Robust Safety Critical Control Under Multiple State and Input Constraints: Volume Control Barrier Function Method

In this paper, the safety-critical control problem for uncertain systems under multiple control barrier function (CBF) constraints and input constraints is investigated. A novel framework is proposed to generate a safety filter that minimizes changes to reference inputs when safety risks arise, ensuring a balance between safety and performance. A nonlinear disturbance observer (DOB) based on the robust integral of the sign of the error (RISE) is used to estimate system uncertainties, ensuring that the estimation error converges to zero exponentially. This error bound is integrated into the safety-critical controller to reduce conservativeness while ensuring safety. To further address the challenges arising from multiple CBF and input constraints, a novel Volume CBF (VCBF) is proposed by analyzing the feasible space of the quadratic programming (QP) problem. % ensuring solution feasibility by keeping the volume as a positive value. To ensure that the feasible space does not vanish under disturbances, a DOB-VCBF-based method is introduced, ensuring system safety while maintaining the feasibility of the resulting QP. Subsequently, several groups of simulation and experimental results are provided to validate the effectiveness of the proposed controller.

Polytope Volume Monitoring Problem: Formulation and Solution via Parametric Linear Program Based Control Barrier Function

Motivated by the latest research on feasible space monitoring of multiple control barrier functions (CBFs) as well as polytopic collision avoidance, this paper studies the Polytope Volume Monitoring (PVM) problem, whose goal is to design a control law for inputs of nonlinear systems to prevent the volume of some state-dependent polytope from decreasing to zero. Recent studies have explored the idea of applying Chebyshev ball method in optimization theory to solve the case study of PVM; however, the underlying difficulties caused by nonsmoothness have not been addressed. This paper continues the study on this topic, where our main contribution is to establish the relationship between nonsmooth CBF and parametric optimization theory through directional derivatives for the first time, so as to solve PVM problems more conveniently. In detail, inspired by Chebyshev ball approach, a parametric linear program (PLP) based nonsmooth barrier function candidate is established for PVM, and then, sufficient conditions for it to be a nonsmooth CBF are proposed, based on which a quadratic program (QP) based safety filter with guaranteed feasibility is proposed to address PVM problems. Finally, a numerical simulation example is given to show the efficiency of the proposed safety filter.

Optimization-free Smooth Control Barrier Function for Polygonal Collision Avoidance

Polygonal collision avoidance (PCA) is short for the problem of collision avoidance between two polygons (i.e., polytopes in planar) that own their dynamic equations. This problem suffers the inherent difficulty in dealing with non-smooth boundaries and recently optimization-defined metrics, such as signed distance field (SDF) and its variants, have been proposed as control barrier functions (CBFs) to tackle PCA problems. In contrast, we propose an optimization-free smooth CBF method in this paper, which is computationally efficient and proved to be nonconservative. It is achieved by three main steps: a lower bound of SDF is expressed as a nested Boolean logic composition first, then its smooth approximation is established by applying the latest log-sum-exp method, after which a specified CBF-based safety filter is proposed to address this class of problems. To illustrate its wide applications, the optimization-free smooth CBF method is extended to solve distributed collision avoidance of two underactuated nonholonomic vehicles and drive an underactuated container crane to avoid a moving obstacle respectively, for which numerical simulations are also performed.

Reflection of Episodes: Learning to Play Game from Expert and Self Experiences

StarCraft II is a complex and dynamic real-time strategy (RTS) game environment, which is very suitable for artificial intelligence and reinforcement learning research. To address the problem of Large Language Model(LLM) learning in complex environments through self-reflection, we propose a Reflection of Episodes(ROE) framework based on expert experience and self-experience. This framework first obtains key information in the game through a keyframe selection method, then makes decisions based on expert experience and self-experience. After a game is completed, it reflects on the previous experience to obtain new self-experience. Finally, in the experiment, our method beat the robot under the Very Hard difficulty in TextStarCraft II. We analyze the data of the LLM in the process of the game in detail, verified its effectiveness.

Minimum Snap Trajectory Generation and Control for an Under-actuated Flapping Wing Aerial Vehicle

Minimum Snap Trajectory Generation and Control for an Under-actuated Flapping Wing Aerial VehicleThis paper presents both the trajectory generation and tracking control strategies for an underactuated flapping wing aerial vehicle (FWAV). First, the FWAV dynamics is analyzed in a practical perspective. Then, based on these analyses, we demonstrate the differential flatness of the FWAV system, and develop a general-purpose trajectory generation strategy. Subsequently, the trajectory tracking controller is developed with the help of robust control and switch control techniques. After that, the overall system asymptotic stability is guaranteed by Lyapunov stability analysis. To make the controller applicable in real flight, we also provide several instructions. Finally, a series of experiment results manifest the successful implementation of the proposed trajectory generation strategy and tracking control strategy. This work firstly achieves the closed-loop integration of trajectory generation and control for real 3-dimensional flight of an underactuated FWAV to a practical level.

Towards Practical Autonomous Flight Simulation for Flapping Wing Biomimetic Robots with Experimental Validation

Tried-and-true flapping wing robot simulation is essential in developing flapping wing mechanisms and algorithms. This paper presents a novel application-oriented flapping wing platform, highly compatible with various mechanical designs and adaptable to different robotic tasks. First, the blade element theory and the quasi-steady model are put forward to compute the flapping wing aerodynamics based on wing kinematics. Translational lift, translational drag, rotational lift, and added mass force are all considered in the computation. Then we use the proposed simulation platform to investigate the passive wing rotation and the wing-tail interaction phenomena of a particular flapping-wing robot. With the help of the simulation tool and a novel statistic based on dynamic differences from the averaged system, several behaviors display their essence by investigating the flapping wing robot dynamic characteristics. After that, the attitude tracking control problem and the positional trajectory tracking problem are both overcome by robust control techniques. Further comparison simulations reveal that the proposed control algorithms compared with other existing ones show apparent superiority. What is more, with the same control algorithm and parameters tuned in simulation, we conduct real flight experiments on a self-made flapping wing robot, and obtain similar results from the proposed simulation platform. In contrast to existing simulation tools, the proposed one is compatible with most existing flapping wing robots, and can inherently drill into each subtle behavior in corresponding applications by observing aerodynamic forces and torques on each blade element.

G$ \mathbf{^2} $VD Planner: An Efficient Motion Planning Approach With Grid-based Generalized Voronoi Diagrams

In this letter, an efficient motion planning approach with grid-based generalized Voronoi diagrams is newly proposed for mobile robots. Different from existing approaches, the novelty of this work is twofold: 1) a new state lattice-based path searching approach is proposed, in which the search space is reduced to a Voronoi corridor to further improve the search efficiency, along with a Voronoi potential field constructed to make the searched path keep a reasonable distance from obstacles to provide sufficient optimization margin for the subsequent path smoothing, and 2) an efficient quadratic programming-based path smoothing approach is presented, wherein the clearance to obstacles is considered in the form of the penalty of the deviation from the safe reference path to improve the path clearance of hard-constrained path smoothing approaches. We validate the efficiency and smoothness of our approach in various challenging simulation scenarios and large-scale outdoor environments. It is shown that the computational efficiency is improved by 17.1% in the path searching stage, and smoothing the path with our approach is 11.86 times faster than a recent gradient-based path smoothing approach. We will release the source code to the robotics community.

EffMoP: Efficient Motion Planning Based on Heuristic-Guided Motion Primitives Pruning and Path Optimization With Sparse-Banded Structure

To solve the autonomous navigation problem in complex environments, an efficient motion planning approach called EffMoP is presented in this paper. Considering the challenges from large-scale, partially unknown complex environments, a three-layer motion planning framework is elaborately designed, including global path planning, local path optimization, and time-optimal velocity planning. Compared with existing approaches, the novelty of this work is twofold: 1) a heuristic-guided pruning strategy of motion primitives is newly designed and fully integrated into the search-based global path planner to improve the computational efficiency of graph search, and 2) a novel soft-constrained local path optimization approach is proposed, wherein the sparse-banded system structure of the underlying optimization problem is fully exploited to efficiently solve the problem. We validate the safety, smoothness, flexibility, and efficiency of EffMoP in various complex simulation scenarios and challenging real-world tasks. It is shown that the computational efficiency is improved by 66.21% in the global planning stage and the motion efficiency of the robot is improved by 22.87% compared with the recent quintic B\'{e}zier curve-based state space sampling approach.

MRPB 1.0: A Unified Benchmark for the Evaluation of Mobile Robot Local Planning Approaches

Local planning is one of the key technologies for mobile robots to achieve full autonomy and has been widely investigated. To evaluate mobile robot local planning approaches in a unified and comprehensive way, a mobile robot local planning benchmark called MRPB 1.0 is newly proposed in this paper. The benchmark facilitates both motion planning researchers who want to compare the performance of a new local planner relative to many other state-of-the-art approaches as well as end users in the mobile robotics industry who want to select a local planner that performs best on some problems of interest. We elaborately design various simulation scenarios to challenge the applicability of local planners, including large-scale, partially unknown, and dynamic complex environments. Furthermore, three types of principled evaluation metrics are carefully designed to quantitatively evaluate the performance of local planners, wherein the safety, efficiency, and smoothness of motions are comprehensively considered. We present the application of the proposed benchmark in two popular open-source local planners to show the practicality of the benchmark. In addition, some insights and guidelines about the design and selection of local planners are also provided. The benchmark website contains all data of the designed simulation scenarios, detailed descriptions of these scenarios, and example code.

Variance Reduced EXTRA and DIGing and Their Optimal Acceleration for Strongly Convex Decentralized Optimization

We study stochastic decentralized optimization for the problem of training machine learning models with large-scale distributed data. We extend the widely used EXTRA and DIGing methods with variance reduction (VR), and propose two methods: VR-EXTRA and VR-DIGing. The proposed VR-EXTRA requires the time of $O((\kappa_s+n)\log\frac{1}{\epsilon})$ stochastic gradient evaluations and $O((\kappa_b+\kappa_c)\log\frac{1}{\epsilon})$ communication rounds to reach precision $\epsilon$, where $\kappa_s$ and $\kappa_b$ are the stochastic condition number and batch condition number for strongly convex and smooth problems, respectively, $\kappa_c$ is the condition number of the communication network, and $n$ is the sample size on each distributed node. The proposed VR-DIGing has a little higher communication cost of $O((\kappa_b+\kappa_c^2)\log\frac{1}{\epsilon})$. Our stochastic gradient computation complexities are the same as the ones of single-machine VR methods, such as SAG, SAGA, and SVRG, and our communication complexities keep the same as those of EXTRA and DIGing, respectively. To further speed up the convergence, we also propose the accelerated VR-EXTRA and VR-DIGing with both the optimal $O((\sqrt{n\kappa_s}+n)\log\frac{1}{\epsilon})$ stochastic gradient computation complexity and $O(\sqrt{\kappa_b\kappa_c}\log\frac{1}{\epsilon})$ communication complexity. Our stochastic gradient computation complexity is also the same as the ones of single-machine accelerated VR methods, such as Katyusha, and our communication complexity keeps the same as those of accelerated full batch decentralized methods, such as MSDA.