Control of Robots with Elastic Joints Interacting with Dynamic Environment

In this paper, the control of robots with elastic joints in contact with dynamic environment is considered. It is shown how control laws synthesized for the robots with rigid joints interacting with dynamic environment can also be used in the case of robots with elastic joints. The proposed control laws are based on a robot model interacting with dynamic environment, including the dynamics of actuators and the elasticity of joints. The proposed control laws possess two feedback loops: the outer, serving for on-line calculation of the motor shaft angle based on the position error or the contact force error, and the inner one, serving for performing stabilization around the calculated motor shaft angle. Simulation results which exhibit the application of the appropriate control laws are also presented.     

Optimal elastic coupling in form of one mechanical spring to improve energy efficiency of walking bipedal robots

This paper presents a method to optimize the energy efficiency of walking bipedal robots by more than 80 % in a speed range from 0.3 to 2.3 m/s using elastic couplings—mechanical springs with movement speed independent parameters. The considered planar robot consists of a trunk, two two-segmented legs, two actuators in the hip joints, two actuators in the knee joints and an elastic coupling between the shanks. It is modeled as underactuated system to make use of its natural dynamics and feedback controlled via input–output linearization. A numerical optimization of the joint angle trajectories as well as the elastic couplings is performed to minimize the average energy expenditure over the whole speed range. The elastic couplings increase the swing leg motion’s natural frequency thus making smaller steps more efficient which reduce the impact loss at the touchdown of the swing leg. The process of energy turnover is investigated in detail for the robot with and without elastic coupling between the shanks. Furthermore, the influences of the elastic couplings’ topology and of joint friction are analyzed. It is shown that the optimization of the robot’s motion and elastic coupling towards energy efficiency leads to a slightly slower convergence rate of the controller, yet no loss of stability, but a lower sensitivity with respect to disturbances. The optimal elastic coupling discovered via numerical optimization is a linear torsion spring with transmissions between the shanks. A design proposal for this elastic coupling—which does not affect the robot’s trunk and parallel shank motion and can be used to enhance an existing robot—is given for planar as well as spatial robots.     

Design of global tracking controllers for flexible-joint robots

An approach to design control laws for trajectory tracking of robots having flexible joints is presented. An application to the adaptive control is also given with reference to a single-link robot with one revolute elastic joint whose parameters are unknown.     

A control for spatial motions of a robot in a rectangular Cartesian coordinate system

Two mathematical models of a robot with elastic or rigid links working in a rectangular Cartesian coordinate system are proposed. The problems of dynamic and kinematic controls for such a robot are posed within the framework of the specified models. The difficulties of mathematical simulation of real robots of such a type with sliding joints are discussed in connection with the presence of elastic flexibility in the actuators. The technique for estimating the accuracy of positioning of the load carried by the robot based on joint use of the specified mathematical models is presented. As an example, solution of the problems of kinematic control of flexible and rigid robots with equivalent geometric and physical parameters functioning in a rectangular Cartesian coordinate system is considered.     

An observer for flexible joint robots

The problem of state observation of robots that have elastic joints is discussed. Outputs are assumed to be the global link coordinates and their time derivatives, and a nonlinear observer is proposed which asymptotically reconstructs all the robot state variables. The dynamic behaviour of the observation algorithm is illustrated by simulation tests referred to a manipulator with three revolute elastic joints. To verify the observer robustness, the previous simulation tests were repeated by using the same observer, designed for a nominal payload of 5 kg, and actual robot payloads of 0 and 10 kg. The differences with respect to the nominal case are not appreciable. However, the steady-state joint errors, which were about 10^-6 rad in the nominal case, became about 10^-4 rad     

Nonlinear H∞ disturbance attenuation for robots with flexible joints

The tracking problem is considered for robots having flexible joints. We propose a state feedback control algorithm which guarantees arbitrary attenuation on the outputs of the effects of time-varying disturbances as well as of parameter uncertainties. Only a lower bound on the values of the elastic constants is required to be known.     

Trajectory tracking control of flexible-joint robots

Inverse dynamics control of flexible-joint robots is addressed. It is shown that, in a flexible-joint robot, the acceleration level inverse dynamic equations are singular because the control torques do not have an instantaneous effect on the end-effector accelerations due to the elastic media. Implicit numerical integration methods that account for the higher order derivative information are utilized for solving the singular set of differential equations. The trajectory tracking control law presented linearizes and decouples the system and yields an asymptotically stable fourth order error dynamics for each end-effector degree of freedom. A 3R spatial robot with all joints flexible is simulated to illustrate the performance of the proposed algorithm.     

Direct method for updating flexible multibody systems applied to a milling robot

Industrial robots are currently used in light milling operations for their low cost and large workspace compared with CNC machine tools. However, milling robots are prone to vibration instabilities (chatter) and process deviations since they are significantly less stiff than machine tools. As a result, robot dynamic response depends on its posture which represents a major challenge. This paper presents a direct method to update any multibody model, enclosing flexible rotational/translational or virtual joints with minimal tuning. The novel method allows determining the elastic parameters of the model based on a curve fitting of the frequency response functions measured at the tool tip. Fitting is fast and efficient as it occurs in the frequency domain without the need to transform the measured data into the model parameter space. It relies on a genetic algorithm followed by a deterministic procedure to ensure a refined solution of the identified global minimum. The method is firstly demonstrated and validated on a simulated flexible manipulator with three rotational joints. Its multibody model is built using minimal coordinates with known elastic parameters that the method recovers accurately. The new fitting algorithm is eventually applied to an actual industrial robot (KUKA KR90 R3100 robotic arm) resulting in the proper fit of its critical resonances. Posture dependency can also be tackled by considering multiple measurements in different poses within the same fitting procedure. Updating procedure was programmed in Matlab and made public so that it can be easily adapted to identify elastic parameters of other flexible mechanical systems.     

Development of flexible joints for a humanoid robot that walks on an oscillating plane

In this study, we develop flexible joints for a humanoid robot that walks on an oscillating plane and discuss their effectiveness in compensating disturbances. Conventional robots have a rigid frame and are composed of rigid joints driven by geared motors. Therefore, disturbances, which may be caused by external forces from other robots, obstacles, vibration and oscillation of the surface upon which the robot is walking, and so on, are transmitted directly to the robot body, causing the robot to fall. To address this problem, we focus on a flexible mechanism. We develop flexible joints and incorporate them in the waist of a humanoid robot; the experimental task of the robot is to walk on a horizontally oscillating plane until it reaches the desired position. The robot with the proposed flexible joints, reached the goal position despite the fact that the controller was the same as that used for a conventional robot walking on a static plane. From these results, we conclude that our proposed mechanism is effective for humanoid robots that walk on an oscillating plane.     

The OmniTread OT‐4 serpentine robot—design and performance

Serpentine robots are slender, multi‐segmented vehicles designed to provide greater mobility than conventional mobile robots. Serpentine robots are ideally suited for urban search and rescue, military intelligence gathering, and inspection tasks in hazardous or inaccessible environments. One such serpentine robot, developed at the University of Michigan, is the “OmniTread OT‐4.” The OT‐4 comprises seven segments, which are linked to each other by six joints. The OT‐4 can climb over obstacles that are much higher than the robot itself, propel itself inside pipes of different diameters, and traverse difficult terrain, such as rocks or the rubble of a collapsed structure. The foremost and unique design characteristic of the OT‐4 is the use of pneumatic bellows to actuate the joints. The pneumatic bellows allow the simultaneous control of position and stiffness for each joint. Controllable stiffness is important in serpentine robots, which require stiff joints to cross gaps and compliant joints to conform to rough terrain for effective propulsion. Another unique feature of the OmniTread design is the coverage of all four sides of each segment with drive tracks. This design makes the robot indifferent to rollovers, which are bound to happen when the slender bodies of serpentine robots travel over rugged terrain. This paper describes the OmniTread concept and some of its technical features in some detail. In the Experiment Results Section, photographs of successful obstacle traverses illustrate the abilities of the OT‐4. © 2007 Wiley Periodicals, Inc.     

Hypermobile Robots – the Survey

This article presents a survey on hypermobile robots – a group of articulated mobile robots that typically comprise of several segments with powered wheels, tracks, or legs to propel the vehicle forward. Segments are connected by 2- or 3-degree-of-freedom (DOF) joints that may or may not be powered and provide better mobility as compared with regular mobile robots. The origins are analyzed and over 14 projects are compared in order to find the best methodology of designing and developing hypermobile robots.     

A Reconfigurable Robot With Lockable Cylindrical Joints

This paper presents a new conceptual design for reconfigurable robots. Unlike conventional reconfigurable robots, our design does not achieve reconfigurability by utilizing modular joints. Rather, the robot is equipped with passive joints, i.e., joints without actuator or sensor, which permit changing the Denavit–Hartenberg (DH) parameters such as the link length and twist angle. The passive joints will become controllable when the robot forms a closed kinematic chain. Also, each passive joint is equipped with a built-in brake mechanism that is normally locked, but the lock can be released whenever the parameters are to be changed. Such a versatile and agile robot is particularly suitable for space application for its simple, compact, and light design. The kinematics and recalibration of this kind of reconfigurable robot are thoroughly analyzed. A stable reconfiguration-control algorithm is devised to take the robot from one configuration to another by directly regulating the passive joints to the associated, desired DH parameters. Conditions for the observability and the controllability of the passive joints are also derived in detail.      

Reliability maps for probabilistic guarantees of task motion for robotic manipulators

There are many applications for which reliable and safe robots are desired. For example, assistant robots for disabled or elderly people and surgical robots are required to be safe and reliable to prevent human injury and task failure. However, different levels of safety and reliability are required for different tasks so that understanding the reliability of robots is paramount. Currently, it is possible to guarantee the completion of a task when the robot is fault tolerant and the task remains in the fault-tolerant workspace (FTW). The traditional definition of FTW does not consider different reliabilities for the robotic manipulator's different joints. The aim of this paper is to extend the concept of a FTW to address the reliability of different joints. Such an extension can offer a wider FTW while maintaining the required level of reliability. This is achieved by associating a probability with every part of the workspace to extend the FTW. As a result, reliable fault-tolerant workspaces (RFTWs) are introduced by using the novel concept of conditional reliability maps. Such a RFTW can be used to improve the performance of assistant robots while providing the confidence that the robot remains reliable for completion of its assigned tasks.     

Design of a multilink-articulated wheeled pipeline inspection robot using only passive elastic joints

This paper presents a multilink-articulated robot with omni and hemispherical wheels (AIRo-2.1) for inspecting and exploring pipelines. To quickly adapt to winding pipes, holonomic rolling movement without moving forward and backward is useful. However, this requires the rolling actuators to replace the driving actuators at the expense of the driving force. Furthermore, so far the number of driving wheels and torsion springs, magnitude of driving forces, stiffness and natural angle of the spring that are required to adapt to various pipelines have not been clarified. In this paper, we investigate the possibility of high maneuverability of multilink-articulated robots in winding pipes with as few driving actuators as possible and only elastic joints (torsion springs) for body bending. We further validate its effectiveness by experimental verification.     

On repelling robotic trajectories: coordination in navigation of multiple mobile robots

The paper attacks the problem of motion planning of a set of mobile robots. While artificial potential fields are the simplest methods of use, they are also locally optimal and can be easily stuck in scenarios. Probabilistic roadmap, elastic roadmaps, elastic strip and similar methods have a weak modelling of coordination between the robots. An inspiration is drawn from the artificial potential field method where the potential is computed in configuration space. In this paper the notion is extended to a ‘trajectory space’, where the complete trajectories of robots repel each other. With the added assumption of communication between the robots and higher computational costs, the resultant approach is near optimal and does not get the robot stuck or trapped. A variant of the algorithm with no direct communication is also presented. The method is experimented by using computer simulations and found to perform better over well-known approaches in the literature.     

The dexterity and singularities of an underactuated robot

Underactuated robots are robotic systems with more joints than actuators. A robot may be underactuated by design as in the case of a hyper‐redundant robot with passive joints or may become underactuated as a result of an actuator failure. In this article, we examine the dexterity of underactuated robots whose passive joints operate in either a locked or free‐swinging mode. The ability to an analyze the dexterity of an underactuated robot has important applications especially for the control of passive joints with brakes and for the fault tolerance analysis of an otherwise fully actuated kinematically redundant robot. The approach applied here is to use kinematics and dynamics‐based formulations of manipulator dexterity. We then characterize passive‐joint singularities, i.e., configurations where full end‐effector control is lost because one or more joints are passive instead of active. Lastly, we introduce a new characterization of joint‐limit singularities, which are configurations where full end‐effector control cannot be achieved because one or more joints are at their joint limits. © 2001 John Wiley & Sons, Inc.     

Design and implementation of an ERLS-based 3-D dynamic formulation for flexible-link robots

Modeling and dynamic analysis of robots with flexible-links are still an open field of research. Indeed, to design and control effective light robot manipulators and high-performance flexible mechanisms for efficient manufacturing systems, an accurate dynamic model representing the system behavior is necessary. In this work, a novel method for dynamic modeling of 3-D robots with large displacements and small elastic deformations is developed by means of an Equivalent Rigid Link System (ERLS) approach. Thanks to this, the kinematic equations of the Equivalent Rigid Link System and the compatibility equations of the displacements at the joints are always decoupled. After the theoretical development, the kinematic and dynamic models have been implemented on a Matlab^™${\mathrm{Matlab}}^{™}$ software simulator and validated.     

一类轮式机器人的重心控制

介绍了一类建筑领域等非结构环境下使用的由6个转动关节和4个直动关节组成的轮式机器人,其特殊的结构加上重心控制,能使机器人在不平整地面上行走而不倾倒。绘制了机器人重心控制原理,推导出使机器人不倾倒的重心控制运动方程。给出了实验用的部分软硬件原理框图,并通过实验验证了方案的可行性。     

Optimal Collision Free Path Planning for Non-Synchronized Motions

This paper treats the path finding problem for robots whose joints cannot be controlled in such a way that the end-effector follows a prespecified trajectory. Hence, if two or more joints are moving at the same time during the motion, the relative positions for the joints, i.e. the exact positions of the end-effector, are not known. This may be due to the low level control of the robot (for example, with heavy load robots), or due to a complicated kinematic structure. For such mechanisms a motion is specified by certain intermediate positions (values for all joints) along a desired path. These intermediate positions (synchronization points) and the requirement that the motions in the single joints are monotonous between consecutive synchronization points guarantee a certain structure of a path. We develop a new algorithm that determines paths for such mechanisms, i.e., a respective sequence of intermediate positions, such that the path is collision free and is shortest with respect to different optimality criteria.