A Comparative Study of Artificial Potential Fields and Safety Filters

In this paper, we have demonstrated that the controllers designed by a classical motion planning tool, namely artificial potential fields (APFs), can be derived from a recently prevalent approach: control barrier function quadratic program (CBF-QP) safety filters. By integrating APF information into the CBF-QP framework, we establish a bridge between these two methodologies. Specifically, this is achieved by employing the attractive potential field as a control Lyapunov function (CLF) to guide the design of the nominal controller, and then the repulsive potential field serves as a reciprocal CBF (RCBF) to define a CBF-QP safety filter. Building on this integration, we extend the design of the CBF-QP safety filter to accommodate a more general class of dynamical models featuring a control-affine structure. This extension yields a special CBF-QP safety filter and a general APF solution suitable for control-affine dynamical models. Through a reach-avoid navigation example, we showcase the efficacy of the developed approaches.

Unifying Controller Design for Stabilizing Nonlinear Systems with Norm-Bounded Control Inputs

This paper revisits a classical challenge in the design of stabilizing controllers for nonlinear systems with a norm-bounded input constraint. By extending Lin-Sontag's universal formula and introducing a generic (state-dependent) scaling term, a unifying controller design method is proposed. The incorporation of this generic scaling term gives a unified controller and enables the derivation of alternative universal formulas with various favorable properties, which makes it suitable for tailored control designs to meet specific requirements and provides versatility across different control scenarios. Additionally, we present a constructive approach to determine the optimal scaling term, leading to an explicit solution to an optimization problem, named optimization-based universal formula. The resulting controller ensures asymptotic stability, satisfies a norm-bounded input constraint, and optimizes a predefined cost function. Finally, the essential properties of the unified controllers are analyzed, including smoothness, continuity at the origin, stability margin, and inverse optimality. Simulations validate the approach, showcasing its effectiveness in addressing a challenging stabilizing control problem of a nonlinear system.

Coordinated Guiding Vector Field Design for Ordering-Flexible Multi-Robot Surface Navigation

We design a distributed coordinated guiding vector field (CGVF) for a group of robots to achieve ordering-flexible motion coordination while maneuvering on a desired two-dimensional (2D) surface. The CGVF is characterized by three terms, i.e., a convergence term to drive the robots to converge to the desired surface, a propagation term to provide a traversing direction for maneuvering on the desired surface, and a coordinated term to achieve the surface motion coordination with an arbitrary ordering of the robotic group. By setting the surface parameters as additional virtual coordinates, the proposed approach eliminates the potential singularity of the CGVF and enables both the global convergence to the desired surface and the maneuvering on the surface from all possible initial conditions. The ordering-flexible surface motion coordination is realized by each robot to share with its neighbors only two virtual coordinates, i.e. that of a given target and that of its own, which reduces the communication and computation cost in multi-robot surface navigation. Finally, the effectiveness of the CGVF is substantiated by extensive numerical simulations.

Quadrotor Stabilization with Safety Guarantees: A Universal Formula Approach

Safe stabilization is a significant challenge for quadrotors, which involves reaching a goal position while avoiding obstacles. Most of the existing solutions for this problem rely on optimization-based methods, demanding substantial onboard computational resources. This paper introduces a novel approach to address this issue and provides a solution that offers fast computational capabilities tailored for onboard execution. Drawing inspiration from Sontag's universal formula, we propose an analytical control strategy that incorporates the conditions of control Lyapunov functions (CLFs) and control barrier functions (CBFs), effectively avoiding the need for solving optimization problems onboard. Moreover, we extend our approach by incorporating the concepts of input-to-state stability (ISS) and input-to-state safety (ISSf), enhancing the universal formula's capacity to effectively manage disturbances. Furthermore, we present a projection-based approach to ensure that the universal formula remains effective even when faced with control input constraints. The basic idea of this approach is to project the control input derived from the universal formula onto the closest point within the control input domain. Through comprehensive simulations and experimental results, we validate the efficacy and highlight the advantages of our methodology.

An alternating peak-optimization method for optimal trajectory generation of quadrotor drones

In this paper, we propose an alternating optimization method to address a time-optimal trajectory generation problem. Different from the existing solutions, our approach introduces a new formulation that minimizes the overall trajectory running time while maintaining the polynomial smoothness constraints and incorporating hard limits on motion derivatives to ensure feasibility. To address this problem, an alternating peak-optimization method is developed, which splits the optimization process into two sub-optimizations: the first sub-optimization optimizes polynomial coefficients for smoothness, and the second sub-optimization adjusts the time allocated to each trajectory segment. These are alternated until a feasible minimum-time solution is found. We offer a comprehensive set of simulations and experiments to showcase the superior performance of our approach in comparison to existing methods. A collection of demonstration videos with real drone flying experiments can be accessed at https://www.youtube.com/playlist?list=PLQGtPFK17zUYkwFT-fr0a8E49R8Uq712l .

CircleFormer: Circular Nuclei Detection in Whole Slide Images with Circle Queries and Attention

Both CNN-based and Transformer-based object detection with bounding box representation have been extensively studied in computer vision and medical image analysis, but circular object detection in medical images is still underexplored. Inspired by the recent anchor free CNN-based circular object detection method (CircleNet) for ball-shape glomeruli detection in renal pathology, in this paper, we present CircleFormer, a Transformer-based circular medical object detection with dynamic anchor circles. Specifically, queries with circle representation in Transformer decoder iteratively refine the circular object detection results, and a circle cross attention module is introduced to compute the similarity between circular queries and image features. A generalized circle IoU (gCIoU) is proposed to serve as a new regression loss of circular object detection as well. Moreover, our approach is easy to generalize to the segmentation task by adding a simple segmentation branch to CircleFormer. We evaluate our method in circular nuclei detection and segmentation on the public MoNuSeg dataset, and the experimental results show that our method achieves promising performance compared with the state-of-the-art approaches. The effectiveness of each component is validated via ablation studies as well. Our code is released at https://github.com/zhanghx-iim-ahu/CircleFormer.

Risk-Aware Reward Shaping of Reinforcement Learning Agents for Autonomous Driving

Reinforcement learning (RL) is an effective approach to motion planning in autonomous driving, where an optimal driving policy can be automatically learned using the interaction data with the environment. Nevertheless, the reward function for an RL agent, which is significant to its performance, is challenging to be determined. The conventional work mainly focuses on rewarding safe driving states but does not incorporate the awareness of risky driving behaviors of the vehicles. In this paper, we investigate how to use risk-aware reward shaping to leverage the training and test performance of RL agents in autonomous driving. Based on the essential requirements that prescribe the safety specifications for general autonomous driving in practice, we propose additional reshaped reward terms that encourage exploration and penalize risky driving behaviors. A simulation study in OpenAI Gym indicates the advantage of risk-aware reward shaping for various RL agents. Also, we point out that proximal policy optimization (PPO) is likely to be the best RL method that works with risk-aware reward shaping.

Automated Formation Control Synthesis from Temporal Logic Specifications

In this paper, we propose a novel framework using formal methods to synthesize a navigation control strategy for a multi-robot swarm system with automated formation. The main objective of the problem is to navigate the robot swarm toward a goal position while passing a series of waypoints. The formation of the robot swarm should be changed according to the terrain restrictions around the corresponding waypoint. Also, the motion of the robots should always satisfy certain runtime safety requirements, such as avoiding collision with other robots and obstacles. We prescribe the desired waypoints and formation for the robot swarm using a temporal logic (TL) specification. Then, we formulate the transition of the waypoints and the formation as a deterministic finite transition system (DFTS) and synthesize a control strategy subject to the TL specification. Meanwhile, the runtime safety requirements are encoded using control barrier functions, and fixed-time control Lyapunov functions ensure fixed-time convergence. A quadratic program (QP) problem is solved to refine the DFTS control strategy to generate the control inputs for the robots, such that both TL specifications and runtime safety requirements are satisfied simultaneously. This work enlights a novel solution for multi-robot systems with complicated task specifications. The efficacy of the proposed framework is validated with a simulation study.

Characterizing bearing equivalence in directed graphs

In this paper, we study bearing equivalence in directed graphs. We first give a strengthened definition of bearing equivalence based on the \textit{kernel equivalence} relationship between bearing rigidity matrix and bearing Laplacian matrix. We then present several conditions to characterize bearing equivalence for both directed acyclic and cyclic graphs. These conditions involve the spectrum and null space of the associated bearing Laplacian matrix for a directed bearing formation. For directed acyclic graphs, all eigenvalues of the associated bearing Laplacian are real and nonnegative, while for directed graphs containing cycles, the bearing Laplacian can have eigenvalues with negative real parts. Several examples of bearing equivalent and bearing non-equivalent formations are given to illustrate these conditions.