This paper presents a methodology for treating energy consistency when considering multiple simultaneous impacts and contacts with friction in the simulation of systems of multiple interconnected bodies. Hard impact and contact is considered where deformation of the impacting surfaces is negligible. The proposed approach uses a discrete algebraic model of impact in conjunction with moment and tangential co-efficients of restitution (CORs) to develop a general impact law for determining post-impact velocities. This process depends on impulse-momentum theory, complementarity conditions, a principle of maximum dissipation, and the determination of contact forces. The proposed methodology also uses an energy-modifying COR to directly control the system's energy. The approach is illustrated on a bicycle-like structure.

This paper presents a method for determining impact forces associated with an abrupt velocity change when a free-flying body comes into contact with another body. Hard impact is considered where deformation of the impacting surfaces is negligible. The proposed approach uses a discrete algebraic model of impact in conjunction with moment and tangential coefficients of restitution (CORs) to develop a general impact law for determining post-impact velocities. This process depends on impulse-momentum theory, complementarity conditions, a principle of maximum dissipation, and the determination of impact and contact forces as well as post-impact accelerations. The proposed methodology also uses an energy-modifying COR to directly control the system's energy profile over time. The approach is illustrated on a planar bicycle-like structure.

The workspace of a robotic system is characterized to determine the actuator inputs required to achieve a desired level of dynamic performance over a chosen percentage of configurations. The dynamic capability equations (DCE) allow designers to predict the dynamic performance of a robotic system for a particular configuration and reference point on the end-effector (i.e.,point design). Here the DCE are used in conjunction with a reliability-based design optimization (RBDO) strategy in order to obtain designs that can meet dynamic performance requirements. The method is illustrated on a robot design problem.

An energetic approach for analysis of the impact problem in three dimensional multi-legged robot locomotion is hereby presented. The goal is to combine rigid and deformable body approaches which come together naturally in a work-energy framework. The proposed hybrid approach can predict both rebound and non-rebound for an energetic coefficient of restitution greater than zero. Zero tangential velocity in the impacting end effectors can be also predicted, a condition known as sticking. The paper presents a method for determining whether the level of compliance in the system at a given configuration is adequate to insure a no-slip, no-rebound impact

In this investigation a robotic system's dynamic performance is optimized for high reliability under uncertainty. The dynamic capability equations (DCE) allow designers to predict the dynamic performance of a robotic system for a particular configuration and reference point on the end-effector (i.e.,point design). Here the DCE are used in conjunction with a reliability-based design optimization (RBDO) strategy in order to obtain designs with robust dynamic performance with respect to the end-effector reference point. In this work a unilevel performance measure approach (PMA) is used to perform RBDO. This is important for the reliable design of robotic systems in which a solution to the DCE is required for each constraint call. The method is illustrated on a robot design problem

An energetic approach to the impact problem in planar legged robot locomotion is hereby presented. The goal is to find the configurations that yield zero tangential velocity at the impacting leg, a condition known as sticking, and restitute the least energy back into the system. With this analysis, the ground contact friction and the inertial properties of the system, including those of the servo motors, play a determinant role in the impact analysis. This approach yields an energetic criterion for the analysis of the transition from impact to contact constraint conditions. This paper presents a simple, robust method that uses the system generalized coordinates and velocities, the Jacobian, the mass matrix, the coulomb friction law, and the energetic coefficient of restitution to determine whether or not the current configuration is advantageous for maintaining contact, and thereby controllability, in the presence of impulsive forces.

This article presents a method for describing the dynamic performance of a multi-legged locomotion robot. It involves examining how well the legged system uses ground contact to produce acceleration of its body; these abilities are referred to as its force and acceleration capabilities. These capabilities are bounded by actuator torque limits and the no-slip condition. The resulting analysis describes the maximum translational and rotational accelerations of the main-body that are guaranteed to be achievable in every direction without causing slipping at the contact points or saturating an actuator. The method is illustrated using a hexapod as an example.

This article illustrates the use of dynamic performance analysis in the design of legged robots, specifically hexapods. This is accomplished by comparing the dynamic performance of a cable-driven hexapod to that of a more conventional design in which the actuators are mounted at the joints. By integrating the actuators into the torso and through the use of cable transmission, the mass and inertias of the legs are reduced in order to attain the high accelerations and backdrivability. The dynamic performance described herein is bounded by the actuator torque limits and the no-slip condition at the ground contact points. The result is a description of how well each hexapod can accelerate its torso without causing slippage at the ground contact points. Although somewhat mixed, the results show some advantage to the use of a cable-driven transmission.

This paper presents a novel gait generation technique for legged robotic systems which utilizes the dynamic capability equations. The method consists of calculating the acceleration capability early in the simulation to determine a specific configuration which easily allows a gait to be generated. This position is calculated to most effectively arrest any body center-of-mass momentum upon impact and allows the system to continue travelling in the desired direction without suffering detrimental effects from the impulse forces normally encountered when walking.

Dynamic capability equations (DCE) provide a new description of robot acceleration and force capabilities. These refer to a manipulator's ability to accelerate its end-effector and to apply forces to the environment at the end-effector. The key features in the development of these equations are that they combine the analysis of end-effector accelerations, velocities, and forces, while addressing the difference in units between translational and rotational quantities. The equations describe the magnitudes of translational and rotational acceleration and force guaranteed to be achievable in every direction, from a particular configuration, given the limitations on the manipulator's motor torques. They also describe the effect of velocities on these capabilities contributed by the Coriolis and centrifugal forces, as well as the reduction of actuator torque capacity due to motor speed. This article focuses on nonredundant manipulators with as many actuators as degrees of freedom.

This work addresses the navigability of a six-legged robot which is accomplished through the development of a simple discretized error correction method used in the closed-loop controller. The control is based on a kinematic model of the hexapod which is used to correct the heading and drift errors from the desired motion. Experimental validation of the controller’s performance is also presented.

This paper presents a method for characterizing the performance limitations imposed by the yielding of the cables in a planar robotic mechanism with a cable-driven transmission. The method involves developing a model for the cable tensions based on a rigid-body model of the system, where the tensions are considered as reaction forces. The kinematic coupling between links in the mechanism due to the cable-drives is also studied. The model allows for analysis of the tensions in a manner similar to that of a recently developed characterization called the Dynamic Capability Hypersurface. In effect the limitations on dynamic performance caused by cable yielding are added to the limitations caused by the bounds on actuator torque capacity, in order to give a more comprehensive description of the capabilities of the cable-driven system. A two degree-of-freedom mechanism is analyzed in order to illustrate the methodology.

Kinematically redundant manipulators have been proven to offer certain advantages over more heavily constrained systems. One such advantage is the extra degrees-of-freedom can be used for other tasks such as maintaining a posture which affords higher acceleration capability in the direction of the desired motion. However certain issues arise when considering the control of these mechanisms due to the lack of invertability of the rectangular Jacobian matrix. Here this issue is addressed by augmenting the rectangular Jacobian with a characterization of the null space motions. This approach allows for a gradient-based control scheme, based upon the dynamic capability equations, to increase or maintain the local performance capability of a manipulator as it performs some task. Simulation results of the application of this control scheme to a six degree-of-freedom (DOF) planar manipulator are given to illustrate the control's advantages on a highly redundant system.

This paper presents an analysis of the dynamic performance of a non-redundant robotic manipulator while in contact with a fixed environment, i.e., a rigid wall. This work extends an earlier performance characterization, the dynamic capability hypersurface, which described a manipulator's ability to accelerate and apply forces at the end-effector, given the limitations on the manipulator's motor torques. The proposed extension includes an analysis of end-effector motion constraints and friction forces and moments associated with environmental contact. This analysis is applied to a PUMA 560 manipulator.

This article presents a performance measure, the actuation efficiency, which describes the imbalance between the end-effector accelerations achievable in different directions of non-redundant robotic manipulators. A key feature of the proposed measure is that in its development the unitary differences between linear and angular accelerations are treated in a physically meaningful manner. The measure also indicates oversized actuators, since this contributes to the imbalance in achievable accelerations. The development of this measure is based on the formulation of the Dynamic Capability Hypersurface. The shape of this hypersurface is a weak indicator of the level of imbalance in achievable end-effector accelerations.

This article presents two methods for selecting actuators based on the dynamic loading criteria, which yield a manipulator with a desired level of dynamic performance. Here, dynamic performance is measured in terms of a robot's acceleration and force capabilities, which describe its ability to accelerate the end-effector and to apply forces to the environment, given the limitations on its actuator torques. The dynamic capability equations are used to model the relationship between actuator torque capacities and the acceleration and force capabilities, because they treat linear and angular quantities in a consistent and physically meaningful way. This article discusses actuator selection for a single configuration, as well as for multiple configurations.

Presents a performance measure, the actuation efficiency, which describes isotropy in acceleration capability for non-redundant manipulators. It measures the imbalance between the end-effector accelerations achievable in different directions. Prior to this, no measure of this characteristic was adequate for a six degree-of-freedom manipulator because its end-effector motions are referenced to a mix of linear and angular coordinates. The proposed measure addresses both linear and angular accelerations. It also indicates oversized actuators, since this contributes to the imbalance in achievable accelerations. The development of this measure is based on the formulation of the motion isotropy hypersurface. The shape of this hypersurface is a weak indicator a acceleration isotropy.

The study of acceleration capability is concerned with the responsiveness of a manipulator to controller commands. We present a general model for the analysis of end-effector linear and angular accelerations that accounts for the velocity effects. The separate treatment of linear and angular motion directly addresses the inhomogeneities of end-effector motions, avoiding the use of indeterminate scaling factors. The velocity effects considered are the Coriolis and centrifugal forces, as well as the relationships associated with actuator's speed-torque performance curves. This study results in a characterization referred to as the "motion isotropy hypersurface" which describes the relationships between isotropic end-effector linear and angular velocities and accelerations. The utility of this surface and its associated information is demonstrated in a design application involving the PUMA 560 manipulator.

This article investigates the problem of redundant manipulator design for optimal dynamic performance as applied to the design of macro/mini structures. The dynamic performance of a manipulator is characterized by the inertial and acceleration properties of the end-effector. However, for redundant manipulators the characteristics of motions in the end effector null space must also be considered. This article presents a methodology for analyzing the performance requirements for the null space motions. The analysis results in a decomposition of the overall design problem into a set of smaller subproblems. Optimization techniques are then used to determine the design parameters which improve manipulator dynamic performance. The decomposition greatly reduces the search space of the overall optimization. Here this methodology is presented along with the models and measures upon which it is based. The approach is illustrated in. The selection of design parameters for a simple six-degree-of-freedom planar mechanism.

Investigates the problem of manipulator design for increased dynamic performance. Optimization techniques are used to determine the design parameters which improve manipulator performance. The dynamic performance of a manipulator is characterized by the inertial and acceleration properties of the end-effector. Our study of inertial and acceleration properties have provided separate descriptions of the characteristics associated with linear and angular motions. This allows a more physically meaningful interpretation of these properties and provides simple models for their analysis. The article presents these models, discusses the design optimization criteria, and formulates the optimization problem. The approach is illustrated in the selection of design parameters of a parallel mechanism.

The study of the acceleration properties at the end effector is important in the analysis, design, and control of robot manipulators. In previous efforts aimed at addressing this problem, the end-effector acceleration has been treated as a vector combining both the linear and angular accelerations. The methodology presented in this article provides characterizations of these two different types of accelerations and describes the relationship between them. This work is an extension of our previous studies on manipulator inertial and acceleration properties. The treatment relies on the ellipsoid expansion model, a simple geometric approach to efficiently analyze end-effector accelerations. Results of the application of this analysis to the PUMA 560 manipulator are discussed.