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.

CAE-RLSM: Consistent and Efficient Redundant Line Segment Merging for Online Feature Map Building

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 (OTO-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.

Real-time Acceleration-continuous Path-constrained Trajectory Planning With Built-in Tradability Between Cruise and Time-optimal Motions

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.

Essential Properties of Numerical Integration for Time-optimal Trajectory Planning Along a Specified Path

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.