A new methodology for designing PID controllers

It is known that it is impossible to select fixed gains for a PD controller that will critically damp the response to disturbances for all configurations of a given robot system. Because of this the potential for overshoot is always present and cannot be avoided unless the system is severely overdamped. This is not necessarily a practical solution and can be an economically unacceptable approach. On the other hand, however, if overshoot is permissible to some degree for some systems in the case of conventional Serial robots it is still prohibited in the case of Parallel robots as it may easily bring the robot to one of its possible singular configurations, causing damage to the system. This paper introduces a new algorithm for the design of PD controllers that ensures uniform and fast dynamic responses, which are free from overshoots for all robot configurations. The technique also satisfies general stability requirements for the system

A hyper-redundant manipulator

“Hyper-redundant” manipulators have a very large number of actuatable degrees of freedom. The benefits of hyper-redundant robots include the ability to avoid obstacles, increased robustness with respect to mechanical failure, and the ability to perform new forms of robot locomotion and grasping. The authors examine hyper-redundant manipulator design criteria and the physical implementation of one particular design: a variable geometry truss

Optimal mapping of joint faults into healthy joint velocity space for fault-tolerant redundant manipulators

redundant manipulator

A modal approach to hyper-redundant manipulator kinematics

This paper presents novel and efficient kinematic modeling techniques for “hyper-redundant” robots. This approach is based on a “backbone curve” that captures the robot's macroscopic geometric features. The inverse kinematic, or “hyper-redundancy resolution,” problem reduces to determining the time varying backbone curve behavior. To efficiently solve the inverse kinematics problem, the authors introduce a “modal” approach, in which a set of intrinsic backbone curve shape functions are restricted to a modal form. The singularities of the modal approach, modal non-degeneracy conditions, and modal switching are considered. For discretely segmented morphologies, the authors introduce “fitting” algorithms that determine the actuator displacements that cause the discrete manipulator to adhere to the backbone curve. These techniques are demonstrated with planar and spatial mechanism examples. They have also been implemented on a 30 degree-of-freedom robot prototype

Kinematically optimal hyper-redundant manipulator configurations

“Hyper-redundant” robots have a very large or infinite degree of kinematic redundancy. This paper develops new methods for determining “optimal” hyper-redundant manipulator configurations based on a continuum formulation of kinematics. This formulation uses a backbone curve model to capture the robot's essential macroscopic geometric features. The calculus of variations is used to develop differential equations, whose solution is the optimal backbone curve shape. We show that this approach is computationally efficient on a single processor, and generates solutions in O(1) time for an N degree-of-freedom manipulator when implemented in parallel on O(N) processors. For this reason, it is better suited to hyper-redundant robots than other redundancy resolution methods. Furthermore, this approach is useful for many hyper-redundant mechanical morphologies which are not handled by known methods

Robot's hand and expansions in non-integer bases

We study a robot hand model in the framework of the theory of expansions in non-integer bases. We investigate the reachable workspace and we study some configurations enjoying form closure properties.Comment: 22 pages, 10 figure

A General Numerical Method for Hyper-Redundant Manipulator Inverse Kinematics

Hyper-redundant robots have a very large or infinite degree of kinematic redundancy. A generalized resolved-rate technique for solving hyper-redundant manipulator inverse kinematics using a backbone curve is introduced. This method is applicable even in cases when explicit representation of the backbone curve intrinsic geometry cannot be written in closed form. Problems of end-effector trajectory tracking which were previously intractable can now be handled with this technique. Examples include configurations generated using the calculus of variations. The method is naturally parallelizable for fast digital and/or analog computation