L. Sciavicco

A solution algorithm to the inverse kinematic problem for redundant manipulators

Based on a recently proposed algorithmic solution technique, the inverse kinematic problem for redundant manipulators is solved. The kinematics of the manipulator is appropriately augmented to include mentioned constraints; the result is an efficient, fast, closed-loop algorithm which only makes use of the direct kinematics of the manipulator. Simulation results illustrate the tracking performance for a given trajectory in the Cartesian space, while guaranteeing a collision-free trajectory and/or not violating a mechanical joint limit. >

The parallel approach to force/position control of robotic manipulators

Force/position control strategies provide an effective framework to deal with tasks involving interaction with the environment. In this paper the parallel approach to force/position control of robotic manipulators is presented. It shows a complete use of the available sensor measurements by operating the control action in a full-dimensional space without using selection matrices. Conflicting situations between the position and force tasks are managed using a priority strategy: the force control loop is designed to prevail over the position control loop. This choice ensures limited deviations from the prescribed force trajectory in every situation, guaranteeing automatic recovery from unplanned collisions. A dynamic force/position parallel control law is presented and its performance in presence of an elastic environment is analyzed; simplification of the dynamic control law is also discussed leading to a PID-type parallel controller. Two case studies are worked out that show the effectiveness of the approach in application to an industrial robot. >

Closed-loop inverse kinematics schemes for constrained redundant manipulators with task space augmentation and task priority strategy

This article presents new closed-loop schemes for solving the inverse kinematics of constrained redundant manipula tors. In order to exploit the space of redundancy, the end- effector task is suitably augmented by adding a constraint task. The success of the technique is guaranteed either by specifying the constraint task ad hoc or by resorting to a task priority strategy. Instead of previous inverse kinemat ics schemes that use the Jacobian pseudoinverse, the schemes in this work are shown to converge using the Jacobian transpose. A number of case studies illustrate different ways of solving redundancy in the context of the proposed schemes.

Global task space manipulability ellipsoids for multiple-arm systems

New definitions of force and velocity manipulability ellipsoids for multiple-arm systems are given. A suitable kinetostatic formulation for multiple cooperating arms is adopted that allows a global task space description of external and internal forces as well as absolute and relative velocities at the object level. The concept of a force manipulability ellipsoid for a single arm is formally extended to the multi-arm case by regarding the whole system as a mechanical transformer from the extended joint space to the global task space. Kinetostatic duality properties are then exploited to derive velocity manipulability ellipsoids for the multiple-arm system. The proposed method is compared with other approaches using numerical examples. >

Robust Control of Robotic Manipulators

Abstract Typically the dynamic control of robotic manipulators is characterized by two levels. The first one requires coordinate transformations to convert the desired path from Cartesian to joint space. The second one requires the computation of generalized torque inputs starting from the knowledge of the manipulator dynamic model. The problems at both levels are difficult to solve because of the high nonlinearities, parametric variations and inaccuracies which occur. Using adaptation control laws, valid for nonlinear time-varying plants, a robust control technique is developed at the second level forcing the controlled manipulator to follow the behaviour of a decoupled linear time invariant system. The problem of converting coordinates is reformulated as a nonlinear dynamic problem and is solved again by making use of robust adaptive techniques. The amount of computation is limited and the precision obtainable is very satisfactory as shown by simulation results.

Robust design of independent joint controllers with experimentation on a high-speed parallel robot

A linear independent joint control scheme is proposed. The design is made robust by closing another feedback loop that uses acceleration information besides the typical position and velocity loops. Reconstruction of acceleration measurements is performed via a suitable state-variable filter. Linear feedforward compensation is used to improve tracking performance of the closed-loop scheme. The control algorithm is tested first in a discrete-time simulation on a single-joint drive system with imposed disturbance torques. Then, real-time implementation on a high-speed parallel robot is presented. The experimental results demonstrate the effectiveness of the proposed technique. >

A dynamic solution to the inverse kinematic problem for redundant manipulators

Redundancy represents one key towards design and synthesis of more versatile manipulators. Obstacle avoidance and limited joint range constitute two kinds of constraints which can be potentially met by a kinematically redundant manipulator. The natural scenario is the inverse kinematic problem which is certainly a crucial point for robotic manipulator analysis and control. Based on a recently proposed dynamic solution technique, the inverse kinematic problem for redundant manipulators is solved in this paper. The kinematics of the manipulator is appropriately augmented in order to include the above mentioned constraints; the result is an efficient, fast dynamic algorithm which only makes use of the direct kinematics of the manipulator. Extensive simulation results illustrate the tracking performance for a given trajectory in the Cartesian space, while guaranteeing a collision-free trajectory and/or not violating a mechanical jointiimit.

Coordinate Transformation: A Solution Algorithm for One Class of Robots

One of the most important features of an advanced control system for articulated robots is the capability of transforming the work space coordinates, which naturally characterize any robot task, into the corresponding joint coordinates, on which control actions are developed. For each task, the coordinate transformation problem consists in calculating one trajectory in the joint space which corresponds to the end effector trajectory, usually given in the Cartesian space. While simple kinematical structures allow for closed-form solutions, there is a class of robots for which this is not true. Typical articulated robot structures have three revolute joints at the end effector; the geometric parameters of these joints actually determine the spatial configuration of the last axes of motion. The large majority of todays nonredundant structures have three intersecting axes at the end effector, and closed form solutions do exist in this case. If the axes intersect two-by-two, as in some rather common arm design, an exact solution seems not to exist. A quite different solution algorithm is established, as compared to the trigonometric approach widely adopted so far, which yields solutions in case of two-by-two intersecting axes. The convergence of the algorithm along any trajectory is proved. Effectiveness of the proposed technique can be argued by the fact that it only makes use of direct kinematics, thus resulting in a contained computational burden. A robot prototype of the kind described above is taken as a reference in order to discuss digital implementation and develop numerical examples.

Hyperstable adaptive model following control of nonlinear plants

Based on hyperstability theory, a new adaptation law for adaptive model-reference control systems is developed, for use with a class of nonlinear time-varying plants. Assuming some structural conditions to be verified, a simple and systematicdesign procedure is suggested whose one prerequisite is a knowledge of the range of variation of the plant parameters. The adaptation mechanism involves no on-line integration of differential equations and it is easily implemented by means of microprocessors. The dynamic behaviour is clarified by treating the adapted system as a variable structure system.

Task space dynamic analysis of multiarm system configurations

The aim of this article is to provide a systematic method to perform dynamic analysis in the task space for a sys tem composed of multiple arms holding a rigid object. The dynamic manipulability ellipsoid is introduced to obtain quantitative indices of the systems capability, in each configuration, of performing object accelerations along given task space directions. The ellipsoid is derived on the basis of the mapping of object accelerations onto joint driving torques via the proper kineto-static and dynamic equations of the system. The maximum joint torque limits are taken into account, and the effects of gravitational loads onto the ellipsoid are evidenced. Anal ysis of multiarm system configurations is carried out in a number of case studies.