Adaptive control of kinematically redundant robots

A redundant robot has more degrees of freedom than those neededto position the Robert end-effector uniquely. In a usual robotictask, only end-effector position trajectory is specified. Thejoint position trajectory is unknown, and it must be selectedfrom a self-motion manifold for a specified end-effector. Inmany situations, the robot dynamic parameters such as the linkmass, inertia, and joint viscous friction are unknown. The lackof knowledge of the joint trajectory and the dynamic parametersmake it difficult to control redundant robots. In this paper we show, through careful formulation of the problem,that the adaptative control of redundant robots can be addressedas a reference-velocity traking problem in the joint space.A control law ensures bounded estimation of the unknown dynamicparameters of the robot, and the convergence to zero of thevelocity traking error is derived. To ensure the joint motionon the self-motion manifold remains bounded, a homeomorphictransformation is found. This transformation decomposes thedynamics of the velocity tracking error into a cascade systemconsisting of the dynamics in the end-effector error coordinatesand the dynamics on the self-motion manifold. The dynamics onthe self-motion manifold is shown to be related to the conceptof zero dynamics. In the shown that, if the reference jointtrajectory is selected to optimize a certain type of objectivefunction, then stable dynamics on the self-motion manifold result.This ensures the overall stability of the adaptive system. Detailedsimulations are given to test the theoretical developments.The proposed adaptive scheme does not require measurements ofthe joint acceleration or the inversion of the inertia matrixof the robot.     

Nonlinear modeling and control of slosh in liquid container transfer via a PPR robot

This paper studies the point-to-point liquid container transfer control problem for a PPR robot. The robot manipulator is represented as three rigid links, and the liquid slosh dynamics are included using a multi-mass-spring model. It is assumed that two forces and a torque applied to the prismatic joints and the revolute joint, respectively, are available as control inputs. The objective is to control the robot end-effector movement while suppressing the sloshing modes. A nonlinear mathematical model that reflects all of these assumptions is first introduced. Then, Lyapunov-based feedback controllers are designed to achieve the control objective. Two cases are considered: partial-state feedback that does not use slosh state information and full-state feedback that uses both robot state and slosh state measurements or estimations. Computer simulations are included to illustrate the effectiveness of the proposed control laws.     

The Lightweight Robot ElRob: Interesting Aspects in Modeling and Control

The articulated robot ElRob, consisting of flexible links and joints, is considered in several publications. Recent developments are presented in this work. The overall goal of the research is to decrease the effects of structural elasticities in lightweight robots. For this purpose model-based control concepts are investigated and very accurate and efficient kinematic and dynamic models are necessary. The robot is split into groups of bodies, the so called subsystems, with separated describing velocities and coordinate systems. To obtain structured equations of motion the Projection Equation is used. The beams are modelled using the floating frame of reference formulation and a Ritz-approach. Because of its flexibility, the examined robot is an underactuated system leading to special difficulties. As an example is it not possible to compute the desired joint angles with respect to a reference path in task space for the flexible system (inverse kinematic problem). Different methods to solve this drawback and other problems resulting from flexibility are discussed with special focus on feed forward control and different feedback control concepts. The resulting end point error, the necessary control input and other interesting results for the laboratory experiment are presented and compared. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Recursive Methods in Modeling and Control of Modular Robotic Systems

This paper addresses the dynamical modeling and control of reconfigurable modular robots. The modular actuators (brushless DC motors with Harmonic Drive gears) for the robots under consideration are connected by rigid links. This way the robot can be assembled in different configurations by rearranging these components. For dynamical modeling the Projection Equation in Subsystem representation is used, taking advantage of its modular structure. Due to the lack of position sensors at the gearbox output shaft, deflections caused by the elasticities in the gears can not be compensated by the PD motor joint controller. Therefore, a correction of the motor trajectory is needed, which can be calculated as part of a flatness based feed-forward control using the exact model of the robot. With the recursive approach proposed in this paper the concept of reconfigurability is retained. For validation a redundant articulated robot arm with seven joints is regarded and results are presented. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling of Reconfigurable Modular Redundant Robotic Systems

This paper deals with the dynamical modeling and control of modular redundant robots. The robots under consideration consist of modular actuators (brushless DC motors with Harmonic Drive gears) connected by rigid links. Different configurations can be designed by rearranging these subsystems. In order to fulfill the requirement for an efficient dynamical modeling, the Projection Equation in subsystem representation is used. The subsystems are connected via the kinematical chain. The Projection Equation offers the possibility to calculate the minimal accelerations recursively, leading to an O(n) computational effectiveness. To validate the proposed method, the model of an articulated robot arm with seven joints is considered. Simulation results are compared to measurements. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Time Optimal Path Planning for Industrial Robots: A Dynamic Programming Approach Considering Torque Derivative and Jerk Constraints

This paper presents a dynamic programming approach for calculating time optimal trajectories for industrial robots, subject to various physical constraints. In addition to path velocity, motor torque, joint velocity and acceleration constraints, the present contribution also shows how to deal with torque derivative and joint jerk limitations. First a Cartesian path for the endeffector is defined by splines using Bernstein polynomials as basis functions and is parameterized via a scalar path parameter. In order to compute the belonging quantities in configuration space, inverse kinematics is solved numerically. Using this and in combination with the dynamical model, joint torques as well as their derivatives can be constrained. For that purpose the equations of motion are calculated with the help of the Projection Equation. As a consequence of the used optimization problem formulation, the dynamical model as well as the restrictions have to be transformed to path parameter space. Due to the additional consideration of jerk and torque derivative constraints, the phase plane is expanded to a phase space. The parameterized restrictions lead to feasible regions in this space, in which the optimal solution is sought. Result of the optimization is the time behavior of the path parameter and subsequently the feed forward torques for the optimal motion on the spatial path defined by previously mentioned splines. Simulation results as well as experimental results for a three axes industrial robot are presented. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Neural network-based nonlinear tracking control of kinematically redundant robot manipulators

In this paper, neural network-based nonlinear dynamical control of kinematically redundant robot manipulators is considered. The neural network-based controller achieves end-effector trajectory tracking as well as subtask tracking effectively. A feedforward neural network is employed to learn the parametric uncertainties, existing in the dynamical model of the robot manipulator. The whole system is shown to be stable in the sense of Lyapunov. Numerical simulation studies are carried out for a 3R planar robot manipulator to show the effectiveness of the control scheme.     

Control concepts for a parallel manipulator with flexible links

Light-weight robots are advantageous considering the low energy consumption and the low material cost. However, in light-weight structures significant oscillations can occur which make the control very challenging. Objective of this research is end-effector trajectory tracking of a parallel manipulator with flexible links. Hereby, only the manipulator's drives are used, and no additional actuation on the flexible bodies is considered. For accurate trajectory tracking, feedforward control of the manipulator is used based on inverse dynamics and servo-constraints, combined with feedback control of the drive positions. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Learning of shared attention in sociable robotics

Sociable robots are embodied agents that are part of a heterogeneous society of robots and humans. They should be able to recognize human beings and each other, and to engage in social interactions. The use of a robotic architecture may strongly reduce the time and effort required to construct a sociable robot. Such architecture must have structures and mechanisms to allow social interaction, behavior control and learning from environment. Learning processes described on Science of Behavior Analysis may lead to the development of promising methods and structures for constructing robots able to behave socially and learn through interactions from the environment by a process of contingency learning. In this paper, we present a robotic architecture inspired from Behavior Analysis. Methods and structures of the proposed architecture, including a hybrid knowledge representation, are presented and discussed. The architecture has been evaluated in the context of a nontrivial real problem: the learning of the shared attention, employing an interactive robotic head. The learning capabilities of this architecture have been analyzed by observing the robot interacting with the human and the environment. The obtained results show that the robotic architecture is able to produce appropriate behavior and to learn from social interaction.     

Optimization of the Internal Dynamics of Underactuated Robots

A robot is underactuated if it possesses less control inputs than degrees of freedom, e.g. due to passive joints. The analysis of the mechanical design of these kinds of underactuated robots often shows that they are non-minimum phase, i.e. they have an internal dynamic which is not asymptotically stable. Therefore, feedback linearization is not possible, and output trajectory tracking becomes a very challenging task. It is shown that through an optimization procedure the mechanical design of an underactuated robot can be altered in such a way that the internal dynamics becomes stable. Thus feedback linearization of the underactuated robot becomes possible. In the optimization procedure, the design parameters are additional masses which are added to defined locations at different un-actuated links of the robot. The optimization criteria is two-stage and firstly requires that all eigenvalues of the linearized zero-dynamics are in the left half-plane and secondly that initial errors in the zero-dynamics decay rapidly. Due to the two-stage criteria computation the optimization problem is discontinuous. Also there might be many local minima. Therefore a particle swarm optimization procedure is used. The efficiency of this optimization approach is demonstrated by simulation of an underactuated robot. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An explicit approach for time-optimal trajectory planning for kinematically redundant serial robots

Kinematically redundant serial robots have become industrially important due their increased workspace and their inherent capability of null space motion resulting in remarkable adaptiveness to specific tasks compared to conventional, non-redundant manipulators. Attempting to increase the cost-effectiveness of industrial processes, introducing minimum-time trajectories may yield economical advantages due to reduced motion cycle times. This contribution presents a method that uses joint space decomposition and analytic inverse kinematics as well as standard optimization techniques to obtain minimum-time B-spline joint trajectories along prescribed task space paths for kinematically redundant serial robots. It is shown that the present method was successfully applied to a planar manipulator. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Control Strategies for a Hybrid Articulated Robot

Due to higher requirements in productivity and cost efficiency of production lines, robots and other manipulators have to move faster. One possibility to fulfill the mentioned goals is to build lightweight constructions having elastic deformations in joints and links. The elastic components tend to vibrations and static deflections. Methods that compensate or minimize these drawbacks are the focus of this paper. An articulated robot with 6 joints and flexibility in joints and links is under consideration. The joints are actuated by DC motors combined with Harmonic Drive gears which offer high gear ratios but undergo elastic deformations. The links are flexible in two bending directions and in torsional sense. To achieve ordinary differential equations, a Ritz approach together with the projection equation is used. The obtained model is used for feedforward and feedback control design. Based on reference trajectories and on a rigid body model, estimations for the elastic deflections are calculated. These deflections are used to alter the reference trajectory in order to minimize the error of the tool center point. For basic active damping, non-local curvature feedback is used. Together with PD joint control and the feedforward control, satisfying results are obtained. Additionally, a sliding control approach is presented. The stiffness of the tool center point is enhanced with the drawback of less active damping. Simulation results and measured data are presented and compared. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hierarchical Constraint-Based Singularity Avoidance for Multi-Axis Robots

A generalized reflexive approach for Hierarchical Constraint-Based Singularity Avoidance (HCB-SA) is proposed and demonstrated for the multi-axis robot control of a six Degrees Of Freedom (DOF) hybrid manipulator system. The concept utilizes a dynamic adaptation of virtual constraints by introducing virtual damped actuation on the velocity control level and an anisotropic reflexive trajectory deflection depending on the robot constraints on the position control level. Redundant or low priority DOFs can be used to minimize the pose error in the more important DOFs reflexively without calculating new trajectories. Accordingly, the end-effector can be safely controlled in the vicinity of singularities and all constraints in the task and joint space can be surely hold. Furthermore, the proposed cascaded feedback control with the generalized HCB-SA algorithm is able to react on the presence of external disturbances which is validated using software-in-the-loop simulation on the real-time control system. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamic Modeling and Force Control of a Redundant Robot for Polishing Applications

For many robotic applications with tasks such as cutting, assembly or polishing, it is necessary to get in contact with the surrounding. In this paper a redundant robot with seven degrees of freedom in a metal polishing task is considered. For simulation as well as for the controller design a dynamic model of the robot and a contact model are required. The equations of motion of the robot are calculated with the Projection Equation in subsystem representation and the contact model contains linear tool elasticities and work piece elasticities. In the case of a polishing task, a constant contact force during the process is required even if the robot moves along a trajectory. Thus some degrees of freedom of the robot tool center point have to be position controlled while the other ones have to be force controlled. The redundant robot offers the possibility to avoid singular positions or to maximize the available end-effector forces within the inverse kinematics and is therefore best suited for polishing large objects. The actual process forces are measured with a six axis force-torque-sensor mounted at the tool center point. These forces are used in a parallel force/position control law to achieve the desired behavior. Results from measurements of a test arrangement are presented. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Motion planning for planar bipeds using flatness: the single support phase

Trajectory planning and control of planar motions of biped robots is considered. The robot is modeled as a hierarchical structure of rigid links with rotational joints, which may be seen as a pendulum tree. Motors are available at all rotational joints. However, by the absence of control torques at the contact points with the ground, the system is underactuated. It is shown how differential flatness and time scaling can be helpful for the design of walking motions. Emphasis is put on the single support phase, when the robot touches the floor at a single point. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

一种机器人的反馈跟踪控制系统

本文对包括机器人在内的一类系统,指明了于跟踪控制所必需的反馈信息;结合速度控制和加速度控制,提出了使机器人跟踪并抓住空间做任意运动的物体的反馈控制方法,其与别种方法的不同之处在于:该方法能用于机器人手爪的方位不能事先确定的场合;数值模拟结果表明:所提出方法行之有效。     

Solución de la cinemática directa de la plataforma Gough-Stewart general usando un algoritmo híbrido de optimización

The direct kinematics problem for parallel robots can be stated as follows: given values of the joint variables, the corresponding Cartesian variable values, the pose of the end-effector, must be found. Most of the times the direct kinematics problem involves the solution of a system of non-linear equations. The most efficient methods to solve such kind of equations assume convexity in a cost function which minimum is the solution of the non-linear system. In consequence, the capacity of such methods depends on the knowledge about an starting point which neighboring region is convex, hence the method can find the global minimum. This article propose a method based on probabilistic learning about an adequate starting point for the Dogleg method which assumes local convexity of the function. The proposed method efficiently avoids the local minima, without need of human intervention or apriori knowledge, thus it shows a more robust performance than the simple Dogleg method or other gradient based methods. To demonstrate the performance of the proposed hybrid method, numerical experiments and the respective discussion are presented. The proposal can be extended to other structures of closed-kinematics chains, to the general solution of systems of non-linear equations, and to the minimization of non-linear functions.     

Fast reinforcement learning for simple physical robots

In the past few years, the field of autonomous robot has been rigorously studied and non-industrial applications of robotics are rapidly emerging. One of the most interesting aspects of this field is the development of the learning ability which enables robots to autonomously adapt to given environments without human guidance. As opposed to the conventional methods of robots’ control, where human logically design the behavior of a robot, the ability to acquire action strategies through some learning processes will not only significantly reduce the production costs of robots but also improves the applicability of robots in wider tasks and environments. However, learning algorithms usually require large calculation cost, which make them unsuitable for robots with limited resources. In this study, we propose a simple two-layered neural network that implements a novel and fast Reinforcement Learning. The proposed learning method requires significantly less calculation resources, hence is applicable to small physical robots running in the real world environments. For this study, we built several simple robots and implemented the proposed learning mechanism to them. In the experiments, to evaluate the efficacy of the proposed learning mechanism, several robots were simultaneously trained to acquire obstacle avoidance strategies in the same environment, thus, forming a dynamic environment where the learning task is substantially harder than in the case of learning in a static environment and promising result was obtained.     

Motion equations of cooperative multi flexible mobile manipulator via recursive Gibbs–Appell formulation

In this paper, the developed model of an N-flexible-link mobile manipulator with revolute-prismatic joints is presented for the cooperative flexible multi mobile manipulator. In this model, the deformation of flexible links is calculated by using the assumed modes method. In additions, non-holonomic constraints of the robots’ mobile platforms that bound its locomotion are considered. This limitation is alleviated through the concurrent motion of revolute and prismatic joints, although it results in computational complexity and changes the final motion equations to time-varying form. Not only is the proposed dynamic model implemented for the multi-mobile manipulators with arms having independent motion, but also for multi-mobile manipulators in cooperation after defining gripper's kinematic constraints. These constraints are imported to the dynamic equations by defining Lagrange multipliers. The recursive Gibbs–Appell formulation is preferred over other similar approaches owing to the capability of solving the equations without the need to use Lagrange multipliers for eliminating non-holonomic constraints in addition to the novel optimized process of obtaining system equations. Hence, cumbersome simultaneous computations for eliminating the constraints of platform and arms are circumvented. Therefore, this formulation is improved for the first time by importing Lagrange multipliers for solving kinematic constrained systems. In the simulation section, the results of forward dynamics solution for two flexible single-arm manipulators with revolute-prismatic joints while carrying a rigid object are presented. Inverse dynamics equations of the system are also presented to obtain the maximum dynamic load-carrying capacity of the two-rigid-link mobile manipulators on a predefined path. Two constraints, namely the capacity of joint motors torque and robot motion stability are considered as the limitation criteria. The concluded motion equations are used to accurately control the movement of sensitive bodies, which is not achievable through the use of one platform.