L. Lanari

A sensitivity approach to optimal spline robot trajectories

Abstract A robot trajectory planning problem is considered. Using smooth interpolating cubic splines as joint space trajectories, the path is parameterized in terms of time intervals between knots. A minimum time optimization problem is formulated under maximum torque and velocity constraints, and is solved by means of a first order derivative-type algorithm for semi-infinite nonlinear programming. Feasible directions in the parameter space are generated using sensitivity coefficients of the active constraints. Numerical simulations are reported for a two-link Scara robot. The proposed approach can be used for optimizing more general objective functions under different types of constraints.

Asymptotically stable set point control laws for flexible robots

Abstract A general family of asymptotically stabilizing control laws is introduced for a class of nonlinear Hamiltonian systems. The inherent passivity property of this class of systems and the Passivity Theorem are used to show the closed loop input/output stability which is then related to the internal state space stability through an observability condition. Applications of these results include fully actuated robots, flexible-joint robots, and robots with link flexibility.

Control of redundant robots on cyclic trajectories

The authors investigate the problem of how to achieve a cyclic joint behavior in redundant robots performing cyclic tasks, motivated by the fact that most singularity-free local resolution methods produce nonrepeatable joint motions. A controllability analysis of the inverse kinematic system makes it possible to recover the well-known repeatability conditions of T. Shamir and Y. Yomdin (1988), and to further conclude that no null space velocity can be specified if a repeatable scheme is sought, unless it is chosen as a linear term in the end-effector velocity. The problem of achieving asymptotic cyclicity for a given inversion strategy has been solved via suitable kinematic controls, which guarantee convergence to cyclic joint trajectories along the desired end-effector path. Depending on the structure of the feedforward and feedback terms in the control law, a number of different schemes are proposed, yielding exact or asymptotic end-effector tracking. The stability proofs and the satisfactory simulation results confirm the advantage of using these simple control strategies.<<ETX>>

Control experiments on a two-link robot with a flexible forearm

A lightweight robot has been built with the aim of testing advanced control algorithms and demonstrating the engineering feasibility of flexible arm control. The robot is a planar two-link manipulator, with revolute joints and a very flexible forearm. A description of this laboratory facility is given, including mechanical structure, actuators and sensors, and interface electronics. A nonlinear dynamic model of the robot is given, in which link deflection is expressed in terms of orthonormal mode shapes of the associated eigenvalue problem. Simple control algorithms are presented, which are composed of a model-based feedforward term plus a linear feedback. These controllers have been implemented for joint trajectory tracking, and comparative experimental results are reported and discussed.<<ETX>>

Global set point control via link position measurement for flexible joint robots

Abstract In this paper it is shown that a linear controller solves the global set point control problem for a flexible joint robot via link position measurements. Moreover, the controller is shown to be robust with respect to uncertainties in the gravity term.

Adaptive disturbance attenuation with global stability for rigid and elastic joint robots

The disturbance attenuation problem with global internal stability is solved for both rigid and elastic joint robots in the presence of unknown constant parameters. The proposed dynamic controller combines adaptive and H~ control techniques.

Rest-to-Rest Motion for Planar Multi-Link Flexible Manipulator Through Backward Recursion

In this work is considered the problem of rest-to-rest motion in a desired pre-fixed time for planar flexible manipulators. We introduce a simple idea permitting the minimization of end-effector residual vibration when reaching a desired angular equilibrium position, in a pre-fixed desired travelling time. The results hold without considering internal elastic damping effect, using a classical controller with feedforward plus joint feedback terms. The new approach concerns the computation of the feedforward control, which is based on backward integration of the elastic dynamics, starting from a rest position of the flexible arms. This backward integration yields basically elastic trajectories permitting to reach the final desired end-effector position without oscillation. The feedback controller is then used to stabilize locally the actual states along these desired trajectories. However, for fast rest to rest motion, the feedback compensator fails to drive the system states along the desired trajectories, this being due to the relatively large initial elastic error. To overcome this limitation, proper joint motion is planned between the desired initial and final positions through optimization techniques, the goal being the minimization of the initial elastic error associated to these joint trajectories. The optimal planning technique is formulated as a Pontryagin optimal control problem. This scheme is validated via numerical tests as well as experiments on a flexible two-link planar manipulator. @DOI: 10.1115/1.1649976#

Robots with elastic joints are linearizable via dynamic feedback

Proves that the complete dynamic model of robots with elastic joints can always be fully transformed into a linear, controllable, and input-output decoupled system through the use of nonlinear dynamic state feedback.

On output feedback tracking control with disturbance attenuation for Euler-Lagrange systems

A solution to the problem of global tracking control with disturbance attenuation of robot systems described by Euler-Lagrange equations has been presented by Battilotti et al. (1997) by full state feedback. In this paper, we show how recent results of Zhang et al. (1997) can be used to solve the same problem for so-called Euler-Lagrange systems without velocity measurement, which is of much interest for robot applications.

A Unified Approach to Global Set Point Control for Rigid and Elastic Joint Robots

Abstract In this paper, we derive in a systematic manner, and using a unified framework, some recent results on global set point control of rigid and elastic joint robots using only position measurements. The controller design procedure consists of splitting up the overall stabilization task into two independent subproblems: one, a state-feedback stabilization problem, the other, an output injection stabilization problem.