of tasks and multiple satellites. This work demonstrates that through solution-chaining and clustering, optimization and machine learning algorithms offer the greatest potential for optimal solutions. This paper notably illustrates that a hybridized quantum-enhanced reinforcement learning agent can achieve a completion percentage of 98.5% over high-priority tasks, significantly improving over the baseline greedy methods with a completion rate of 75.8%. The results presented in this work pave the way to quantum-enabled solutions in the space industry and, more generally, future mission planning problems across industries.

Formation flight has a vast potential for aerial robot swarms in various applications. However, existing methods lack the capability to achieve fully autonomous large-scale formation flight in dense environments. To bridge the gap, we present a complete formation flight system that effectively integrates real-world constraints into aerial formation navigation. This paper proposes a differentiable graph-based metric to quantify the overall similarity error between formations. This metric is invariant to rotation, translation, and scaling, providing more freedom for formation coordination. We design a distributed trajectory optimization framework that considers formation similarity, obstacle avoidance, and dynamic feasibility. The optimization is decoupled to make large-scale formation flights computationally feasible. To improve the elasticity of formation navigation in highly constrained scenes, we present a swarm reorganization method that adaptively adjusts the formation parameters and task assignments by generating local navigation goals. A novel swarm agreement strategy called global-remap-local-replan and a formation-level path planner is proposed in this work to coordinate the global planning and local trajectory optimizations. To validate the proposed method, we design comprehensive benchmarks and simulations with other cutting-edge works in terms of adaptability, predictability, elasticity, resilience, and efficiency. Finally, integrated with palm-sized swarm platforms with onboard computers and sensors, the proposed method demonstrates its efficiency and robustness by achieving the largest scale formation flight in dense outdoor environments.