Modifications to test-time sampling have emerged as an important extension to diffusion algorithms, with the goal of biasing the generative process to achieve a given objective without having to retrain the entire diffusion model. However, generating jointly correlated samples from multiple pre-trained diffusion models while simultaneously enforcing task-specific constraints without costly retraining has remained challenging. To this end, we propose Projected Coupled Diffusion (PCD), a novel test-time framework for constrained joint generation. PCD introduces a coupled guidance term into the generative dynamics to encourage coordination between diffusion models and incorporates a projection step at each diffusion step to enforce hard constraints. Empirically, we demonstrate the effectiveness of PCD in application scenarios of image-pair generation, object manipulation, and multi-robot motion planning. Our results show improved coupling effects and guaranteed constraint satisfaction without incurring excessive computational costs.

Abstract-- This paper addresses a drone ball-balancing task, in which a drone stabilizes a ball atop a movable beam through cable-based interaction. We propose a hierarchical control framework that decouples high-level balancing policy from low-level drone control, and train a reinforcement learning (RL) policy to handle the high-level decision-making. Simulation results show that the RL policy achieves superior performance compared to carefully tuned PID controllers within the same hierarchical structure. Through systematic comparative analysis, we demonstrate that RL's advantage stems not from improved parameter tuning or inherent nonlinear mapping capabilities, but from its ability to effectively utilize richer state observations. These findings underscore the critical role of comprehensive state representation in learning-based systems and suggest that enhanced sensing could be instrumental in improving controller performance.

We introduce an unsupervised motion-compensated image reconstruction algorithm for free-breathing and ungated 3D cardiac magnetic resonance imaging (MRI). We express the image volume corresponding to each specific motion phase as the deformation of a single static image template. The main contribution of the work is the low-rank model for the compact joint representation of the family of diffeomorphisms, parameterized by the motion phases. The diffeomorphism at a specific motion phase is obtained by integrating a parametric velocity field along a path connecting the reference template phase to the motion phase. The velocity field at different phases is represented using a low-rank model. The static template and the low-rank motion model parameters are learned directly from the k-space data in an unsupervised fashion. The more constrained motion model is observed to offer improved recovery compared to current motion-resolved and motion-compensated algorithms for free-breathing 3D cine MRI.

To safely traverse non-flat terrain, robots must account for the influence of terrain shape in their planned motions. Terrain-aware motion planners use an estimate of the vehicle roll and pitch as a function of pose, vehicle suspension, and ground elevation map to weigh the cost of edges in the search space. Encoding such information in a traditional two-dimensional cost map is limiting because it is unable to capture the influence of orientation on the roll and pitch estimates from sloped terrain. The research presented herein addresses this problem by encoding kinodynamic information in the edges of a recombinant motion planning search space based on the Efficiently Adaptive State Lattice (EASL). This approach, which we describe as a Kinodynamic Efficiently Adaptive State Lattice (KEASL), differs from the prior representation in two ways. First, this method uses a novel encoding of velocity and acceleration constraints and vehicle direction at expanded nodes in the motion planning graph. Second, this approach describes additional steps for evaluating the roll, pitch, constraints, and velocities associated with poses along each edge during search in a manner that still enables the graph to remain recombinant. Velocities are computed using an iterative bidirectional method using Eulerian integration that more accurately estimates the duration of edges that are subject to terrain-dependent velocity limits. Real-world experiments on a Clearpath Robotics Warthog Unmanned Ground Vehicle were performed in a non-flat, unstructured environment. Results from 2093 planning queries from these experiments showed that KEASL provided a more efficient route than EASL in 83.72% of cases when EASL plans were adjusted to satisfy terrain-dependent velocity constraints. An analysis of relative runtimes and differences between planned routes is additionally presented.

--Cooperative transportation, a key aspect of logistics cyber-physical systems (CPS), is typically approached using distributed control and optimization-based methods. The distributed control methods consume less time, but poorly handle and extend to multiple constraints. Instead, optimization-based methods handle constraints effectively, but they are usually centralized, time-consuming and thus not easily scalable to numerous robots. T o overcome drawbacks of both, we propose a novel cooperative transportation method for nonholonomic mobile robots by improving conventional formation control, which is distributed, has a low time-complexity and accommodates scalable constraints. The proposed control-based method is testified on a cable-suspended payload and divided into two parts, including robot trajectory generation and trajectory tracking. Unlike most time-consuming trajectory generation methods, ours can generate trajectories with only constant time-complexity, needless of global maps. As for trajectory tracking, our control-based method not only scales easily to multiple constraints as those optimization-based methods, but reduces their time-complexity from polynomial to linear . Simulations and experiments can verify the feasibility of our method. ECENTL Y, logistics cyber-physical systems (CPS), particularly multi-robot cooperative transportation, have garnered increasing attention due to their advantages, such as cost reduction and enhanced productivity [1]-[17]. In this scenario, robots are required to coordinately transport the payload from a starting place to the desired destination quickly. Typically, the robot formation is subject to numerous constraints in practical transportation, such as obstacle avoidance, inter-robot collision avoidance, velocity constraints, payload protection, nonholonomic kinematics, etc. So far, how to overcome as many constraints as possible in the shortest time has become an important issue in cooperative transportation problems. Most cooperative transportation algorithms are based on two frameworks, including distributed control [3]-[8] and optimization [10]-[17].

Parallel manipulators, also called parallel kinematics machines (PKM), enable robotic solutions for highly dynamic handling and machining applications. The safe and accurate design and control necessitates high-fidelity dynamics models. Such modeling approaches have already been presented for PKM with simple limbs (i.e. each limb is a serial kinematic chain). A systematic modeling approach for PKM with complex limbs (i.e. limbs that possess kinematic loops) was not yet proposed despite the fact that many successful PKM comprise complex limbs. This paper presents a systematic modular approach to the kinematics and dynamics modeling of PKM with complex limbs that are built as serial arrangement of closed loops. The latter are referred to as hybrid limbs, and can be found in almost all PKM with complex limbs, such as the Delta robot. The proposed method generalizes the formulation for PKM with simple limbs by means of local resolution of loop constraints, which is known as constraint embedding in multibody dynamics. The constituent elements of the method are the kinematic and dynamic equations of motions (EOM), and the inverse kinematics solution of the limbs, i.e. the relation of platform motion and the motion of the limbs. While the approach is conceptually independent of the used kinematics and dynamics formulation, a Lie group formulation is employed for deriving the EOM. The frame invariance of the Lie group formulation is used for devising a modular modeling method where the EOM of a representative limb are used to derived the EOM of the limbs of a particular PKM. The PKM topology is exploited in a parallel computation scheme that shall allow for computationally efficient distributed evaluation of the overall EOM of the PKM. Finally, the method is applied to the IRSBot-2 and a 3\underline{R}R[2RR]R Delta robot, which is presented in detail.

Singularities, manifesting as special configuration states, deteriorate robot performance and may even lead to a loss of control over the system. This paper addresses the kinematic singularity concerns in robotic systems with model mismatch and actuator constraints through control barrier functions (CBFs). We propose a learning-based control strategy to prevent robots entering singularity regions. More precisely, we leverage Gaussian process (GP) regression to learn the unknown model mismatch, where the prediction error is restricted by a deterministic bound. Moreover, we offer the criteria for parameter selection to ensure the feasibility of CBFs subject to actuator constraints. The proposed approach is validated by high-fidelity simulations on a 2 degrees-of-freedom (DoFs) planar robot.

In the field of control engineering, the connection between Signal Temporal Logic (STL) and time-varying Control Barrier Functions (CBF) has attracted considerable attention. CBFs have demonstrated notable success in ensuring the safety of critical applications by imposing constraints on system states, while STL allows for precisely specifying spatio-temporal constraints on the behavior of robotic systems. Leveraging these methodologies, this paper addresses the safety-critical navigation problem, in Socially Responsible Navigation (SRN) context, presenting a CBF-based STL motion planning methodology. This methodology enables task completion at any time within a specified time interval considering a dynamic system subject to velocity constraints. The proposed approach involves real-time computation of a smooth CBF, with the computation of a dynamically adjusted parameter based on the available path space and the maximum allowable velocity. A simulation study is conducted to validate the methodology, ensuring safety in the presence of static and dynamic obstacles and demonstrating its compliance with spatio-temporal constraints under non-linear velocity constraints.

A motion planning methodology based on the combination of Control Barrier Functions (CBF) and Signal Temporal Logic (STL) is employed in this paper. This methodology allows task completion at any point within a specified time interval, considering a dynamic system subject to velocity constraints. In this work, we apply this approach into the context of Socially Responsible Navigation (SRN), introducing a rotation constraint. This constraint is designed to maintain the user within the robot's field of view (FOV), enhancing human-robot interaction with the concept of side-by-side human-robot companion. This angular constraint offers the possibility to customize social navigation to specific needs, thereby enabling safe SRN. Its validation is carried out through simulations demonstrating the system's effectiveness in adhering to spatio-temporal constraints, including those related to robot velocity, rotation, and the presence of static and dynamic obstacles.

One of the most important challenges of Smart City Applications is to adapt the system to interact with non-expert users. Robot imitation frameworks aim to simplify and reduce times of robot programming by allowing users to program directly through demonstrations. In classical frameworks, actions are modeled using joint or Cartesian space trajectories. Other features, such as visual ones, are not always well represented with these pure geometrical approaches. Continuous Goal-Directed Actions (CGDA) is an alternative to these methods, as it encodes actions as changes of any feature that can be extracted from the environment. As a consequence of this, the robot joint trajectories for execution must be fully computed to comply with this feature-agnostic encoding. This is achieved using Evolutionary Algorithms (EA), which usually requires too many evaluations to perform this evolution step in the actual robot. Current strategies involve performing evaluations in a simulation, transferring the final joint trajectory to the actual robot. Smart City applications involve working in highly dynamic and complex environments, where having a precise model is not always achievable. Our goal is to study the tractability of performing these evaluations directly in a real-world scenario. Two different approaches to reduce the number of evaluations using EA, are proposed and compared. In the first approach, Particle Swarm Optimization (PSO)-based methods have been studied and compared within CGDA: naive PSO, Fitness Inheritance PSO (FI-PSO), and Adaptive Fuzzy Fitness Granulation with PSO (AFFG-PSO). The second approach studied the introduction of geometrical and velocity constraints within CGDA. The effects of both approaches were analyzed and compared in the wax and paint actions, two CGDA commonly studied use cases. Results from this paper depict an important reduction in the number of evaluations.