Abstract-- In a companion paper, we present a modular framework for unicycle stabilization in polar coordinates that provides smooth steering laws through backstepping. Surprisingly, the same problem also allows application of integrator forwarding. In this work, we leverage this feature and construct new smooth steering laws together with control Lyapunov functions (CLFs), expanding the set of CLFs available for inverse optimal control design. In the case of constant forward velocity (Dubins car), backstepping produces finite-time (deadbeat) parking, and we show that integrator forwarding yields the very same class of solutions. This reveals a fundamental connection between backstepping and forwarding in addressing both the unicycle and, the Dubins car parking problems.

Abstract-- Since the mid-1990s, it has been known that, unlike in Cartesian form where Brockett's condition rules out static feedback stabilization, the unicycle is globally asymptotically stabilizable by smooth feedback in polar coordinates. In this note, we introduce a modular framework for designing smooth feedback laws that achieve global asymptotic stabilization in polar coordinates. These laws are bidirectional, enabling efficient parking maneuvers, and are paired with families of strict control Lyapunov functions (CLFs) constructed in a modular fashion. The resulting CLFs guarantee global asymptotic stability with explicit convergence rates and include barrier variants that yield "almost global" stabilization, excluding only zero-measure subsets of the rotation manifolds. The strictness of the CLFs is further leveraged in our companion paper, where we develop inverse-optimal redesigns with meaningful cost functions and infinite gain margins.

-- Motion planning problems for physically-coupled multi-robot systems in cluttered environments are challenging due to their high dimensionality. We propose Physically-coupled discontinuity-bounded Conflict-Based Search (pc-dbCBS), an anytime kinodynamic motion planner, that extends discontinuity-bounded CBS to rigidly-coupled systems. Our approach proposes a tri-level conflict detection and resolution framework that includes the physical coupling between the robots. Moreover, pc-dbCBS alternates iteratively between state space representations, thereby preserving probabilistic completeness and asymptotic optimality while relying only on single-robot motion primitives. Across 25 simulated and six real-world problems involving multirotors carrying a cable-suspended payload and differential-drive robots linked by rigid rods, pc-dbCBS solves up to 92% more instances than a state-of-the-art baseline and plans trajectories that are 50-60% faster while reducing planning time by an order of magnitude. Physically-coupled systems, such as multirotors collabora-tively transporting cable-suspended payloads [1] or multiple mobile manipulators transporting objects [2], are increasingly used in real-world tasks requiring coordinated interaction. These systems are particularly valuable in environments such as construction sites for carrying tools or materials and in precision tasks requiring synchronized motion. The robot coupling introduces additional challenges, as the planned motions must respect both inter-robot dependencies and the system's dynamic constraints. There has been a significant focus on controlling such systems [3, 4] and only limited work on planning feasible motions in cluttered environments that require team formation changes. Moreover, existing planners produce motions that are rather slow and fail to exploit the agility of the underlying single-robot systems.

Abstract-- We present a novel approach for generating motion primitives for kinodynamic motion planning using diffusion models. The motions generated by our approach are adapted to each problem instance by utilizing problem-specific parameters, allowing for finding solutions faster and of better quality. The diffusion models used in our approach are trained on randomly cut solution trajectories. These trajectories are created by solving randomly generated problem instances with a kinodynamic motion planner. Experimental results show significant improvements up to 30 percent in both computation time and solution quality across varying robot dynamics such as secondorder unicycle or car with trailer.

We propose a self-contained, resilient and fully distributed solution for locating the maximum of an unknown 3D scalar field using a swarm of robots that travel at constant speeds. Unlike conventional reactive methods relying on gradient information, our methodology enables the swarm to determine an ascending direction so that it approaches the source with arbitrary precision. Our source-seeking solution consists of three algorithms. The first two algorithms run sequentially and distributively at a high frequency providing barycentric coordinates and the ascending direction respectively to the individual robots. The third algorithm is the individual control law for a robot to track the estimated ascending direction. We show that the two algorithms with higher frequency have an exponential convergence to their eventual values since they are based on the standard consensus protocol for first-order dynamical systems; their high frequency depends on how fast the robots travel through the scalar field. The robots are not constrained to any particular geometric formation, and we study both discrete and continuous distributions of robots within swarm shapes. The shape analysis reveals the resiliency of our approach as expected in robot swarms, i.e., by amassing robots we ensure the source-seeking functionality in the event of missing or misplaced individuals or even if the robot network splits into two or more disconnected subnetworks. In addition, we also enhance the robustness of the algorithm by presenting conditions for \emph{optimal} swarm shapes, in the sense that the ascending directions can be closely parallel to the field's gradient. We exploit such an analysis so that the swarm can adapt to unknown environments by morphing its shape and maneuvering while still following an ascending direction.

This paper introduces CBFKit, a Python/ROS toolbox for safe robotics planning and control under uncertainty. The toolbox provides a general framework for designing control barrier functions for mobility systems within both deterministic and stochastic environments. It can be connected to the ROS open-source robotics middleware, allowing for the setup of multi-robot applications, encoding of environments and maps, and integrations with predictive motion planning algorithms. Additionally, it offers multiple CBF variations and algorithms for robot control. The CBFKit is demonstrated on the Toyota Human Support Robot (HSR) in both simulation and in physical experiments.

In this work, we propose a collision-free source-seeking control framework for unicycle robots traversing an unknown cluttered environment. In this framework, obstacle avoidance is guided by the control barrier functions (CBF) embedded in quadratic programming and the source seeking control relies solely on the use of on-board sensors that measure the signal strength of the source. To tackle the mixed relative degree of the CBF, we proposed three different CBFs, namely the zeroing control barrier functions (ZCBF), exponential control barrier functions (ECBF), and reciprocal control barrier functions (RCBF) that can directly be integrated with our recent gradient-ascent source-seeking control law. We provide rigorous analysis of the three different methods and show the efficacy of the approaches in simulations using Matlab, as well as, using a realistic dynamic environment with moving obstacles in Gazebo/ROS.

Unfortunately, we observe that the common employed Collision Cone Control Barrier Function (C3BF) [15]-[18] Formation control, one of the most actively studied topics is not enough to guarantee a collision-free environment when within multi-robot systems, aims to coordinate multiple robots unicycles cannot brake. For example, one robot might have to spatially since its practical applications in current robotic take an impossible decision to avoid two robots, i.e., to turn to challenges [1]. The idea of formation can be understood in the right and to the left simultaneously. To solve this problem, different ways. One way is by looking at how robots are we present a scalable overtaking rule, that in combination positioned in relation to each other, like how far apart they with an adaptive-collision radius, and the guiding vector field are or the angles between them, also known as distance-based presented in [19], ensures a collision-free environment for and bearing-based formation control, respectively [2]. Another unicycles that follow the same path with constant but different way, called the behavioral approach, does not worry too much speeds. In particular, the usage of the guiding vector field about exact positions but keeps cohesion and ensures robots in [19], [20] facilitates one mild condition so that we can do not crash into each other [3]. Although the bio-inspired extend the results to convex closed paths. In addition, the and heuristic strategies fit more into the latter approach [4], decision making process is completely distributed, i.e., there there also exist rigorous behavioral-based studies [5]. is no centralized computation with global information, but an In this paper, we present and analyze rigorously a circular individual robot can figure out a safe action to avoid a collision formation algorithm that fits more into the behavioralbased on its own with local information and, more importantly, it approach, in the sense that we aim at the order that will not harm others' decisions concerning their safety as it emerges from having a large number of robots following the is crucial to scale up robot swarms [9], [10].

AI Art Generator App. ✅ Fast ✅ Free ✅ Easy. Create amazing artworks using artificial intelligence.

Underlying symbolic representations are opaque within neural networks that perform pattern recognition. Neural network weights are sub-symbolic, they commonly do not have a direct symbolic correlates. This work shows that by implementing network dynamics differently, during the testing phase instead of the training phase, pattern recognition can be performed using symbolically relevant weights. This advancement is an important step towards the merging of neural-symbolic representation, memory, and reasoning with pattern recognition.