Fuzzy logic control of telerobot manipulators

Telerobot systems for advanced applications will require manipulators with redundant 'degrees of freedom' (DOF) that are capable of adapting manipulator configurations to avoid obstacles while achieving the user specified goal. Conventional methods for control of manipulators (based on solution of the inverse kinematics) cannot be easily extended to these situations. Fuzzy logic control offers a possible solution to these needs. A current research program at SRI developed a fuzzy logic controller for a redundant, 4 DOF, planar manipulator. The manipulator end point trajectory can be specified by either a computer program (robot mode) or by manual input (teleoperator). The approach used expresses end-point error and the location of manipulator joints as fuzzy variables. Joint motions are determined by a fuzzy rule set without requiring solution of the inverse kinematics. Additional rules for sensor data, obstacle avoidance and preferred manipulator configuration, e.g., 'righty' or 'lefty', are easily accommodated. The procedure used to generate the fuzzy rules can be extended to higher DOF systems

Investigation of cyclicity of kinematic resolution methods for serial and parallel planar manipulators

Kinematic redundancy of manipulators is a well-understood topic, and various methods were developed for the redundancy resolution in order to solve the inverse kinematics problem, at least for serial manipulators. An important question, with high practical relevance, is whether the inverse kinematics solution is cyclic, i.e., whether the redundancy solution leads to a closed path in joint space as a solution of a closed path in task space. This paper investigates the cyclicity property of two widely used redundancy resolution methods, namely the projected gradient method (PGM) and the augmented Jacobian method (AJM), by means of examples. Both methods determine solutions that minimize an objective function, and from an application point of view, the sensitivity of the methods on the initial configuration is crucial. Numerical results are reported for redundant serial robotic arms and for redundant parallel kinematic manipulators. While the AJM is known to be cyclic, it turns out that also the PGM exhibits cyclicity. However, only the PGM converges to the local optimum of the objective function when starting from an initial configuration of the cyclic trajector

An inverse kinematics algorithm for a highly redundant variable-geometry-truss manipulator

A new class of robotic arm consists of a periodic sequence of truss substructures, each of which has several variable-length members. Such variable-geometry-truss manipulator (VGTMs) are inherently highly redundant and promise a significant increase in dexterity over conventional anthropomorphic manipulators. This dexterity may be exploited for both obstacle avoidance and controlled deployment in complex workspaces. The inverse kinematics problem for such unorthodox manipulators, however, becomes complex because of the large number of degrees of freedom, and conventional solutions to the inverse kinematics problem become inefficient because of the high degree of redundancy. A solution is presented to this problem based on a spline-like reference curve for the manipulator's shape. Such an approach has a number of advantages: (1) direct, intuitive manipulation of shape; (2) reduced calculation time; and (3) direct control over the effective degree of redundancy of the manipulator. Furthermore, although the algorithm was developed primarily for variable-geometry-truss manipulators, it is general enough for application to a number of manipulator designs

A linear optimization approach to inverse kinematics of redundant robots with respect to manipulability

The solution of the inverse kinematics is required in many technical applications. In this contribution a concept is proposed which reformulates the inverse kinematics (IK) of kinematically redundant manipulators as a linear programming (LP) problem. This formulation enables the explicit consideration of technical constraints as for example mechanical end-stops, velocity and, if necessary, acceleration limits as linear inequality constraints. Besides that, automatic collision avoidance within the workspace of the manipulator can be included. The kinematic redundancy is resolved with respect to quadratic criteria. As the LP problem at hand belongs to the small-size problems, the optimal solution can be found numerically in appropriate time using standard algorithms such as the simplex algorithm or interior point methods. This article closes with a numerical example of the LP-IK of a planar 4-link manipulato

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

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

Characterization and control of self-motions in redundant manipulators

The presence of redundant degrees of freedom in a manipulator structure leads to a physical phenomenon known as a self-motion, which is a continuous motion of the manipulator joints that leaves the end-effector motionless. In the first part of the paper, a global manifold mapping reformulation of manipulator kinematics is reviewed, and the inverse kinematic solution for redundant manipulators is developed in terms of self-motion manifolds. Global characterizations of the self-motion manifolds in terms of their number, geometry, homotopy class, and null space are reviewed using examples. Much previous work in redundant manipulator control has been concerned with the redundancy resolution problem, in which methods are developed to determine, or resolve, the motion of the joints in order to achieve end-effector trajectory control while optimizing additional objective functions. Redundancy resolution problems can be equivalently posed as the control of self-motions. Alternatives for redundancy resolution are briefly discussed

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