Providing smooth reference trajectories can effectively increase performance and accuracy of tracking control applications while overshoot and unwanted vibrations are reduced. Trajectory planning computations can often be simplified significantly by transforming the system dynamics into decoupled integrator chains using methods such as feedback linearization, differential flatness or the controller canonical form. We present an efficient method to plan time optimal trajectories for integrator chains subject to derivative bound constraints. Therefore, an algebraic precomputation algorithm formulates the necessary conditions for time optimality in form of a set of polynomial systems, followed by a symbolic polynomial elimination using Gröbner bases. A fast online algorithm then plans the trajectories by calculating the roots of the decomposed polynomial systems. These roots describe the switching time instants of the input signal and the full trajectory simply follows by multiple integration. This method presents a systematic way to compute time optimal trajectories exactly via algebraic calculations without numerical approximation iterations. It is applied to various trajectory types with different continuity order, asymmetric derivative bounds and non-rest initial and final states.
This paper addresses the problem of efficiently computing higher-order variational integrators in simulation and trajectory optimization of mechanical systems as those often found in robotic applications. We develop $O(n)$ algorithms to evaluate the discrete Euler-Lagrange (DEL) equations and compute the Newton direction for solving the DEL equations, which results in linear-time variational integrators of arbitrarily high order. To our knowledge, no linear-time higher-order variational or even implicit integrators have been developed before. Moreover, an $O(n^2)$ algorithm to linearize the DE…
This article provides extensions to existing path-velocity decomposition based time optimal trajectory planning algorithm \cite{kant1986toward} to scenarios in which agents move in 2D obstacle environment under double integrator dynamics with drag term (damped double integrator). Particularly, we extend the idea of a tangent graph \cite{liu1992path} to $\calC^1$-Tangent graph to find continuously differentiable ($\calC^1$) shortest path between any two points. $\calC^1$-Tangent graph has a continuously differentiable ($\calC^1$) path between any two nodes. We also provide analytical expression…
An Optimized Path Planning of Manipulator Using Spline Curves and Real Quantifier Elimination Based on Comprehensive Gröbner Systems
Graduate School of Pure and Applied Sciences, University of Tsukuba（筑波大学文理学研究院）；Faculty of Pure and Applied Sciences, University of Tsukuba（筑波大学文理学院）；Faculty of Library, Information and Media Science, University of Tsukuba（筑波大学图书馆、信息与媒体科学学院）
本文提出利用Comprehensive Gröbner System (CGS)与CGS-QE方法高效求解机械臂逆运动学并认证轨迹解，结合三次样条插值与最短路径算法实现路径与关节配置的优化规划。
We study an adaptive source seeking problem, in which a mobile robot must identify the strongest emitter(s) of a signal in an environment with background emissions. Background signals may be highly heterogeneous and can mislead algorithms that are based on receding horizon control. We propose AdaSearch, a general algorithm for adaptive source seeking in the face of heterogeneous background noise. AdaSearch combines global trajectory planning with principled confidence intervals in order to concentrate measurements in promising regions while guaranteeing sufficient coverage of the entire area. …
SANDO: Safe Autonomous Trajectory Planning for Dynamic Unknown Environments
Departments of Aeronautics and Astronautics, and Mechanical Engineering, Massachusetts Institute of Technology（航空工程与机械工程系，麻省理工学院）；Department of Electronics, Automation, and Communications, Comillas ICAI（电子、自动化与通讯系，Comillas ICAI）
RoboCup Middle Size League (RoboCup MSL) provides a standardized testbed for research on mobile robot navigation, multi-robot cooperation, communication and integration via robot soccer competition in which the environment is highly dynamic and adversarial. One of important research topic in such area is kinodynamic motion planning that plan the trajectory of the robot while avoiding obstacles and obeying its dynamics. Kinodynamic motion planning for omnidirectional robot based on kinodynamic-RRT* method is presented in this work. Trajectory tracking control to execute the planned trajectory i…
This work addresses the problem of kinematic trajectory planning for mobile manipulators with non-holonomic constraints, and holonomic operational-space tracking constraints. We obtain whole-body trajectories and time-varying kinematic feedback controllers by solving a Constrained Sequential Linear Quadratic Optimal Control problem. The employed algorithm features high efficiency through a continuous-time formulation that benefits from adaptive step-size integrators and through linear complexity in the number of integration steps. In a first application example, we solve kinematic trajectory p…
PathCover: A Fast Convex Decomposition along a Path via Randomized Iterative Space Partitioning (RISP) on Point Clouds
University of Delaware（特拉华大学）；Athena Research Center（雅典娜研究中心）；National Technical University of Athens（雅典国家技术大学）；HERON–Center of Excellence in Robotics（赫伦机器人卓越中心）
Carnegie Mellon University（卡内基梅隆大学）；Georgia Institute of Technology（佐治亚理工学院）
This paper presents a novel factor graph-based approach to solve the discrete-time finite-horizon Linear Quadratic Regulator problem subject to auxiliary linear equality constraints within and across time steps. We represent such optimal control problems using constrained factor graphs and optimize the factor graphs to obtain the optimal trajectory and the feedback control policies using the variable elimination algorithm with a modified Gram-Schmidt process. We prove that our approach has the same order of computational complexity as the state-of-the-art dynamic programming approach. Furtherm…
This paper presents a kinodynamic motion planner that is able to produce energy efficient motions by taking the full robot dynamics into account, and making use of gravity, inertia, and momentum to reduce the effort. Given a specific goal state for the robot, we use factor graphs and numerical optimization to solve for an optimal trajectory, which meets not only the requirements of collision avoidance, but also all kinematic and dynamic constraints, such as velocity, acceleration and torque limits. By exploiting the sparsity in factor graphs, we can solve a kinodynamic motion planning problem …
Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology（麻省理工学院计算机科学与人工智能实验室）；California Institute of Technology（加州理工学院）
Hybrid locomotion, which combines multiple modalities of locomotion within a single robot, enables robots to carry out complex tasks in diverse environments. This paper presents a novel method for planning multi-modal locomotion trajectories using approximate dynamic programming. We formulate this problem as a shortest-path search through a state-space graph, where the edge cost is assigned as optimal transport cost along each segment. This cost is approximated from batches of offline trajectory optimizations, which allows the complex effects of vehicle under-actuation and dynamic constraints …
Coupled Routing and Configuration Optimization for Multi-Viewpoint Robotic Inspection
Center for Artificial Intelligence Research (CAIR), VinUniversity（VinUniversity人工智能研究中心（CAIR））；VinRobotics JSC（VinRobotics股份公司）；Division of Computer and Mathematical Sciences, Mohamed bin Zayed University of Artificial Intelligence (MBZUAI)（穆罕默德·本·扎耶德人工智能大学计算机与数学科学系）
Institute for Robotics and Intelligent Machines（机器人与智能机器研究所）；College of Computing, Georgia Institute of Technology（佐治亚理工学院计算学院）
We present a locally optimal tracking controller for Cable Driven Parallel Robot (CDPR) control based on a time-varying Linear Quadratic Gaussian (TV-LQG) controller. In contrast to many methods which use fixed feedback gains, our time-varying controller computes the optimal gains depending on the location in the workspace and the future trajectory. Meanwhile, we rely heavily on offline computation to reduce the burden of online implementation and feasibility checking. Following the growing popularity of probabilistic graphical models for optimal control, we use factor graphs as a tool to form…
We present Kinodynamic RRT*, an incremental sampling-based approach for asymptotically optimal motion planning for robots with linear differential constraints. Our approach extends RRT*, which was introduced for holonomic robots (Karaman et al. 2011), by using a fixed-final-state-free-final-time controller that exactly and optimally connects any pair of states, where the cost function is expressed as a trade-off between the duration of a trajectory and the expended control effort. Our approach generalizes earlier work on extending RRT* to kinodynamic systems, as it guarantees asymptotic optima…
Institut de Recherche en Communications et Cybernétique de Nantes（南特通信与控制论研究所）；INRIA Paris-Rocquencourt（法国国家信息与自动化研究所巴黎-罗克库尔中心）；Institut de Mathématiques de Jussieu（朱西厄数学研究所）；INRIA Nancy-Grand Est（法国国家信息与自动化研究所南锡-大东部中心）
Trajectory planning is a critical step while programming the parallel manipulators in a robotic cell. The main problem arises when there exists a singular configuration between the two poses of the end-effectors while discretizing the path with a classical approach. This paper presents an algebraic method to check the feasibility of any given trajectories in the workspace. The solutions of the polynomial equations associated with the tra-jectories are projected in the joint space using Gr{ö}bner based elimination methods and the remaining equations are expressed in a parametric form where the …
Center for Ubiquitous Computing, Faculty of Information Technology and Electrical Engineering, University of Oulu（奥卢大学信息技术与电气工程学院普适计算中心）
This paper presents methods for dramatically improving the performance of sampling-based kinodynamic planners. The key component is the first-known complete, exact steering method that produces a time-optimal trajectory between any states for a vector of synchronized double integrators. This method is applied in three ways: 1) to generate RRT edges that quickly solve the two-point boundary-value problems, 2) to produce a (quasi)metric for more accurate Voronoi bias in RRTs, and 3) to iteratively time-optimize a given collision-free trajectory. Experiments are performed for state spaces with up…
In this paper, we propose a novel trajectory learning method that exploits motion trajectories on topological map using recurrent neural network for temporally consistent geolocalization of object. Inspired by human's ability to both be aware of distance and direction of self-motion in navigation, our trajectory learning method learns a pattern representation of trajectories encoded as a sequence of distances and turning angles to assist self-localization. We pose the learning process as a conditional sequence prediction problem in which each output locates the object on a traversable path in …
