Kinematically redundant robot manipulators

Research on control, design and programming of kinematically redundant robot manipulators (KRRM) is discussed. These are devices in which there are more joint space degrees of freedom than are required to achieve every position and orientation of the end-effector necessary for a given task in a given workspace. The technological developments described here deal with: kinematic programming techniques for automatically generating joint-space trajectories to execute prescribed tasks; control of redundant manipulators to optimize dynamic criteria (e.g., applications of forces and moments at the end-effector that optimally distribute the loading of actuators); and design of KRRMs to optimize functionality in congested work environments or to achieve other goals unattainable with non-redundant manipulators. Kinematic programming techniques are discussed, which show that some pseudo-inverse techniques that have been proposed for redundant manipulator control fail to achieve the goals of avoiding kinematic singularities and also generating closed joint-space paths corresponding to close paths of the end effector in the workspace. The extended Jacobian is proposed as an alternative to pseudo-inverse techniques

Resolved rate and torque control schemes for large scale space based kinematically redundant manipulators

Resolved rate control of kinematically redundant ground based manipulators is a challenging problem. The structural, actuator, and control loop frequency characteristics of industrial grade robots generally allow operation with resolved rate control; a rate command is achievable with good accuracy. However, space based manipulators are different, typically have less structural stiffness, more motor and joint friction, and lower control loop cycle frequencies. These undesirable characteristics present a considerable Point of Resolution (POR) control problem for space based, kinematically redundant manipulators for the following reason: a kinematically redundant manipulator requires an arbitrary constraint to solve for the joint rate commands. A space manipulator will not respond to joint rate commands because of these characteristics. A space based manipulator simulation, including free end rigid body dynamics, motor dynamics, motor striction/friction, gearbox backlash, joint striction/friction, and Space Station Remote Manipulator System type configuration parameters, is used to evaluate the performance of a documented resolved rate control law. Alternate schemes which include torque control are also evaluated

An optimal resolved rate law for kinematically redundant manipulators

The resolved rate law for a manipulator provides the instantaneous joint rates required to satisfy a given instantaneous hand motion. When the joint space has more degrees of freedom than the task space, the manipulator is kinematically redundant and the kinematic rate equations are underdetermined. These equations can be locally optimized, but the resulting pseudo-inverse solution has been found to cause large joint rates in some cases. A weighting matrix in the locally optimized (pseudo-inverse) solution is dynamically adjusted to control the joint motion as desired. Joint reach limit avoidance is demonstrated in a kinematically redundant planar arm model. The treatment is applicable to redundant manipulators with any number of revolute joints and to non-planar manipulators

An optimal resolved rate law for kindematically redundant manipulators

The resolved rate law for a manipulator provides the instantaneous joint rates required to satisfy a given instantaneous hand motion. When the joint space has more degrees of freedom than the task space, the manipulator is kinematically redundant and the kinematic rate equations are underdetermined. These equations can be locally optimized, but the resulting pseudo-inverse solution was found to cause large joint rates in some case. A weighting matrix in the locally optimized (pseudo-inverse) solution is dynamically adjusted to control the joint motion as desired. Joint reach limit avoidance is demonstrated in a kinematically redundant planar arm model. The treatment is applicable to redundant manipulators with any number of revolute joints and to nonplanar manipulators

A global approach for using kinematic redundancy to minimize base reactions of manipulators

An important consideration in the use of manipulators in microgravity environments is the minimization of the base reactions, i.e. the magnitude of the force and the moment exerted by the manipulator on its base as it performs its tasks. One approach which was proposed and implemented is to use the redundant degree of freedom in a kinematically redundant manipulator to plan manipulator trajectories to minimize base reactions. A global approach was developed for minimizing the magnitude of the base reactions for kinematically redundant manipulators which integrates the Partitioned Jacobian method of redundancy resolution, a 4-3-4 joint-trajectory representation and the minimization of a cost function which is the time-integral of the magnitude of the base reactions. The global approach was also compared with a local approach developed earlier for the case of point-to-point motion of a three degree-of-freedom planar manipulator with one redundant degree-of-freedom. The results show that the global approach is more effective in reducing and smoothing the base force while the local approach is superior in reducing the base moment

Reflexive obstacle avoidance for kinematically-redundant manipulators

Dexterous telerobots incorporating 17 or more degrees of freedom operating under coordinated, sensor-driven computer control will play important roles in future space operations. They will also be used on Earth in assignments like fire fighting, construction and battlefield support. A real time, reflexive obstacle avoidance system, seen as a functional requirement for such massively redundant manipulators, was developed using arm-mounted proximity sensors to control manipulator pose. The project involved a review and analysis of alternative proximity sensor technologies for space applications, the development of a general-purpose algorithm for synthesizing sensor inputs, and the implementation of a prototypical system for demonstration and testing. A 7 degree of freedom Robotics Research K-2107HR manipulator was outfitted with ultrasonic proximity sensors as a testbed, and Robotics Research's standard redundant motion control algorithm was modified such that an object detected by sensor arrays located at the elbow effectively applies a force to the manipulator elbow, normal to the axis. The arm is repelled by objects detected by the sensors, causing the robot to steer around objects in the workspace automatically while continuing to move its tool along the commanded path without interruption. The mathematical approach formulated for synthesizing sensor inputs can be employed for redundant robots of any kinematic configuration

Method and apparatus for configuration control of redundant robots

A method and apparatus to control a robot or manipulator configuration over the entire motion based on augmentation of the manipulator forward kinematics is disclosed. A set of kinematic functions is defined in Cartesian or joint space to reflect the desirable configuration that will be achieved in addition to the specified end-effector motion. The user-defined kinematic functions and the end-effector Cartesian coordinates are combined to form a set of task-related configuration variables as generalized coordinates for the manipulator. A task-based adaptive scheme is then utilized to directly control the configuration variables so as to achieve tracking of some desired reference trajectories throughout the robot motion. This accomplishes the basic task of desired end-effector motion, while utilizing the redundancy to achieve any additional task through the desired time variation of the kinematic functions. The present invention can also be used for optimization of any kinematic objective function, or for satisfaction of a set of kinematic inequality constraints, as in an obstacle avoidance problem. In contrast to pseudoinverse-based methods, the configuration control scheme ensures cyclic motion of the manipulator, which is an essential requirement for repetitive operations. The control law is simple and computationally very fast, and does not require either the complex manipulator dynamic model or the complicated inverse kinematic transformation. The configuration control scheme can alternatively be implemented in joint space

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

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

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

redundant manipulator