Local and trajectory-based indexes for task-related energetic performance optimization of robotic manipulators

In this paper a task-dependent energy analysis of robotic manipulators is presented. The proposed approach includes a novel performance index, which relates the energetic consumption of a robotic manipulator to its inertia ellipsoid. To validate the method, the dynamic and electro-mechanic models of a 3-DOF SCARA robot are implemented and the influence of the location of a predefined point-to-point task (such as a pick-and-place operation) within the robot workspace is considered. The task-dependent analysis provides energy consumption maps that are compared with the prediction of the theoretical formulation based on the proposed Trajectory Energy Index (TEI), which can be used to optimally locate the task to obtain minimal energy consumption without having to compute it through extensive dynamic simulations. Results show the effectiveness of the method and the good agreement between the TEI and the effective energy consumption within the whole workspace of the robot for several trajectories.

Pre-Impact Configuration Designing of a Robot Manipulator for Impact Minimization

This paper studies the collision problem of a robot manipulator and presents a method to minimize the impact force by pre-impact configuration designing. First, a general dynamic model of a robot manipulator capturing a target is established by spatial operator algebra (SOA) and a simple analytical formula of the impact force is obtained. Compared with former models proposed in literatures, this model has simpler form, wider range of applications, O(n) computation complexity, and the system Jacobian matrix can be provided as a production of the configuration matrix and the joint matrix. Second, this work utilizes the impulse ellipsoid to analyze the influence of the pre-impact configuration and the impact direction on the impact force. To illustrate the inertia message of each body in the joint space, a new concept of inertia quasi-ellipsoid (IQE) is introduced. We find that the impulse ellipsoid is constituted of the inertia ellipsoids of the robot manipulator and the target, while each inertia ellipsoid is composed of a series of inertia quasi-ellipsoids. When all inertia quasi-ellipsoids exhibit maximum (minimum) coupling, the impulse ellipsoid should be the flattest (roundest). Finally, this paper provides the analytical expression of the impulse ellipsoid, and the eigenvalues and eigenvectors are used as measurements to illustrate the size and direction of the impulse ellipsoid. With this measurement, the desired pre-impact configuration and the impact direction with minimum impact force can be easily solved. The validity and efficiency of this method are verified by a PUMA robot and a spatial robot.

Optimization design for a jumping leg robot based on generalized inertia ellipsoid

SUMMARYThe isotropy of the generalized inertia ellipsoid is an evaluation index that can measure dynamic performance of a robot. This has significance in motion planning and design of a jumping robot. The generalized inertia of a jumping robot is analyzed. The generalized inertia tensor and the generalized inertia ellipsoid (GIE) are derived from the kinetic energy of the robot mechanism. From the viewpoint of geometrical shape change of the GIE, nonlinear characteristics of a jumping robot are analyzed. With the goal of minimizing nonlinear effects during its movement, the mechanism parameters of a jumping robot are optimized by adopting isotropy of the generalized inertia ellipsoid as its objective function. Example results demonstrate the efficiency and validity of the proposed optimization method.

Dynamic Performance and Modular Design of Redundant Macro-/Minimanipulators

This paper presents methodologies for the analysis and design of redundant manipulators, especially macro-/ministructures, for improved dynamic performance. Herein, the dynamic performance of a redundant manipulator is characterized by the end-effector inertial and acceleration properties. The belted inertia ellipsoid is used to characterize inertial properties, and the recently developed dynamic capability equations are used to analyze acceleration capability. The approach followed here is to design the ministructure to achieve the task performance and then to design the macrostructure to support and complement the ministructure, referred to here as modular design. The methodology is illustrated in the design of a six-degree-of-freedom planar manipulator.

A Geometrical Representation of Manipulator Dynamics and Its Application to Arm Design

A new approach to the geometrical representation of manipulator dynamics is presented. The inertia ellipsoid, which is used to represent dynamic characteristics of a single rigid body, is extended to a general ellipsoid for a series of rigid bodies in order to represent the manipulator dynamics. The geometrical configuration of the generalized inertia ellipsoid (GIE) represents the characteristics of the manipulator as a whole. One can understand the complicated inertial effect and nonlinearity of multi-degree-of-freedom motion by simply investigating the GIE configuration. In the latter half of the paper, this method is applied to aid the design of a mechanical arm, in which dimensions of an arm structure and its mass distribution are optimized through the evaluation and graphical representation of the arm dynamics.