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.     

Adaptive control of redundant multiple robots in cooperative motion

A redundant robot has more degrees of freedom than what is needed to uniquely position the robot end-effector. In practical applications the extra degrees of freedom increase the orientation and reach of the robot. Also the load carrying capacity of a single robot can be increased by cooperative manipulation of the load by two or more robots. In this paper, we develop an adaptive control scheme for kinematically redundant multiple robots in cooperative motion.In a usual robotic task, only the end-effector position trajectory is specified. The joint position trajectory will therefore be unknown for a redundant multi-robot system and it must be selected from a self-motion manifold for a specified end-effector or load motion. In this paper, it is shown that the adaptive control of cooperative multiple redundant robots can be addressed as a reference velocity tracking problem in the joint space. A stable adaptive velocity control law is derived. This controller ensures the bounded estimation of the unknown dynamic parameters of the robots and the load, the exponential convergence to zero of the velocity tracking errors, and the boundedness of the internal forces. The individual robot joint motions are shown to be stable by decomposing the joint coordinates into two variables, one which is homeomorphic to the load coordinates, the other to the coordinates of the self-motion manifold. The dynamics on the self-motion manifold are directly shown to be related to the concept of zero-dynamics. It is shown that if the reference joint trajectory is selected to optimize a certain type of objective functions, then stable dynamics on the self-motion manifold result. The overall stability of the joint positions is established from the stability of two cascaded dynamic systems involving the two decomposed coordinates.     

Collision-Free Cartesian Trajectory Generation Using Raster Scanning and Genetic Algorithms

An algorithm for Cartesian trajectory generation by redundant robots in environments with obstacles is presented. The algorithm combines a raster scanning technique, genetic algorithms and functions for interpolation in the joint coordinates space in order to approximate a desired Cartesian curve by the robot's hand tip under maximum allowed position deviation. A raster scanning technique determines a minimal set of knot points on the desired curve in order to generate a Cartesian trajectory with bounded position approximation error. Genetic algorithms are used to determine an acceptable robot configuration under obstacle avoidance constraints corresponding to a knot point. Robot motion between two successive knot points is finally achieved using well known interpolation techniques in the joint coordinates space. The proposed algorithm is analyzed and its performance is demonstrated through simulated experiments carried out on planar redundant robots.     

On controlling robots with redundancy

Recently there has been considerable interest in increasing the applicability and utility of robots by developing manipulators which possess kinematic and/or actuator redundancy. This paper presents a unified approach to controlling these redundant robots. The proposed control system consists of two subsystems: an adaptive position controller which generates the Cartesian-space control force FR^m required to track the desired end-effector position trajectory, and an algorithm that maps this control input to a robot joint torque vector TRⁿ. The F → T map is constructed so that the robot redundancy (kinematic and/or actuator) is utilized to improve the performance of the robot. The control scheme does not require knowledge of the complex robot dynamic model or parameter values for the robot or the payload. As a result, the controller is very general and is computationally efficient for on-line implementation. Computer simulation results are given for a kinematically redundant robot, for a robot with actuator redundancy, and for a robot which possesses both kinematic and actuator redundancy. In each case the results demonstrate that accurate end-effector trajectory tracking and effective redundancy utilization can be achieved simultaneously with the proposed scheme.     

Torque Optimizing Control with Singularity-Robustness for Kinematically Redundant Robots

A new control method for kinematically redundant manipulators having the properties of torque-optimality and singularity-robustness is developed. A dynamic control equation, an equation of joint torques that should be satisfied to get the desired dynamic behavior of the end-effector, is formulated using the feedback linearization theory. The optimal control law is determined by locally optimizing an appropriate norm of joint torques using the weighted generalized inverses of the manipulator Jacobian-inertia product. In addition, the optimal control law is augmented with fictitious joint damping forces to stabilize the uncontrolled dynamics acting in the null-space of the Jacobian-inertia product. This paper also presents a new method for the robust handling of robot kinematic singularities in the context of joint torque optimization. Control of the end-effector motions in the neighborhood of a singular configuration is based on the use of the damped least-squares inverse of the Jacobian-inertia product. A damping factor as a function of the generalized dynamic manipulability measure is introduced to reduce the end-effector acceleration error caused by the damping. The proposed control method is applied to the numerical model of SNU-ERC 3-DOF planar direct-drive manipulator.     

Task-based configuration control of redundant manipulators

This article establishes new goals for redundancy resolution based on manipulator dynamics and end-effector characteristics. These goals can be accomplished by employing the recently developed configuration control approach. Redundancy resolution is achieved by controlling the joint inertia matrix or the end-effector mass matrix that affect the inertial torques or by reducing the joint torques due to gravity loading and payload. The manipulator mechanical advantage and velocity ratio are also used as performance measures to be improved by proper utilization of redundancy. Furthermore, end-effector compliance, sensitivity, and impulsive force at impact are introduced as redundancy-resolution criteria. The new goals for redundancy resolution presented in this article allow a more efficient utilization of the redundant joints based on the desired task requirements. Simple case studies using computer simulations are described for illustration.     

Collision-avoidance for redundant robots through control of the self-motion of the manipulator

A new method to on-line collision-avoidance of the links of redundant robots with obstacles is presented. The method allows the use of redundant degrees of freedom such that a manipulator can avoid obstacles while tracking the desired end-effector trajectory. It is supposed that the obstacles in the workspace of the manipulator are presented by convex polygons. The recognition of collisions of the links of the manipulator with obstacles results on-line through a nonsensory method. For every link of the redundant manipulator and every obstacle a boundary ellipse is defined in workspace such that there is no collision if the robot joints are outside these ellipses. In case a collision is imminent, the collision-avoidance algorithm compute the self-motion movements necessary to avoid the collision. The method is based on coordinate transformation and inverse kinematics and leads to the favorable use of the abilities of redundant robots to avoid the collisions with obstacles while tracking the end-effector trajectory. This method has the advantage that the configuration of the manipulator after collision-avoidance can be influenced by further requirements such as avoidance of singularities, joint limits, etc. The effectiveness of the proposed method is discussed by theoretical considerations and illustrated by simulation of the motion of three-and four-link planar manipulators between obstacles.     

Obstacle avoidance for redundant robots using configuration control

The article presents a new and simple solution to the obstacle avoidance problem for redundant robots. In the proposed approach, called configuration control, the redundancy is utilized to configure the robot so as to satisfy a set of kinematic inequality constraints representing obstacle avoidance, while the end-effector is tracking a desired trajectory. The robot control scheme is very simple, and uses on-line adaptation to eliminate the need for the complex dynamic model and parameter values of the robot. Several simulation results for a four-link planar robot are presented to illustrate the versatility of the approach. These include reaching around a stationary obstacle, simultaneous avoidance of two obstacles, robot reconfiguration to avoid a moving obstacle, and avoidance of rectangular obstacles. The simplicity and computational efficiency of the proposed scheme allows on-line implementation with a high sampling rate for real-time obstacle avoidance in a dynamically varying environment.     

Real-Time Motion Tracking of Robot Manipulators Using Adaptive Genetic Algorithms

The paper presents a genetic algorithm approach to real-time motion tracking of redundant and non-redundant manipulators. The joint angle trajectories are found by applying genetic operators to a set of suitably generated configurations so that the end-effector follows a desired workspace trajectory accurately. The probability of applying a particular genetic operator is adapted on-line to achieve fast convergence to the solution. The adaptation is based on two measures, namely, diversity and fitness of the generated configurations. In order to achieve real time tracking, special provisions are made so that only an appropriate small region in the joint space is searched. The tracking problem is solved at the position level rather the then velocity level. As such the proposed method does not use the manipulator Jacobian inverse or pseudo-inverse matrix and is shown to be free from problems such as excessive joint velocities due to singularities. Simulation results are presented for the 6-DOF Puma and the 7-DOF Robotic Research arm that demonstrate good tracking accuracy and reasonable joint velocities.     

Inversion techniques for trajectory control of flexible robot arms

A general framework is given for computing the torques that are needed for moving a flexible arm exactly along a given trajectory. This torque computation requires a dynamic generator system, as opposed to the rigid case, and can be accomplished both in an open- or in a closed-loop fashion. In the open-loop case, the dynamic generator is the full or reduced order inverse system associated to the arm dynamics and outputs. In order to successfully invert the arm dynamics, the torque generator should be a stable system. The stability properties depend on the chosen system output, that is on the robot variables (e.g., joint or end-effector) to be controlled. The same inversion technique can be applied for closed-loop trajectory control of flexible robots. A simple but meaningful nonlinear dynamic model of a one-link flexible arm is used to illustrate different feasible control strategies. Simulation results are reported that display the effects of the system output choice on the closed-loop stability and on the overall tracking performance.     

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.     

A recurrent neural network for minimum infinity-norm kinematiccontrol of redundant manipulators with an improved problem formulationand reduced architecture complexity

This paper presents an improved neural computation where scheme for kinematic control of redundant manipulators based on infinity-norm joint velocity minimization. Compared with a previous neural network approach to minimum infinity-non kinematic control, the present approach is less complex in terms of cost of architecture. The recurrent neural network explicitly minimizes the maximum component of the joint velocity vector while tracking a desired end-effector trajectory. The end-effector velocity vector for a given task is fed into the neural network from its input and the minimum infinity-norm joint velocity vector is generated at its output instantaneously. Analytical results are given to substantiate the asymptotic stability of the recurrent neural network. The simulation results of a four-degree-of-freedom planar robot arm and a seven-degree-of-freedom industrial robot are presented to show the proposed neural network can effectively compute the minimum infinity-norm solution to redundant manipulators.     

A Formal-Numerical Approach for Robust In-Workspace Singularity Detection

Singularity is a major problem for parallel robots as in these configurations the robot cannot be controlled, and there may be infinite forces/torques in its joints, possibly leading to its breakdown. Hence, such a configuration must usually be avoided, and certifying the absence of singularity within a prescribed workspace or on a given trajectory is essential for a practical use of this type of robots. Singularity conditions are usually quite complex, and therefore a purely analytical analysis is difficult. We present here an algorithm that combines formal and numerical calculations for detecting singularity or closeness to a singularity within an arbitrary workspace or trajectory. This algorithm has the very important advantage of being able to deal with any robot mechanical structure and to manage uncertainties in the robot control and in the robot modeling.     

Two recurrent neural networks for local joint torque optimizationof kinematically redundant manipulators

This paper presents two neural network approaches to real-time joint torque optimization for kinematically redundant manipulators. Two recurrent neural networks are proposed for determining the minimum driving joint torques of redundant manipulators for the eases without and with taking the joint torque limits into consideration, respectively. The first neural network is called the Lagrangian network and the second one is called the primal-dual network. In both neural-network-based computation schemes, while the desired accelerations of the end-effector for a specific task are given to the neural networks as their inputs, the signals of the minimum driving joint torques are generated as their outputs to drive the manipulator arm. Both proposed recurrent neural networks are shown to be capable of generating minimum stable driving joint torques. In addition, the driving joint torques computed by the primal-dual network are shown never exceeding the joint torque limits.     

A biomimetic approach to inverse kinematics for a redundant robot arm

Redundant robots have received increased attention during the last decades, since they provide solutions to problems investigated for years in the robotic community, e.g. task-space tracking, obstacle avoidance etc. However, robot redundancy may arise problems of kinematic control, since robot joint motion is not uniquely determined. In this paper, a biomimetic approach is proposed for solving the problem of redundancy resolution. First, the kinematics of the human upper limb while performing random arm motion are investigated and modeled. The dependencies among the human joint angles are described using a Bayesian network. Then, an objective function, built using this model, is used in a closed-loop inverse kinematic algorithm for a redundant robot arm. Using this algorithm, the robot arm end-effector can be positioned in the three dimensional (3D) space using human-like joint configurations. Through real experiments using an anthropomorphic robot arm, it is proved that the proposed algorithm is computationally fast, while it results to human-like configurations compared to previously proposed inverse kinematics algorithms. The latter makes the proposed algorithm a strong candidate for applications where anthropomorphism is required, e.g. in humanoids or generally in cases where robotic arms interact with humans.     

Direct adaptive impedance control of robot manipulators

This article presents an adaptive scheme for controlling the end-effector impedance of robot manipulators. The proposed control system consists of three subsystems: a simple “filter” that characterizes the desired dynamic relationship between the end-effector position error and the end-effector/environment contact force, an adaptive controller that produces the Cartesian-space control input required to provide this desired dynamic relationship, and an algorithm for mapping the Cartesian-space control input to a physically realizable joint-space control torque. The controller does not require knowledge of either the structure or the parameter values of the robot dynamics and is implemented without calculation of the robot inverse kinematic transformation. As a result, the scheme represents a general and computationally efficient approach to controlling the impedance of both nonredundant and redundant manipulators. Furthermore, the method can be applied directly to trajectory tracking in free-space motion by removing the impedance filter. Computer simulation results are given for a planar four degree-of-freedom redundant robot under adaptive impedance control. These results demonstrate that accurate end-effector impedance control and effective redundancy utilization can be achieved simultaneously by using the proposed controller.     

Reducing flexible base vibrations through local redundancy resolution

Future space systems will use teleoperated robotic systems mounted on flexible bases such as the Shuttle Remote Manipulator System. Due to dynamic coupling, a major control issue associated with these systems is the effect of flexible base vibrations on the performance of the robot. If uncompensated, flexible vibrations can lead to inertial tracking errors and an overall degradation in system performance. One way to overcome this problem is to use kinematically redundant robots. Thus, this article presents research results obtained from locally resolving kinematic redundancies to reduce or damp flexible vibrations. Using a planar, three-link rigid robot example, numerical simulations were performed to evaluate the feasibility of three vibration damping redundancy control algorithms. Results showed that compared to a zero redundancy baseline, the three controllers were able to reduce base vibration by as much as 90% in addition to decreasing the required amount of joint torque. However, similar to locally optimizing joint torques, excessive joint velocities often occurred. To improve stability, fixed weight, multi-criteria optimizations were performed. © 1995 John Wiley & Sons, Inc.     

Self motion determination based on actuator velocity bounds for redundant manipulators

The movement of redundant manipulator joints that does not cause any end-effector motion is referred to as its self motion. Control schemes for redundant manipulators utilize its self motion to optimize a performance criterion. Thus, commanded joint motion at each sampling step is the sum of the minimum joint motion required for the desired end-effector motion and the self motion. However, the amount of self motion is limited by the bounds on actuator velocities, which are limited by the actuator torque bounds. A scheme is presented to determine the magnitude of self motion, the direction of which is determined by a gradient projection scheme. Implementation of this scheme on a Motorola 68020 VMEbus-based controller of a seven-degree-of-freedom manipulator is described.     

Passive Compliance from Robot Limbs and its Usefulness in Robotic Automation

Robots have been traditionally used as positioning devices without muchregard to external forces experienced by the tool. This has limited furtherpotential applications of robots in automation. Most tasks that remain to beautomated require constrained robot motion and/or involve work done by therobot on the environment. Such tasks require both force and positioncontrol. The ability to control the end-effector compliance is critical tosuccessful force and position control tasks. Although the end-effectorcompliance can be actively controlled through the joint flexibilitiesprovided by the joint servos or by active force sensing, the usefulness ofhaving the minimum passive compliance in addition to active compliancecontrol can improve performance. In surface following, for example, it isnecessary to make the end-point of a robot have the right compliance toprevent jamming. The usefulness of passive compliance has been demonstratedby the use of compliance-devices on the robot end-effector such as theRemote Center Compliance. The natural compliance inherent in light weightand flexible robot structures, however, can be exploited to provide thenecessary passive compliance required.In this paper we present a novel framework for computing the end-effectorcompliance from the compliance offered by the limbs of a serial robot. Theemphasis is on the explanation of the passive end-effector complianceresulting from these structures, and particular attention is given to theuse of these results in the selection of the type of robot for a particulartask. We show examples of end-effector compliances as functions of jointconfigurations for the SCARA- and PUMA-type robots. The joint-configurationdependent end-effector compliance can be used to select the desired robotpose for the performance of a robotic task.     

Path Planning of Free Floating Prismatic-Jointed Manipulators

Reaching a desired position with a specific orientationin space by a robot, mounted on a freely floating base, is an importantpath planning and control problem. Research in this area has mainlyconcentrated on the use of revolute-jointed serial manipulators. It iswell known that the dynamic equations of such manipulators are quitecomplex.In this paper, we propose the use of a 6-link fully prismatic-jointedrobot to achieve a desired position and orientation in space instead of arevolute-jointed robot. The use of pure prismatic-jointed robots forsuch a purpose is counter intuitive. On earth, such a structure is unableto provide a desired orientation to the end-effector. However, it can beshown that in space, arbitrary end-effector orientations are possible.Due to the relative simplicity of kinematics, dynamics and workspace ofprismatic-jointed robots compared to revolute-jointed robots, their useresults in significant computational advantages in path planning andcontrol.Also, in this paper, we adopt an unconventional motion planning methodthat avoids inversion of the Jacobian matrix and results in singularityfree paths for the end-effector. In this method, the joint trajectoriesare considered to be modal sums of basis functions of time. Within this framework, constraints on jointangles and joint rates can be imposed. The results are demonstratedwith an example of a 6-link fully prismatic-jointed robot.