This paper addresses the problem of hierarchical task control, where a robotic system must perform multiple subtasks with varying levels of priority. A commonly used approach for hierarchical control is the null-space projection technique, which ensures that higher-priority tasks are executed without interference from lower-priority ones. While effective, the state-of-the-art implementations of this method rely on low-level controllers, such as PID controllers, which can be prone to suboptimal solutions in complex tasks. This paper presents a novel framework for hierarchical task control, integrating the null-space projection technique with the path integral control method. Our approach leverages Monte Carlo simulations for real-time computation of optimal control inputs, allowing for the seamless integration of simpler PID-like controllers with a more sophisticated optimal control technique. Through simulation studies, we demonstrate the effectiveness of this combined approach, showing how it overcomes the limitations of traditional

This work proposes a novel multi-robot task allocation framework for robots that can switch between multiple modes, e.g., flying, driving, or walking. We first provide a method to encode the multi-mode property of robots as a graph, where the mode of each robot is represented by a node. Next, we formulate a constrained optimization problem to decide both the task to be allocated to each robot as well as the mode in which the latter should execute the task. The robot modes are optimized based on the state of the robot and the environment, as well as the energy required to execute the allocated task. Moreover, the proposed framework is able to encompass kinematic and dynamic models of robots alike. Furthermore, we provide sufficient conditions for the convergence of task execution and allocation for both robot models.

Feasible Force Set Shaping for a Payload-Carrying Platform Consisting of Tiltable Multiple UA Vs Connected Via Passive Hinge Joints Takumi Ito 1, Hayato Kawashima 1, Riku Funada 1, and Mitsuji Sampei 1 Abstract -- This paper presents a method for shaping the feasible force set of a payload-carrying platform composed of multiple Unmanned Aerial V ehicles (UA Vs) and proposes a control law that leverages the advantages of this shaped force set. The UA Vs are connected to the payload through passively rotatable hinge joints. The joint angles are controlled by the differential thrust produced by the rotors, while the total force generated by all the rotors is responsible for controlling the payload. The shape of the set of the total force depends on the tilt angles of the UA Vs, which allows us to shape the feasible force set by adjusting these tilt angles. This paper aims to ensure that the feasible force set encompasses the required shape, enabling the platform to generate force redundantly--meaning in various directions. We then propose a control law that takes advantage of this redundancy. I. INTRODUCTION The advancement of Unmanned Aerial V ehicles (UA Vs) has enabled applications to be conducted automatically, such as agriculture [1], environmental monitoring [2], and inspection [3]. Additionally, there is potential for using UA Vs in payload transportation [4] due to increased package supplies and a labor shortage. Despite these diverse applications, conventional UA Vs, consisting of multiple rotors pointing upward and placed on the same plane, are known as an un-deractuated system at SE(3) space (six-dimensional space).

This paper presents a novel VTOL UAV that owns a link connecting four rotors and a fuselage by a passive joint, allowing the control of the rotor's tilting angle by adjusting the rotors' thrust. This unique structure contributes to eliminating additional actuators, such as servo motors, to control the tilting angles of rotors, resulting in the UAV's weight lighter and simpler structure. We first derive the dynamical model of the newly designed UAV and analyze its controllability. Then, we design the controller that leverages the tiltable link with four rotors to accelerate the UAV while suppressing a deviation of the UAV's angle of attack from the desired value to restrain the change of the aerodynamic force. Finally, the validity of the proposed control strategy is evaluated in simulation study.

This paper proposes a collision avoidance method for ellipsoidal rigid bodies, which utilizes a control barrier function (CBF) designed from a supporting hyperplane. We formulate the problem in the Special Euclidean Group SE(2) and SE(3), where the dynamics are described as rigid body motion (RBM). Then, we consider the condition for separating two ellipsoidal rigid bodies by employing a signed distance from a supporting hyperplane of a rigid body to the other rigid body. Although the positive value of this signed distance implies that two rigid bodies are collision-free, a naively prepared supporting hyperplane yields a smaller value than the actual distance. To avoid such a conservative evaluation, the supporting hyperplane is rotated so that the signed distance from the supporting hyperplane to the other rigid body is maximized. We prove that the maximum value of this optimization problem is equal to the actual distance between two ellipsoidal rigid bodies, hence eliminating excessive conservativeness. We leverage this signed distance as a CBF to prevent collision while the supporting hyperplane is rotated via a gradient-based input. The designed CBF is integrated into a quadratic programming (QP) problem, where each rigid body calculates its collision-free input in a distributed manner, given communication among rigid bodies. The proposed method is demonstrated with simulations. Finally, we exemplify our method can be extended to a vehicle having nonholonomic dynamics.

We propose a path planning methodology for a mobile robot navigating through an obstacle-filled environment to generate a reference path that is traceable with moderate sensing efforts. The desired reference path is characterized as the shortest path in an obstacle-filled Gaussian belief manifold equipped with a novel information-geometric distance function. The distance function we introduce is shown to be an asymmetric quasi-pseudometric and can be interpreted as the minimum information gain required to steer the Gaussian belief. An RRT*-based numerical solution algorithm is presented to solve the formulated shortest-path problem. To gain insight into the asymptotic optimality of the proposed algorithm, we show that the considered path length function is continuous with respect to the topology of total variation. Simulation results demonstrate that the proposed method is effective in various robot navigation scenarios to reduce sensing costs, such as the required frequency of sensor measurements and the number of sensors that must be operated simultaneously.