Path-constrained control of a redundant manipulator in a task space

This study addresses the problem of controlling a redundant manipulator with both state and control dependent constraints. The task of the robot is to follow by the end-effector a prescribed geometric path given in the task space. The control constraints resulting from the physical abilities of robot actuators are also taken into account during the robot movement. Provided that a solution to the aforementioned robot task exists, the Lyapunov stability theory is used to derive the control scheme. The numerical simulation results, carried out for a planar manipulator whose end-effector follows a prescribed geometric path given in a task space, illustrate the trajectory performance of the proposed control scheme.     

Path following by the end-effector of a redundant manipulator operating in a dynamic environment

This paper addresses the problem of generating at the control-loop level a collision-free trajectory for a redundant manipulator operating in dynamic environments which include moving obstacles. The task of the robot is to follow, by the end-effector, a prescribed geometric path given in the work space. The control constraints resulting from the physical abilities of robot actuators are also taken into account during the robot movement. Provided that a solution to the aforementioned robot task exists, the Lyapunov stability theory is used to derive the control scheme. The numerical simulation results for a planar manipulator whose end-effector follows a prescribed geometric path, given in both an obstacle-free work space and a work space including the moving obstacles, illustrate the trajectory performance of the proposed control scheme.     

BA*: an online complete coverage algorithm for cleaning robots

This paper presents a novel approach to solve the online complete coverage task of autonomous cleaning robots in unknown workspaces based on the boustrophedon motions and the A* search algorithm (BA*). In this approach, the robot performs a single boustrophedon motion to cover an unvisited region until it reaches a critical point. To continue covering the next unvisited region, the robot wisely detects backtracking points based on its accumulated knowledge, determines the best backtracking point as the starting point of the next boustrophedon motion, and applies an intelligent backtracking mechanism based on the proposed A* search with smoothed path on tiling so as to reach the starting point with the shortest collision-free path. The robot achieves complete coverage when no backtracking point is detected. Computer simulations and experiments in real workspaces prove that our proposed BA* is efficient for the complete coverage task of cleaning robots.     

Human robot cooperation with compliance adaptation along the motion trajectory

In this paper we propose a novel approach for intuitive and natural physical human–robot interaction in cooperative tasks. Through initial learning by demonstration, robot behavior naturally evolves into a cooperative task, where the human co-worker is allowed to modify both the spatial course of motion as well as the speed of execution at any stage. The main feature of the proposed adaptation scheme is that the robot adjusts its stiffness in path operational space, defined with a Frenet–Serret frame. Furthermore, the required dynamic capabilities of the robot are obtained by decoupling the robot dynamics in operational space, which is attached to the desired trajectory. Speed-scaled dynamic motion primitives are applied for the underlying task representation. The combination allows a human co-worker in a cooperative task to be less precise in parts of the task that require high precision, as the precision aspect is learned and provided by the robot. The user can also freely change the speed and/or the trajectory by simply applying force to the robot. The proposed scheme was experimentally validated on three illustrative tasks. The first task demonstrates novel two-stage learning by demonstration, where the spatial part of the trajectory is demonstrated independently from the velocity part. The second task shows how parts of the trajectory can be rapidly and significantly changed in one execution. The final experiment shows two Kuka LWR-4 robots in a bi-manual setting cooperating with a human while carrying an object.     

Motion control for a wheeled robot following a curvilinear path

A control synthesis problem for planar motion of a wheeled robot with regard to the steering gear dynamics is considered. The control goal is to bring the robot to a given curvilinear path and to stabilize its motion along the path. The trajectory is assumed to be an arbitrary parameterized smooth curve satisfying some additional curvature constraints. A change of variables is found by means of which the system of differential equations governing controlled motion of the robot reduces to the form that admits feedback linearization. A control law is synthesized for an arbitrary target path with regard to phase and control constraints. The form of the boundary manifold and the phase portrait of the system for the case of the straight target trajectory are studied. Results of numerical experiments are presented.     

Minimum-time control of robotic manipulators with geometric path constraints

Conventionally, robot control algorithms are divided into two stages, namely, path or trajectory planning and path tracking (or path control). This division has been adopted mainly as a means of alleviating difficulties in dealing with complex, coupled manipulator dynamics. Trajectory planning usually determines the timing of manipulator position and velocity without considering its dynamics. Consequently, the simplicity obtained from the division comes at the expense of efficiency in utilizing robot's capabilities. To remove at least partially this inefficiency, this paper considers a solution to the problem of moving a manipulator in minimum time along a specified geometric path subject to input torque/force constraints. We first describe the manipulator dynamics using parametric functions which represent geometric path constraints to be honored for collision avoidance as well as task requirements. Second, constraints on input torques/ forces are converted to those on the parameters. Third, the minimum-time solution is deduced in an algorithm form using phase-plane techniques. Finally, numerical examples are presented to demonstrate utility of the trajectory planning method developed.     

基于改进快速行进平方法的多移动机器人聚集路径规划与控制

针对多移动机器人聚集的路径规划与控制问题,本文提出了基于改进快速行进平方法的路径规划策略.首先,运用分段函数改进了速度图,实现了更安全、更高效的路径规划,可以将快速行进网格地图上的速度映射到真实机器人速度上,并且减少传统快速行进平方法在回溯路径过程中产生的冗余路径；接着,针对多移动机器人聚集过程总能耗最小、聚集点附近空间最大、聚集队形约束下的聚集过程总能耗最小三种任务需求,分析设计不同的目标函数,给出多移动机器人的聚集点和对应规划路径,展示本文方法的有效性以及在不同场景下的适用性.最后,在车辆动力学模型基础上,使用模型预测控制以改进后的快速行进网格地图上的速度作为机器人参考速度进行了轨迹跟踪仿真实验,实现结果显示跟踪误差减小,验证了本文改进速度场的有效性,可适用于真实环境下多移动机器人聚集路径规划与控制.     

Path feasibility and modification

Kinematic feasibility of a planned robot path is restrained by the kinematic constraints of the robot executing the task, such as workspace, configuration, and singularity. Since these kinematic constraints can be described utilizing the geometry of the given robot, corresponding regions within the robot workspace can be expressed in geometrical representation. Consequently, geometric information can be derived from the planned path and the geometric boundaries of these regions. Then, by utilizing the geometric information and proper modification strategies, a Cartesian robot path that is kinematically infeasible can be modified according to different task requirements. To demonstrate the proposed feasibility and modification schemes, simulations for a 6R robot manipulator are executed.     

A multisine approach for trajectory optimization based on information gain

This paper presents a multisine approach for trajectory optimization based on information gain, with distance and orientation sensing to known beacons. It addresses the problem of active sensing, i.e. the selection of a robot motion or sequence of motions, which make the robot arrive in its desired goal configuration (position and orientation) with maximum accuracy, given the available sensor information. The optimal trajectory is parameterized as a linear combination of sinusoidal functions. An appropriate optimality criterion is selected which takes into account various requirements (such as maximum accuracy and minimum time). Several constraints can be formulated, e.g. with respect to collision avoidance. The optimal trajectory is then determined by numerical optimization techniques. The approach is applicable to both nonholonomic and holonomic robots. Its effectiveness is illustrated here for a nonholonomic wheeled mobile robot (WMR) in an environment with and without obstacles.     

Global Path-Planning for Constrained and Optimal Visual Servoing

Visual servoing consists of steering a robot from an initial to a desired location by exploiting the information provided by visual sensors. This paper deals with the problem of realizing visual servoing for robot manipulators taking into account constraints such as visibility, workspace (that is obstacle avoidance), and joint constraints, while minimizing a cost function such as spanned image area, trajectory length, and curvature. To solve this problem, a new path-planning scheme is proposed. First, a robust object reconstruction is computed from visual measurements which allows one to obtain feasible image trajectories. Second, the rotation path is parameterized through an extension of the Euler parameters that yields an equivalent expression of the rotation matrix as a quadratic function of unconstrained variables, hence, largely simplifying standard parameterizations which involve transcendental functions. Then, polynomials of arbitrary degree are used to complete the parametrization and formulate the desired constraints and costs as a general optimization problem. The optimal trajectory is followed by tracking the image trajectory with an IBVS controller combined with repulsive potential fields in order to fulfill the constraints in real conditions.     

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.     

Real-time navigation using randomized kinodynamic planning with arrival time field

In this paper, we propose a novel path planning algorithm for a mobile robot in dynamic and cluttered environments with kinodynamic constraints. We compute the arrival time field as a bias which gives larger weights for shorter and safer paths toward a goal. We then implement a randomized path search guided by the arrival time field for building the path considering kinematic and dynamic (kinodynamic) constraints of an actual robot. We also consider path quality by adding heuristic constraints on the randomized path search, such as reducing unstable movements of the robot by using a heading criterion. The path will be extracted by backtracking the nodes which reach the goal area to the root of the tree generated by the randomized search, and the motion from the very first node will be sent to the robot controller. We provide a brief comparison between our algorithm and other existing algorithms. Simulation and experimental results prove that our algorithm is fast and reliable to be implemented on the real robot and is able to handle kinodynamic problems effectively.     

Feed-rate and trajectory optimization for CNC machine tools

The key task performed by CNCs is the generation of the time-sequence of set-points for driving each physical axis of the machine tool during program execution. This interpolation of axes movement must satisfy a number of constraints on axes dynamics (velocity, acceleration, and jerk), and on process outcome (smooth tool movement and precise tracking of the nominal tool-path at the desired feed-rate). This paper presents an algorithm for CNC kernels that aims at solving the axes interpolation problem by exploiting an Optimal Control Problem formulation. With respect to other solutions proposed in the literature, the approach presented here takes an original approach by assuming a predefined path tracking tolerance—to be added to the constraints listed above—and calculating the whole trajectory (path and feed-rate profile) that satisfies the given constraints. The effectiveness of the proposed solution is benchmarked against the trajectory generated by an industrial, state-of-the-art CNC, proving a significant advantage in efficiency and smoothness of axes velocity profiles.     

Safe and intuitive manual guidance of a robot manipulator using adaptive admittance control towards robot agility

Key areas of robot agility include methods that increase capability and flexibility of industrial robots and facilitate robot re-tasking. Manual guidance can achieve robot agility effectively, provided that a safe and smooth interaction is guaranteed when the user exerts an external force on the end effector. We approach this by designing an adaptive admittance law that can adjust its parameters to modify the robot compliance in critical areas of the workspace, such as near and on configuration singularities, joint limits, and workspace limits, for a smooth and safe operation. Experimental validation was done with two tests: a constraint activation test and a 3D shape tracing task. In the first one, we validate the proper response to constraints and in the second one, we compare the proposed approach with different admittance parameter tuning strategies using a drawing task where the user is asked to guide the robot to trace a 3D profile with an accuracy or speed directive and evaluate performance considering path length error and execution time as metrics, and a questionnaire for user perception. Results show that appropriate response to individual and simultaneous activation of the aforementioned constraints for a safe and intuitive manual guidance interaction is achieved and that the proposed parameter tuning strategy has better performance in terms of accuracy, execution time, and subjective evaluation of users.     

An online collision-free trajectory generation algorithm for human–robot collaboration

The premise of human–robot collaboration is that robots have adaptive trajectory planning strategies in hybrid work cell. The aim of this paper is to propose a new online collision avoidance trajectory planning algorithm for moderate dynamic environments to insure human safety when sharing collaborative tasks. The algorithm contains two parts: trajectory generation and local optimization. Firstly, based on empirical Dirichlet Process Gaussian Mixture Model (DPGMM) distribution learning, a neural network trajectory planner called Collaborative Waypoint Planning network (CWP-net) is proposed to generate all key waypoints required for dynamic obstacle avoidance in joint space according to environmental inputs. These points are used to generate quintic spline smooth motion trajectories with velocity and acceleration constraints. Secondly, we present an improved Stochastic Trajectory Optimization for Motion Planning (STOMP) algorithm which locally optimizes the generated trajectories of CWP-net by constraining the trajectory optimization range and direction through the DPGMM model. Simulations and real experiments from an industrial use case of human–robot collaboration in the field of aircraft assembly testing show that the proposed algorithm can smoothly adjust the nominal path online and effectively avoid collisions during the collaboration.     

Optimization of layout and path planning of surgical robotic system

Positioning a surgical robot for optimal operation in a crowded operating room is a challenging task. In the robotic-assisted surgical procedures, the surgical robot’s end-effector must reach the patient’s anatomical targets because repositioning of the patient or surgical robot requires additional time and labor. This paper proposes an optimization algorithm to determine the best layout of the operating room, combined with kinematics criteria and optical constraints applied to the surgical assistant robot system. A new method is also developed for trajectory of robot’s end-effector for path planning of the robot motion. The average deviations obtained from repeatability tests for surgical robot’s layout optimization were 1.4 and 4.2 mm for x and y coordinates, respectively. The results of this study show that the proposed optimization method successfully solves the placement problem and path planning of surgical robotic system in operating room.

     

Discriminative and adaptive imitation in uni-manual and bi-manual tasks

This paper addresses the problems of what to imitate and how to imitate in simple uni and bi-manual manipulatory tasks. To solve the what to imitate issue, we use a probabilistic method, based on Hidden Markov Models (HMM), to extract the relative importance of reproducing either the gesture or the specific hand path in a given task. This allows us to determine a metric of imitation performance. To solve the how to imitate issue, we compute the trajectory that optimizes the metric given the constraints of the robot’s body. We validate the methods using a series of experiments where a human demonstrator uses kinesthetics in order to teach a robot how to manipulate simple objects.     

基于状态空间的机械臂轨迹规划

提出一种基于状态空间的机械臂轨迹规划方法,定义并构造了机械臂系统的状态空间,根据内在机构约束与外部环境约束描述出系统状态的可达范围,并给出了任务的可实现条件.对于可实现任务,在状态空间能搜索到任务完成的最优解.如果任务无法完成,则修改系统配置或约束,在新的状态空间确定任务实现的转化条件,并对任务的设计与规划给予指导.研究了障碍约束下两连杆机械臂的点到点任务,实验结果验证了该方法的有效性.     

Path Planning for a Statically Stable Biped Robot Using PRM and Reinforcement Learning

In this paper path planning and obstacle avoidance for a statically stable biped robot using PRM and reinforcement learning is discussed. The main objective of the paper is to compare these two methods of path planning for applications involving a biped robot. The statically stable biped robot under consideration is a 4-degree of freedom walking robot that can follow any given trajectory on flat ground and has a fixed step length of 200 mm. It is proved that the path generated by the first method produces the shortest smooth path but it also increases the computational burden on the controller, as the robot has to turn at almost all steps. However the second method produces paths that are composed of straight-line segments and hence requires less computation for trajectory following. Experiments were also conducted to prove the effectiveness of the reinforcement learning based path planning method.     

An efficient local approach for the path generation of robot manipulators

In this article an efficient local approach for the path generation of robot manipulators is presented. The approach is based on formulating a simple nonlinear programming problem. This problem is considered as a minimization of energy with given robot kinematics and subject to the robot requirements and a singularities avoidance constraint. From this formulation a closed form solution is derived which has the properties that allows to pursue both singularities and obstacle avoidance simultaneously; and that it can incorporate global information. These properties enable the accomplishment of the important task that while a specified trajectory in the operational space can be closely followed, also a desired joint configuration can be attained accurately at a given time. Although the proposed approach is primarily developed for redundant manipulators, its application to nonredundant manipulators is examplified by considering a particular commercial manipulator.