Dynamically-Stable Motion Planning for Humanoid Robots

We present an approach to path planning for humanoid robots that computes dynamically-stable, collision-free trajectories from full-body posture goals. Given a geometric model of the environment and a statically-stable desired posture, we search the configuration space of the robot for a collision-free path that simultaneously satisfies dynamic balance constraints. We adapt existing randomized path planning techniques by imposing balance constraints on incremental search motions in order to maintain the overall dynamic stability of the final path. A dynamics filtering function that constrains the ZMP (zero moment point) trajectory is used as a post-processing step to transform statically-stable, collision-free paths into dynamically-stable, collision-free trajectories for the entire body. Although we have focused our experiments on biped robots with a humanoid shape, the method generally applies to any robot subject to balance constraints (legged or not). The algorithm is presented along with computed examples using both simulated and real humanoid robots.     

基于运动微分约束的无人车辆纵横向协同规划算法的研究

为了满足在动态环境中快速行驶的要求,现有无人车辆普遍采用在传统规划系统的两层结构（路径规划-路径跟踪）之间增加局部规划的方法,通过在路径跟踪的同时进行避障来减少耗时的全局路径重规划. 本文针对这种三层结构规划系统存在的问题,提出基于运动微分约束的纵横向协同规划算法,在真实环境中实现速度不超过40km/h的无人驾驶. 根据车辆的实时运动状态,用高阶多项式模型在预瞄距离内对可行驶曲线进行建模,不仅使行驶过程中的转向平稳,而且在较高速时仍具有良好的路径跟踪能力. 由横向规划提供横向安全性的同时,在动力学约束的速度容许空间中进行纵向规划,实现平顺的加速与制动,并保证了纵向安全性和侧向稳定性. 该算法根据实时的局部环境自动决定纵横向期望运动参数,不需要人为设定行驶模式或调整参数. 采用该算法的无人驾驶平台在2011年和2012年智能车未来挑战赛的真实交通环境中,用统一的程序框架顺利完成全程的无人驾驶.     

Visual Servoing Path Planning for Cameras Obeying the Unified Model

Abstract

This paper proposes a path planning visual servoing strategy for a class of cameras that includes conventional perspective cameras, fisheye cameras and catadioptric cameras as special cases. Specifically, these cameras are modeled by adopting a unified model recently proposed in the literature and the strategy consists of designing image trajectories for eye-in-hand robotic systems that allow the robot to reach a desired location while satisfying typical visual servoing constraints. To this end, the proposed strategy introduces the projection of the available image features onto a virtual plane and the computation of a feasible image trajectory through polynomial programming. Then, the computed image trajectory is tracked by using an image-based visual servoing controller. Experimental results with a fisheye camera mounted on a 6-d.o.f. robot arm are presented in order to illustrate the proposed strategy.     

Navigation function-based visual servo control

In this paper, the mapping between the desired camera feature vector and the desired camera pose (i.e., the position and orientation) is investigated to develop a measurable image Jacobian-like matrix. An image-space path planner is then proposed to generate a desired image trajectory based on this measurable image Jacobian-like matrix and an image-space navigation function (NF) (i.e., a special potential field function) while satisfying rigid body constraints. An adaptive, homography-based visual servo tracking controller is then developed to navigate the position and orientation of a camera held by the end-effector of a robot manipulator to a goal position and orientation along the desired image-space trajectory while ensuring the target points remain visible (i.e., the target points avoid self-occlusion and remain in the field-of-view (FOV)) under certain technical restrictions. Due to the inherent nonlinear nature of the problem and the lack of depth information from a monocular system, a Lyapunov-based analysis is used to analyze the path planner and the adaptive controller. Simulation results are provided to illustrate the performance of the proposed approach.     

One step at a time: animating virtual characters based on foot placement

Especially in a constrained virtual environment, precise control of foot placement during character locomotion is crucial to avoid collisions and to ensure a natural locomotion. In this paper, we present an extension of the step space: a novel technique for generating animations of a character walking over a set of desired foot steps in real time. We use an efficient greedy nearest-neighbor approach and warp the resulting animation so that it adheres to both spatial and temporal constraints. We will show that our technique can generate realistic locomotion animations over an input path very efficiently even though we impose many constraints on the animation. We also present a simple footstep planning technique that automatically plans regular stepping and sidestepping based on an input path with clearance information generated by a path planner.     

Towards a Trajectory Planning Concept: Augmenting Path Planning Methods by Considering Speed Limit Constraints

Trajectory planning is an essential part of systems controlling autonomous entities such as vehicles or robots. It requires not only finding spatial curves but also that dynamic properties of the vehicles (such as speed limits for certain maneuvers) must be followed. In this paper, we present an approach for augmenting existing path planning methods to support basic dynamic constraints, concretely speed limit constraints. We apply this approach to the well known A* and state-of-the-art Theta* and Lazy Theta* path planning algorithms. We use a concept of trajectory planning based on a modular architecture in which spatial and dynamic parts can be easily implemented. This concept allows dynamic aspects to be processed during planning. Existing systems based on a similar concept usually add dynamics (velocity) into spatial curves in a post-processing step which might be inappropriate when the curves do not follow the dynamics. Many existing trajectory planning approaches, especially in mobile robotics, encode dynamic aspects directly in the representation (e.g. in the form of regular lattices) which requires a precise knowledge of the environmental and dynamic properties of particular autonomous entities making designing and implementing such trajectory planning approaches quite difficult. The concept of trajectory planning we implemented might not be as precise but the modular architecture makes the design and implementation easier because we can use (modified) well known path planning methods and define models of dynamics of autonomous entities separately. This seems to be appropriate for simulations used in feasibility studies for some complex autonomous systems or in computer games etc. Our basic implementation of the augmented A*, Theta* and Lazy Theta* algorithms is also experimentally evaluated. We compare (i) the augmented and basic A*, Theta* and Lazy Theta* algorithms and (ii) optimizing of augmented Theta* and Lazy Theta* for distance (the trajectory length) and duration (time needed to move through the trajectory).     

非完整移动机器人的人工势场法路径规划

基于人工势场的移动机器人路径规划方法在最近20多年里受到了广泛关注.然而研究者主要将目光集中于解决其各种理论问题,在研究中大都将机器人看作无约束的质点或刚体,通常无法直接应用于受到非完整约束限制的轮式移动机器人.针对人工势场法在轮式移动机器人上的实现问题,本文对两种已有实现方法进行了理论分析,指出其存在目标不可达的隐患和无法在不同环境下兼顾路径规划性能的问题,并提出一种基于模糊规则的新方法,通过在不同的情况下调整控制方式和参数解决前述问题.仿真研究表明,该方法在保证目标可达的前提下能够在多种环境中获得更好的总体规划性能.     

A semi-optimal path generation scheme for a frame articulated steering-type vehicle

A wheel loader is one of the main machines that is used in various applications. The present authors have been interested in autonomous control of its locomotion and navigation. An inevitable step in achieving this is path planning. The authors choose a technique of designing a steering method for car-like vehicles by proposing a semi-optimal path generation scheme using a canonical path skeleton consisting of three line segments and two clotohid pairs. Taking such a path skeleton, for any given pair of a locally desired initial configuration and a locally desired destination configuration, path planning is equivalent to finding the suitable values of parameters which characterize this skeleton. Due to the lower number of constraints than the number of parameters, ascertaining the values of parameters comes from the optimizations of the authors' formulated non-linear programmings with equality constraints. In addition, the realizable path must be subject to the upper-bounded curvature and curvature derivative. Adopting a genetic algorithm as the search tool in one of the optimizations makes it possible to allow the use of only a single canonical skeleton for the desired path planning.     

基于集成约束无人机两步制航迹规划方法

无人机航迹规划是一个富含地形威胁、雷达威胁和自身可飞性等多约束的优化问题.采用两步制的规划框架,提出一种基于集成约束的无人机航迹规划方法.规划第1阶段采用基于多种群策略的差分进化优化方法,规划第2阶段采用海洋捕食者算法的Lévy运动优化;集成约束机制在搜索过程中动态更新约束策略来补偿可行解数量骤减,抑制搜索停滞.与典型算法和约束处理策略进行对比,实验结果表明,所提出无人机航迹规划方法收敛性好、稳定性强,能够有效地求解复杂多约束无人机航迹规划问题.     

Curved Path Following Control for Fixed-wing Unmanned Aerial Vehicles with Control Constraint

The control inputs of a fixed-wing unmanned aerial vehicle (UAV) are affected by external environment, the largest mechanical limits and energy limits. It is essential to consider the control constraints for the curved path following problem when the curvature of the desired path is continuing-changed. This paper presents two approaches to address the curved path following problem of fixed-wing UAVs subject to wind and we explicitly account for the control constraints. First, a proper state feedback controller is developed that is based on the tracking error equation defined in the Frenet-Serret frame to confirm that there is a control Lyapunov function (CLF) for input constrained case. Second, a stabilizing guidance law with control damping based on the designed CLF, which satisfies the small control property, is implemented to ensure the global asymptotic stability of the fixed-wing UAV curved path following subject to wind. Meanwhile, a control scheme with the nested saturation (NS) theory for curved path following is also developed with proven stability. The simulation results are presented to illustrate the effectiveness and high tracking performances of the proposed control strategies.     

Model Predictive Control for Constrained Image‐Based Visual Servoing in Uncalibrated Environments

This paper presents a novel approach for image‐based visual servoing (IBVS) of a robotic system by considering the constraints in the case when the camera intrinsic and extrinsic parameters are uncalibrated and the position parameters of the features in 3‐D space are unknown. Based on the model predictive control method, the robotic system's input and output constraints, such as visibility constraints and actuators limitations, can be explicitly taken into account. Most of the constrained IBVS controllers use the traditional image Jacobian matrix, the proposed IBVS scheme is developed by using the depth‐independent interaction matrix. The unknown parameters can appear linearly in the prediction model and they can be estimated by the identification algorithm effectively. In addition, the model predictive control determines the optimal control input and updates the estimated parameters together with the prediction model. The proposed approach can simultaneously handle system constraints, unknown camera parameters and depth parameters. Both the visual positioning and tracking tasks can be achieved desired performances. Simulation results based on a 2‐DOF planar robot manipulator for both the eye‐in‐hand and eye‐to‐hand camera configurations are used to demonstrate the effectiveness of the proposed method.     

Automated camera planning to film robot operations

Automatic 3D animation generation techniques are becoming increasingly popular in different areas related to computer graphics such as video games and animated movies. They help automate the filmmaking process even by non professionals without or with minimal intervention of animators and computer graphics programmers. Based on specified cinematographic principles and filming rules, they plan the sequence of virtual cameras that the best render a 3D scene. In this paper, we present an approach for automatic movie generation using linear temporal logic to express these filming and cinematography rules. We consider the filming of a 3D scene as a sequence of shots satisfying given filming rules, conveying constraints on the desirable configuration (position, orientation, and zoom) of virtual cameras. The selection of camera configurations at different points in time is understood as a camera plan, which is computed using a temporal-logic based planning system (TLPlan) to obtain a 3D movie. The camera planner is used within an automated planning application for generating 3D tasks demonstrations involving a teleoperated robot arm on the the International Space Station (ISS). A typical task demonstration involves moving the robot arm from one configuration to another. The main challenge is to automatically plan the configurations of virtual cameras to film the arm in a manner that conveys the best awareness of the robot trajectory to the user. The robot trajectory is generated using a path-planner. The camera planner is then invoked to find a sequence of configurations of virtual cameras to film the trajectory.     

Adding inclusion dependencies to an object-oriented data model with uniqueness constraints

We study an object-oriented data model that allows to express both uniqueness constraints and inclusion dependencies as semantic constraints. The data model is based on a subset of F-logic. Uniqueness constraints comprise path functional dependencies which generalise functional dependencies and reflect the navigational power of object-oriented query languages. As inclusion dependencies, we consider explicit class inclusion constraints, besides inclusions required by class hierarchies, and onto constraints that enforce reachability of objects. For these classes of semantic constraints we present an axiomatisation and prove its inference rules to be correct and complete with respect to general logical implication, leaving the decision problem open. The completeness proof combines the known construction for path functional dependencies alone with a possibly infinite model generation process to enforce onto constraints. The results prepare the grounds for normal forms in object-oriented data models and subsequently for computer aided object-oriented database design, following the decomposition approach for the relational data model. Beyond the application for schema design, the achievements could also be exploited for related tasks like semantic query optimisation and mediated data integration within a variety of graph based data models. Received: 11 October 2000 / 27 January 2003     

场景摄像机构型下图像空间内的无标定路径规划研究

基于图像的视觉伺服可用于对机械臂的运动进行有效的控制。然而,正如许多研究者指出的,当初始位置和期望位置相距较远时,此种控制策略将因其局部特性而存在收敛性、稳定性问题。通过在图像平面内定义充分的图像特征轨迹,并对这些轨迹进行跟踪,我们可以充分利用基于图像的视觉伺服所固有的局部收敛性及稳定性特性这一优势,从而避免初始位置与期望位置相距较远时所面临的问题。因此,近年来,图像空间路径规划已成为机器人领域的一个热点研究问题。但是,目前几乎所有的有关结果均是针对手眼视觉系统提出的。本文将针对场景摄像机视觉系统提出一种未标定视觉路径规划算法。此算法在射影空间中直接计算图像特征的轨迹,这样可保证它们与刚体运动一致。通过将旋转及平移运动的射影表示分解为规范化形式,我们可以很容易地对其射影空间内的路径进行插值。在此之后,图像平面中的图像特征轨迹可通过射影路径产生。通过这种方式,此算法并不需要特征点结构和摄像机内部参数的有关知识。为了验证所提算法的可行性及系统性能,本文最后给出了基于PUMA560机械臂的仿真研究结果。     

Nonlinear predictive controller based on S-PARAFAC Volterra models applied to a communicating two-tank system

This paper proposes a new predictive controller approach for nonlinear process based on a reduced complexity homogeneous, quadratic discrete-time Volterra model called quadratic S-PARAFAC Volterra model. The proposed model is yielded by using the symmetry property of the Volterra kernels and their tensor decomposition using the PARAFAC technique that provides a parametric reduction compared to the conventional Volterra model. This property allows synthesising a new nonlinear-model-based predictive control (NMBPC). We develop the general form of a new predictor, and therefore, we propose an optimisation algorithm formulated as a quadratic programming under linear and nonlinear constraints. The performances of the proposed quadratic S-PARAFAC Volterra model and the developed NMBPC algorithm are illustrated on a numerical simulation and validated on a benchmark as a continuous stirred-tank reactor system. Moreover, the efficiency of the proposed quadratic S-PARAFAC Volterra model and the NMBPC approach are validated on an experimental communicating two-tank system.     

基于改进粒子群算法的机器人路径规划方法

提出一种基于粒子群算法的机器人路径规划方法.将路径规划看作一个带约束的优化问题,约束条件为路径不能经过障碍物,优化目标为整个路径的长度最短.机器人工作空间中的障碍物描述为多边型,对障碍物的顶点进行编号.利用粒子群算法进行路径规划,每一个粒子定义为一个由零或障碍物顶点编号组成的集合,在粒子的迭代过程中考虑约束条件,惯性权重随迭代次数动态改变,使算法既有全局搜索能力也有较强的局部搜索能力.仿真结果表明该方法的正确性和有效性.     

Optimal Camera Trajectory under Visibility Constraint in Visual Servoing: A Variational Approach

The principal deficiency of an image-based servo is that the induced three-dimensional (3-D) trajectories are not optimal and sometimes, especially when the displacements to realize are large, these trajectories are not physically valid, leading to the failure of the servoing process. In this paper, we adress the problem of generating trajectories of some image features that correspond to optimal 3-D trajectories in order to control efficiently a robotic system using an image-based control strategy. First, a collineation path between given the start and end points is obtained, and then the trajectories of the image features are derived. Path planning is formulated as a variational problem that allows us to consider simultaneously optimality and inequality constraints (visibility). A numerical method is employed for solving the path planning problem in the variational form.     

Optimization-based path planning framework for industrial manufacturing processes with complex continuous paths

The complexity of robotic path planning problems in industrial manufacturing increases significantly with the current trends of product individualization and flexible production systems. In many industrial processes, a robotic tool has to follow a desired manufacturing path most accurately, while certain deviations, also called process tolerances and process windows, are allowed. In this work, a path planning framework is proposed, which systematically incorporates all process degrees of freedom (DoF), tolerances and redundant DoF of the considered manufacturing process as well as collision avoidance. Based on the specified process DoF and tolerances, the objective function and the hard and soft constraints of the underlying optimization problem can be easily parametrized to find the optimal joint-space path. By providing the analytical gradients of the objective function and the constraints and utilizing modern multi-core CPUs, the computation performance can be significantly improved. The proposed path planning framework is demonstrated for an experimental drawing process and a simulated spraying process. The planner is able to solve complex planning tasks of continuous manufacturing paths by systematically exploiting the process DoF and tolerances while allowing to move through singular configurations, which leads to solutions that cannot be found by state-of-the-art concepts.     

Receding horizon maneuver generation for automated highway driving

This paper focuses on the problem of decision-making and control in an autonomous driving application for highways. By considering the decision-making and control problem as an obstacle avoidance path planning problem, the paper proposes a novel approach to path planning, which exploits the structured environment of one-way roads. As such, the obstacle avoidance path planning problem is formulated as a convex optimization problem within a receding horizon control framework, as the minimization of the deviation from a desired velocity and lane, subject to a set of constraints introduced to avoid collision with surrounding vehicles, stay within the road boundaries, and abide the physical limitations of the vehicle dynamics. The ability of the proposed approach to generate appropriate traffic dependent maneuvers is demonstrated in simulations concerning traffic scenarios on a two-lane, one-way road with one and two surrounding vehicles.     

基于方向约束的A*算法

实际机器人路径规划问题经常需要考虑路径的转弯约束以及路径起始/目标角要求,为此提出一种基于方向约束的A*算法.新算法区分同一路径点处不同方向的各条路径,通过定向扩展机制来满足路径方向约束,并采用节点合并策略和不一致队列降低算法复杂度.理论分析和典型地图集上的实验结果证明,所提算法总是能够保证给出符合转弯约束和起始/目标角约束的最短路径,且相比于现有算法,能够有效提高方向约束路径规划问题的求解能力.