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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.

In general-sum games, the interaction of self-interested learning agents commonly leads to socially worse outcomes, such as defect-defect in the iterated stag hunt (ISH). Previous works address this challenge by sharing rewards or shaping their opponents' learning process, which require too strong assumptions. In this paper, we demonstrate that agents trained to optimize expected returns are more likely to choose a safe action that leads to guaranteed but lower rewards. However, there typically exists a risky action that leads to higher rewards in the long run only if agents cooperate, e.g., cooperate-cooperate in ISH. To overcome this, we propose using action value distribution to characterize the decision's risk and corresponding potential payoffs. Specifically, we present Adaptable Risk-Sensitive Policy (ARSP). ARSP learns the distributions over agent's return and estimates a dynamic risk-seeking bonus to discover risky coordination strategies. Furthermore, to avoid overfitting training opponents, ARSP learns an auxiliary opponent modeling task to infer opponents' types and dynamically alter corresponding strategies during execution. Empirically, agents trained via ARSP can achieve stable coordination during training without accessing opponent's rewards or learning process, and can adapt to non-cooperative opponents during execution. To the best of our knowledge, it is the first method to learn coordination strategies between agents both in iterated prisoner's dilemma (IPD) and iterated stag hunt (ISH) without shaping opponents or rewards, and can adapt to opponents with distinct strategies during execution. Furthermore, we show that ARSP can be scaled to high-dimensional settings., Comment: arXiv admin note: substantial text overlap with arXiv:2205.15859

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.

While various multi-agent reinforcement learning methods have been proposed in cooperative settings, few works investigate how self-interested learning agents achieve mutual coordination in decentralized general-sum games and generalize pre-trained policies to non-cooperative opponents during execution. In this paper, we present Generalizable Risk-Sensitive Policy (GRSP). GRSP learns the distributions over agent's return and estimate a dynamic risk-seeking bonus to discover risky coordination strategies. Furthermore, to avoid overfitting to training opponents, GRSP learns an auxiliary opponent modeling task to infer opponents' types and dynamically alter corresponding strategies during execution. Empirically, agents trained via GRSP can achieve mutual coordination during training stably and avoid being exploited by non-cooperative opponents during execution. To the best of our knowledge, it is the first method to learn coordination strategies between agents both in iterated prisoner's dilemma (IPD) and iterated stag hunt (ISH) without shaping opponents or rewards, and firstly consider generalization during execution. Furthermore, we show that GRSP can be scaled to high-dimensional settings., Comment: the paper will be updated soon

In this paper, an efficient motion planning approach with grid-based generalized Voronoi diagrams (G$ \mathbf{^2} $VD) 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 novel Voronoi corridor to further improve the search efficiency; 2) an efficient quadratic programming-based path smoothing approach is presented, wherein the clearance to obstacles is considered 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 outdoor environments. It is shown that the computational efficiency is improved by 17.1% in the path searching stage, and path smoothing with the proposed approach is 6.6 times faster than an advanced sparse-banded structure-based path smoothing approach and 53.3 times faster than the popular timed-elastic-band planner. A video showing outdoor navigation on our campus is available at https://youtu.be/iMXGthgvp58., Comment: This paper has been accepted for publication in the IEEE Transactions on Automation Science and Engineering

The objective of this paper is to derive the essential invariance and contraction properties for the geometric periodic systems, which can be formulated as a category of differential inclusions, and primarily rendered in the phase coordinate, or the cycle coordinate. First, we introduce the geometric averaging method for this category of systems, and also analyze the accuracy of its averaging approximation. Specifically, we delve into the details of the geometrically periodic system through the tunnel of considering the convergence between the system and its geometrically averaging approximation. Under different corresponding conditions, the approximation on infinite time intervals can achieve certain accuracies, such that one can use the stability result of either the original system or the averaging system to deduce the stability of the other. After that, we employ the graphical stability to investigate the "pattern stability" with respect to the phase-based system. Finally, by virtue of the contraction analysis on the Finsler manifold, the idea of accentuating the periodic pattern incremental stability and convergence is nurtured in the phase-based differential inclusion system, and comes to its preliminary fruition in application to biomimetic mechanic robot control problem., Comment: Still in progress

To solve the autonomous navigation problem in complex environments, an efficient motion planning approach is newly 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 novel heuristic-guided pruning strategy of motion primitives is proposed and fully integrated into the state lattice-based global path planner to further improve the computational efficiency of graph search, and 2) a new 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 our approach 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. We name the proposed motion planning framework E$ \mathrm{^3} $MoP, where the number 3 not only means our approach is a three-layer framework but also means the proposed approach is efficient in three stages., Comment: This paper has been accepted for publication in the IEEE Transactions on Automation Science and Engineering

Due to the limitation of the drone's load capacity, various specific tasks need to be accomplished by multiple drones in collaboration. In some transportation tasks, two drones are required to lift the load together, which brings even more significant challenges to the control problem because the transportation system is underactuated and it contains very complex dynamic coupling. When transporting bar-shaped objects, the load's attitude, the rope's swing motion, as well as the distance between the drones, should be carefully considered to ensure the security of the system. So far, few works have been implemented for double drone transportation systems to guarantee their transportation performance, especially in the aforementioned aspect. In this paper, a nonlinear cooperative control method is proposed, with both rigorous stability analysis and experimental results demonstrating its great performance. Without the need to distinguish the identities between the leader and the follower, the proposed method successfully realizes effective control for the two drones separately, mainly owning to the deep analysis for the system dynamics and the elaborate design for the control law. By utilizing Lyapunov techniques, the proposed controller achieves simultaneous positioning and mutual distance control of the drones, meanwhile, it efficiently eliminates the swing of the load. Flight experiments are presented to demonstrate the performance of the proposed nonlinear cooperative control strategy., Comment: 13 pages, original complete manuscript

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., Comment: 2021 IEEE International Conference on Robotics and Automation (ICRA), accepted

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 $\epsilon$, which are the best complexities among the non-accelerated gradient-type methods, 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.

In order to obtain a compact line segment-based map representation for localization and planning of mobile robots, it is necessary to merge redundant line segments which physically represent the same part of the environment in different scans. In this paper, a consistent and efficient redundant line segment merging approach (CAE-RLSM) is proposed for online feature map building. The proposed CAE-RLSM is composed of two newly proposed modules: one-to-many incremental line segment merging (OTM-ILSM) and multi-processing global map adjustment (MP-GMA). Different from state-of-the-art offline merging approaches, the proposed CAE-RLSM can achieve real-time mapping performance, which not only reduces the redundancy of incremental merging with high efficiency, but also solves the problem of global map adjustment after loop closing to guarantee global consistency. Furthermore, a new correlation-based evaluation metric is proposed for the quality evaluation of line segment maps. This evaluation metric does not require manual measurement of the environmental metric information, instead it makes full use of globally consistent laser scans obtained by simultaneous localization and mapping (SLAM) systems to compare the performance of different line segment-based mapping approaches in an objective and fair manner. Comparative experimental results with respect to a mean shift-based offline redundant line segment merging approach (MS-RLSM) and an offline version of one-to-one incremental line segment merging approach (O$^2$TO-ILSM) on both public data sets and self-recorded data set are presented to show the superior performance of CAE-RLSM in terms of efficiency and map quality in different scenarios.

In this paper, a novel real-time acceleration-continuous path-constrained trajectory planning algorithm is proposed with an appealing built-in tradability mechanism between cruise motion and time-optimal motion. Different from existing approaches, the proposed approach smoothens time-optimal trajectories with bang-bang input structures to generate acceleration-continuous trajectories while preserving the completeness property. More importantly, a novel built-in tradability mechanism is proposed and embedded into the trajectory planning framework, so that the proportion of the cruise motion and time-optimal motion can be flexibly adjusted by changing a user-specified functional parameter. Thus, the user can easily apply the trajectory planning algorithm for various tasks with different requirements on motion efficiency and cruise proportion. Moreover, it is shown that feasible trajectories are computed more quickly than optimal trajectories. Rigorous mathematical analysis and proofs are provided for these aforementioned results. Comparative simulation and experimental results on omnidirectional wheeled mobile robots demonstrate the capability of the proposed algorithm in terms of flexible tunning between cruise and time-optimal motions, as well as higher computational efficiency., Comment: 12 pages, 19 figures

This letter summarizes some known properties and also presents several new properties of the Numerical Integration (NI) method for time-optimal trajectory planning along a specified path. The contribution is that rigorous mathematical proofs of these properties are presented, most of which cannot be found in existing literatures. We first give some properties regarding switch points and accelerating/decelerating curves of the NI method. Then, for the fact that when kinematic constraints are considered, the original version of NI which only considers torque constraints may result in failure of trajectory planning, we give the concrete failure conditions with rigorous mathematical proof. Accordingly, a failure detection algorithm is given in a run-and-test manner. Some simulation results on a unicycle vehicle are provided to verify those presented properties. Note that though those known properties are not discovered first, their mathematical proofs are given first in this letter. The detailed proofs make the theory of NI more complete and help interested readers to gain a thorough understanding of the method., Comment: 1. 8 pages, 10 figures, and submission for RA-L and ICRA 2017 2. Added reference [23] and its statements 3. Added Fig. 1 to explain various notations clearer 4. Moved proofs of Properties 2-5 into Appendix A-D to improve readability 5. Corrected typos