Robert A. Freeman

Geometric analysis of antagonistic stiffness in redundantly actuated parallel mechanisms

Parallel closed-chain mechanical architectures allow for redundant actuation in the force domain. Antagonistic actuation, afforded by this input force redundancy, in conjunction with nonlinear linkage geometry creates an effective stiffness directly analogous to that of a wound metal spring. A general stiffness model for such systems is derived and it is shown that the constitutive relationship between actuation effort and active stiffness is the second-order kinematic constraint set relating the actuation sites. The extent of stiffness modulation possible is then evaluated and necessary conditions for full stiffness modulation are obtained. Configuration-dependent, second-order, geometric singularities affecting stiffness generation are illustrated in terms of a three-degree-of-freedom parallel spherical mechanism example and discussed in relation to their more commonly investigated first-order counterparts that affect force and velocity transmission. Finally, a load distribution methodology for simultaneous motion and stiffness generation is introduced, and it is shown that with hyperredundant actuation the internal load state of the mechanism can be controlled independent of its motion and effective stiffness.

Distribution of dynamic loads for multiple cooperating robot manipulators

For the situation of multiple cooperating manipulators handling a single object, a formulation is presented which allows load distribution of the combined system to be made while taking manipulator dynamics into account. First, object dynamics are used to transform the motion task. An integrated procedure for modeling arm dynamics are used to transform the motion task. An integrated procedure for modeling arm dynamics is detailed. Then, a method is introduced which transforms the object load to the joint level. At this level, various methods of load distribution that allow subtask performance are proposed. These methods allow desired object motion while selecting loads desirable to alleviate manipulator dynamic loads.

Internal object loading for multiple cooperating robot manipulators

For an object being rigidly grasped and manipulated by multiple robotic mechanisms, the internal loading characteristics at a common coordinate set within the object are considered. It is demonstrated that representation of internal forces and moments in these common coordinates give insight into force and load distribution schemes developed previously. In particular, it is shown how internal loads may be created in some end-effector force distribution schemes even when no component in the null-space of the grasp matrix is included. It is further shown that a particular pseudoinverse of the grasp matrix, which can be shown to be consistent with the kinematic constraints, may be used to eliminate this situation. The case of a two-arm system is used to illustrate the concepts introduced.<<ETX>>

Open-loop stiffness control of overconstrained mechanisms/robotic linkage systems

A novel approach for the control of task-space stiffness characteristics in systems consisting of a superabundance of kinematically dependent inputs is proposed. When there are more input actuations than operational degrees of freedom, internal preloads can be generated that produce effective restoring forces in the face of displacement or disturbances imposed on the system. Examples of this excessive actuation can be found in certain modes of structurally overconstrained parallel manipulators and in antagonistically structured serial manipulators. The input loads are synthesized offline (prior to operation) and entered as a feedforward component so that the desired effective loads on objects are obtained, and (simultaneously) significant disturbances at the task level can be largely rejected in an open-loop fashion. This reduces the burden and shortcomings of standard feedback schemes. Moreover, a layered feedback scheme is used to compensate for small perturbations and unmodeled dynamics. The open-loop task-based stiffness control scheme as applied to structurally parallel mechanism/robotic linkage systems is investigated. The schemes applicability as a programmable active compliance device is also discussed.<<ETX>>

Dynamic task distribution for multiple cooperating robot manipulators

The issue of distributing the task among the multiple robot arms while considering the manipulator dynamics is considered. The forces and moments required to move an object are distributed in such a way that extra degrees of freedom within the system may be used to satisfy or optimize criteria related to the manipulator dynamics. A method to perform such subtasks is introduced, and examples of possible criteria noted. It is expected that such techniques will produce trajectories which will be more desirable for the individual arms, dynamically, since the dynamics are considered in the task distribution.<<ETX>>

Null space damping method for local joint torque optimization of redundant manipulators

In this article, a null space damping method is proposed that solves the stability problem commonly encountered in existing local joint torque optimization techniques applied to redundant manipulators. The damped joint motion is stable and globally outperforms undamped techniques in the sense of torque minimization capability. In addition, simulation results show that the resulting damped joint motion becomes conservative after an initial transient stage for cyclic end-effector trajectories, while undamped pseudoinverse solutions are reported to never lead to conservative motion. Three undamped and damped joint torque optimization algorithms are considered and discussed with comparison to the previous literature. The effectiveness of the proposed null space damping method is demonstrated by the results of two computer simulations. In addition, the minimization of electrical power consumption is addressed with respect to the results of this article.

Geometric stability in force control

Previous implementations of robot force control seldom produced satisfactory results, and researchers in the past have experienced significant instability problems associated with their force controllers. When a manipulator is constrained to an environment (force-controlled), geometric stability due to the manipulator configuration and the force-controlled direction is shown to be a significant factor in overall system stability. This exploratory study points out a rather intuitive, geometrically based stability and analyzes the phenomenon both analytically and graphically. Sequential joint self-motion algorithms for kinematically redundant manipulators are suggested for reduced transitional impact and greater stability in the ensuing force-controlled operation.<<ETX>>

Geometric characteristics of antagonistic stiffness in redundantly actuated mechanisms

Parallel closed-chain mechanical architectures allow for redundant actuation in the force domain. Antagonistic actuation, afforded by this input force redundancy, in conjunction with nonlinear linkage geometry, creates an effective stiffness directly analogous to that of a wound metal spring. A general stiffness model for such systems is derived, and it is shown that the constitutive relationship between actuation effort and active stiffness is the second-order kinematic constraint(s) relating the actuation sites. The extent of stiffness modulation possible is evaluated and necessary conditions for full stiffness modulation are obtained. Configuration dependent, second-order, geometric singularities affecting stiffness generation are illustrated in terms of a three degree-of-freedom parallel spherical mechanism example, and discussed in relation to their first-order counterparts.<<ETX>>

Joint torque optimization of redundant manipulators via the null space damping method

A null space damping method is proposed which solves the stability problem commonly encountered in existing local joint torque optimization techniques applied to redundant manipulators. The damped joint motion is quite stable and globally outperforms undamped techniques in the sense of torque minimization capability. In addition, simulation results show that the resulting damped joint motion becomes conservative after an initial transient stage for cyclic end-effector trajectories, while undamped pseudo-inverse solutions are reported to never lead to conservative motion. Three undamped and damped joint torque optimization algorithms are considered and discussed with comparison to the previous literature. The effectiveness of the proposed null space damping method is demonstrated by computer simulation.<<ETX>>

The dynamic and stiffness modeling of general robotic manipulator systems with antagonistic actuation

A modeling procedure for a completely general kinematic system and a stiffness formulation technique for antagonistically actuated systems are given, in a format which is directly applicable to the design of high-stiffness robotic manipulator controllers. The formulation is developed in terms of kinematic influence coefficients. This involves some generalization of an existing modeling technique so that hybrid manipulator systems (combinations of parallel and serial manipulator systems) can be systematically treated. Antagonistic stiffness, which is developed extensively, is seen to be very promising for the design and control of future manipulators with high precision requirements under various operational disturbances.<<ETX>>