A fast approach for the robust trajectory planning of redunant robot manipulators

In this article, a fast approach for robust trajectory planning, in the task space, of redundant robot manipulators is presented. The approach is based on combining an original method for obstacle avoidance by the manipulator configuration with the traditional potential field approach for the motion planning of the end-effector. This novel method is based on formulating an inverse kinematics problem under an inexact context. This procedure permits dealing with the avoidance of obstacles with an appropriate and easy to compute null space vector; whereas the avoidance of singularities is attained by the proper pseudoinverse perturbation. Furthermore, it is also shown that this formulation allows one to deal effectively with the local minimum problem frequently associated with the potential field approaches. The computation of the inverse kinematics problem is accomplished by numerically solving a linear system, which includes the vector for obstacle avoidance and a scheme for the proper pseudoinverse perturbation to deal with the singularities and/or the potential function local minima. These properties make the proposed approach suitable for redundant robots operating in real time in a sensor-based environment. The developed algorithm is tested on the simulation of a planar redundant manipulator. From the results obtained it is observed that the proposed approach compares favorably with the other approaches that have recently been proposed. © 1995 John Wiley & Sons, Inc.     

A dynamic programming approach to trajectory planning of robotic manipulators

This paper presents a solution to the problem of minimizing the cost of moving a robotic manipulator along a specified geometric path subject to input torque/force constraints, taking the coupled, nonlinear dynamics of the manipulator into account. The proposed method uses dynamic programming (DP) to find the positions, velocities, accelerations, and torques that minimize cost. Since the use of parametric functions reduces the dimension of the state space from2nfor ann- jointed manipulator, to two, the DP method does not suffer from the "curse of dimensionality." While maintaining the elegance of our previous trajectory planning method, we have developed the DP method for the general case where 1) the actuator torque limits are dependent on one another, 2) the cost functions can have an arbitrary form, and 3) there are constraints on the jerk, or derivative of the acceleration. Also, we have shown that the DP solution converges as the grid size decreases. As numerical examples, the trajectory planning method is simulated for the first three joints of the PACS arm, which is a cylindrical arm manufactured by the Bendix Corporation.     

On optimal constrained trajectory planning in 3D environments

A novel approach to generating acceleration-based optimal smooth piecewise trajectories is proposed. Given two configurations (position and orientation) in 3D, we search for the minimal energy trajectory that minimizes the integral of the squared acceleration, opposed to curvature, which is widely investigated. The variation in both components of acceleration: tangential (forces on gas pedal or brakes) and normal (forces that tend to drive a car on the road while making a turn) controls the smoothness of generated trajectories. In the optimization process, our objective is to search for the trajectory along which a free moving robot is able to accelerate (decelerate) to a safe speed in an optimal way. A numerical iterative procedure is devised for computing the optimal piecewise trajectory as a solution of a constrained boundary value problem. The resulting trajectories are not only smooth but also safe with optimal velocity (acceleration) profiles and therefore suitable for robot motion planning applications. Experimental results demonstrate this fact.     

Robust trajectory planning for robotic manipulators under payload uncertainties

A number of trajectory planning algorithms are available for determining the joint torques, positions, and velocities required to move a manipulator along a given geometric path in minimum time. These schemes require knowledge of the robot's dynamics, which in turn depend upon the characteristics of the payload which the robot is carrying. In practice, the dynamic properties of the payload will not be known exactly, so that the dynamics of the robot, and hence the required joint torques, must be calculated for a nominal set of payload characteristics. But since these trajectory planners generate nominal joint torques which are at the limits of the robot's capabilities, moving the robot along the desired geometric path at speeds calculated for the nominal payload may require torques which exceed the robot's capabilities. In this paper, bounds on joint torque uncertainties are derived in terms of payload uncertainties. Using these bounds, a new trajectory planner is developed to incorporate payload uncertainties such that all the trajectories generated can be realized with given joint torques. Finally, the trajectory planner is applied to the first three joints of the Bendix PACS arm, a cylindrical robot to demonstrate its use and power.     

A frequentist approach to mapping under uncertainty

An asynchronous stochastic approximation based (frequentist) approach is proposed for mapping using noisy mobile sensors under two different scenarios: (1) perfectly known sensor locations and (2) uncertain sensor locations. The frequentist methodology has linear complexity in the map components, is immune to the data association problem and is provably consistent. The frequentist methodology, in conjunction with a Bayesian estimator, is applied to the Simultaneous Localization and Mapping (SLAM) problem of Robotics. Several large maps are estimated using the hybrid Bayesian/Frequentist scheme and results show that the technique is robust to the computational and performance issues inherent in the purely Bayesian approaches to the problem.     

Experimental validation and comparative analysis of optimal time-jerk algorithms for trajectory planning

In this paper, two minimum time-jerk trajectory planning algorithms for robotic manipulators have been considered, evaluated and experimentally validated. These algorithms consider both the execution time and the integral of the squared jerk along the whole trajectory, so as to take into account the need for fast execution and the need for a smooth trajectory, by adjusting the values of two weights. A comparative analysis of these algorithms with two different trajectory planning techniques taken from the literature has been carried out, by means of experimental tests performed on a real robotic manipulator. The results prove the experimental effectiveness of the proposed techniques.     

Path homotopy invariants and their application to optimal trajectory planning

We consider the problem of optimal path planning in different homotopy classes in a given environment. Though important in robotics applications, path-planning with reasoning about homotopy classes of trajectories has typically focused on subsets of the Euclidean plane in the robotics literature. The problem of finding optimal trajectories in different homotopy classes in more general configuration spaces (or even characterizing the homotopy classes of such trajectories) can be difficult. In this paper we propose automated solutions to this problem in several general classes of configuration spaces by constructing presentations of fundamental groups and giving algorithms for solving the word problem in such groups. We present explicit results that apply to knot and link complements in 3-space, discuss how to extend to cylindrically-deleted coordination spaces of arbitrary dimension, and also present results in the coordination space of robots navigating on an Euclidean plane.     

A resilience optimization approach for workforce-inventory control dynamics under uncertainty

The presence of uncertainties in manufacturing systems and supply chains can cause undesirable behavior. Failure to account for these in the design phase can further impair the capability of systems to respond to changes effectively. In this work, we consider a dynamic workforce-inventory control problem wherein inventory planning, production releases, and workforce hiring decisions need to be made. The objective is to develop planning rules to achieve important requirements related to dynamic transient behavior when system parameters are imprecisely known. To this end, we propose a resilience optimization model for the problem and develop a novel local search procedure that combines the strengths of recent developments in robust optimization technology and small signal stability analysis of dynamic systems. A numerical case study of the problem demonstrates significant improvements of the proposed solution in controlling fluctuations and high variability found in the system’s inventory, work-in-process, and workforce levels. Overall, the proposed model is shown to be computationally efficient and effective in hedging against model uncertainties.     

Simulation-based optimal sensor scheduling with application to observer trajectory planning

The sensor scheduling problem can be formulated as a controlled hidden Markov model and this paper solves the problem when the state, observation and action spaces are continuous. This general case is important as it is the natural framework for many applications. The aim is to minimise the variance of the estimation error of the hidden state w.r.t. the action sequence. We present a novel simulation-based method that uses a stochastic gradient algorithm to find optimal actions.     

考虑不确定性的供应链计划模型

对供应链计划建立了考虑不确定性的战略层模型和运作层模型。以一啤酒厂进行了实例研究,对所建模型和确定性的供应链计划模型进行了比较,并对柔性参数进行了灵敏度分析。结果表明,该模型能帮助设计具有柔性的供应链系统,通过灵敏度分析,可以更好地理解供应链的特性。     

Logistics planning under uncertainty for disposition of radioactive wastes

The US Department of Energy (DOE) faces an enormous environmental remediation challenge involving highly radioactive wastes at former weapons production facilities. The purpose of this analysis is to focus on equipment acquisition and fleet sizing issues related to transportation of wastes from remediation sites to disposal sites. Planning for the transportation of these wastes must be done with recognition of important uncertainties related to overall quantities of waste to be moved, the rate at which the wastes will be prepared for transport, and the certification of suitable transportation containers for use in the effort. However, deadlines for completion of the effort have already been set by the political process, without much regard for these uncertainties. To address this fleet sizing problem, we have created a robust optimization model that focuses on equipment investment decisions. Through this robust optimization, we illustrate how modeling can be used to explore the effects of uncertainty on the equipment acquisition strategy. The disposition of radioactive wastes from DOE sites is an important illustration of a category of problems where equipment investments must be made under conditions of considerable uncertainty. The methodology illustrated in this paper can be applied to this general class of problems.     

A rough set approach to reasoning under uncertainty

Abstract

Reasoning with uncertain information is a problem of key importance when dealing with information about the real world. Obtaining the precise numbers required by many uncertainty handling formalisms can be a problem. The theory of rough sets makes it possible to handle uncertainty without the need for precise numbers, and so has some advantages in such situations. This paper presents an introduction to various forms of reasoning under uncertainty that are based on rough sets. In particular, a number of sets of numerical and symbolic truth values which may be used to augment propositional logic are developed, and a semantics for these values is provided based upon the notion of possible worlds. Methods of combining the truth values are developed so that they may be propagated when augmented logic formulae are combined, and their use is demonstrated in theorem proving.     

Scenario driven optimal sequencing under deep uncertainty

The optimal sequencing/scheduling of activities is vital in many areas of environmental and water resources planning and management. In order to account for deep uncertainty surrounding future conditions, a new optimal scheduling approach is introduced in this paper, which consists of three stages. Firstly, a portfolio of diverse sequences that are optimal under a range of plausible future conditions is generated. Next, global sensitivity analysis is used to assess the robustness of these sequences and to determine the relative contribution of future uncertain variables to this robustness. Finally, an optimal sequence is selected for implementation. The approach is applied to the optimal sequencing of additional potential water supply sources, such as desalinated-, storm- and rain-water, for the southern Adelaide water supply system, over a 40 year planning horizon at 10-year intervals. The results indicate that the proposed approach is useful in identifying optimal sequences under deep uncertainty.     

A simulation‐based algorithm for optimal pricing policy under demand uncertainty

We propose a simulation‐based algorithm for computing the optimal pricing policy for a product under uncertain demand dynamics. We consider a parameterized stochastic differential equation (SDE) model for the uncertain demand dynamics of the product over the planning horizon. In particular, we consider a dynamic model that is an extension of the Bass model. The performance of our algorithm is compared to that of a myopic pricing policy and is shown to give better results. Two significant advantages with our algorithm are as follows: (a) it does not require information on the system model parameters if the SDE system state is known via either a simulation device or real data, and (b) as it works efficiently even for high‐dimensional parameters, it uses the efficient smoothed functional gradient estimator.     

Sequentially optimal repeated coalition formation under uncertainty

Coalition formation is a central problem in multiagent systems research, but most models assume common knowledge of agent types. In practice, however, agents are often unsure of the types or capabilities of their potential partners, but gain information about these capabilities through repeated interaction. In this paper, we propose a novel Bayesian, model-based reinforcement learning framework for this problem, assuming that coalitions are formed (and tasks undertaken) repeatedly. Our model allows agents to refine their beliefs about the types of others as they interact within a coalition. The model also allows agents to make explicit tradeoffs between exploration (forming “new” coalitions to learn more about the types of new potential partners) and exploitation (relying on partners about which more is known), using value of information to define optimal exploration policies. Our framework effectively integrates decision making during repeated coalition formation under type uncertainty with Bayesian reinforcement learning techniques. Specifically, we present several learning algorithms to approximate the optimal Bayesian solution to the repeated coalition formation and type-learning problem, providing tractable means to ensure good sequential performance. We evaluate our algorithms in a variety of settings, showing that one method in particular exhibits consistently good performance in practice. We also demonstrate the ability of our model to facilitate knowledge transfer across different dynamic tasks.     

基于强化学习的挖掘机时间最优轨迹规划

针对挖掘机的自主作业场景,提出基于强化学习的时间最优轨迹规划方法.首先,搭建仿真环境用于产生数据,以动臂、斗杆和铲斗关节的角度、角速度为状态观测变量,以各关节的角加速度值为动作信息,通过状态观测信息实现仿真环境与自主学习算法的交互;然后,设计以动臂、斗杆和铲斗关节运动是否超出允许范围、完成任务 总时间和目标相对距离为奖励函数对策略网络参数进行训练;最后,利用改进的近端策略优化算法(proximal policy optimization, PPO)实现挖掘机的时间最优轨迹规划.与此同时,与不同连续动作空间的强化学习算法进行对比,实验结果表明:所提出优化算法效率更高,收敛速度更快,作业轨迹更平滑,可有效避免各关节受到较大冲击,有助于挖掘机高效、平稳地作业.     

Flatness-based trajectory planning for diffusion–reaction systems in a parallelepipedon—A spectral approach

Spectral analysis is considered for the flatness-based solution of the trajectory planning problem for a boundary controlled diffusion–reaction system defined on a 1≤r-dimensional parallelepipedon. By exploiting the Riesz spectral properties of the system operator, it is shown that a suitable reformulation of the resolvent operator allows a systematic introduction of a basic output, which yields a parametrization of both the system state and the boundary input in terms of differential operators of infinite order. Their convergence is verified for both infinite-dimensional and finite-dimensional actuator configurations by restricting the basic output to certain Gevrey classes involving non-analytic functions. With this, a systematic approach is introduced for basic output trajectory assignment and feedforward tracking control towards the realization of finite-time transitions between stationary profiles.     

Smooth and time‐optimal trajectory planning for industrial manipulators along specified paths

This article presents a method for determining smooth and time‐optimal path constrained trajectories for robotic manipulators and investigates the performance of these trajectories both through simulations and experiments. The desired smoothness of the trajectory is imposed through limits on the torque rates. The third derivative of the path parameter with respect to time, the pseudo‐jerk, is the controlled input. The limits on the actuator torques translate into state‐dependent limits on the pseudo‐acceleration. The time‐optimal control objective is cast as an optimization problem by using cubic splines to parametrize the state space trajectory. The optimization problem is solved using the flexible tolerance method. The experimental results presented show that the planned smooth trajectories provide superior feasible time‐optimal motion. © 2000 John Wiley & Sons, Inc.     

Simultaneous algorithm for trajectory planning

This paper addresses the solution of smooth trajectory planning for industrial robots in environments with obstacles using a direct method, creating the trajectory gradually as the robot moves. The presented method deals with the uncertainties associated with the lack of knowledge of kinematic properties of intermediate via‐points since they are generated as the algorithm evolves looking for the solution. Several cost functions are also proposed, which use the time that has been calculated to guide the robot motion. The method has been applied successfully to a PUMA 560 robot and four operational parameters (execution time, computational time, distance travelled and number of configurations) have been computed to study the properties and influence of each cost function on the trajectory obtained. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society