DMPs-based skill learning for redundant dual-arm robotic synchronized cooperative manipulation

Dual-arm robot manipulation is applicable to many domains, such as industrial, medical, and home service scenes. Learning from demonstrations is a highly effective paradigm for robotic learning, where a robot learns from human actions directly and can be used autonomously for new tasks, avoiding the complicated analytical calculation for motion programming. However, the learned skills are not easy to generalize to new cases where special constraints such as varying relative distance limitation of robotic end effectors for human-like cooperative manipulations exist. In this paper, we propose a dynamic movement primitives (DMPs) based skills learning framework for redundant dual-arm robots. The method, with a coupling acceleration term to the DMPs function, is inspired by the transient performance control of Barrier Lyapunov Functions. The additional coupling acceleration term is calculated based on the constant joint distance and varying relative distance limitations of end effectors for object-approaching actions. In addition, we integrate the generated actions in joint space and the solution for a redundant dual-arm robot to complete a human-like manipulation. Simulations undertaken in Matlab and Gazebo environments certify the effectiveness of the proposed method.

Extracting Time-Accurate Acceleration Vectors From Nontrivial Accelerometer Arrangements

Sports-related concussions are of significant concern in many impact sports, and their detection relies on accurate measurements of the head kinematics during impact. Among the most prevalent recording technologies are videography, and more recently, the use of single-axis accelerometers mounted in a helmet, such as the HIT system. Successful extraction of the linear and angular impact accelerations depends on an accurate analysis methodology governed by the equations of motion. Current algorithms are able to estimate the magnitude of acceleration and hit location, but make assumptions about the hit orientation and are often limited in the position and/or orientation of the accelerometers. The newly formulated algorithm presented in this manuscript accurately extracts the full linear and rotational acceleration vectors from a broad arrangement of six single-axis accelerometers directly from the governing set of kinematic equations. The new formulation linearizes the nonlinear centripetal acceleration term with a finite-difference approximation and provides a fast and accurate solution for all six components of acceleration over long time periods (>250 ms). The approximation of the nonlinear centripetal acceleration term provides an accurate computation of the rotational velocity as a function of time and allows for reconstruction of a multiple-impact signal. Furthermore, the algorithm determines the impact location and orientation and can distinguish between glancing, high rotational velocity impacts, or direct impacts through the center of mass. Results are shown for ten simulated impact locations on a headform geometry computed with three different accelerometer configurations in varying degrees of signal noise. Since the algorithm does not require simplifications of the actual impacted geometry, the impact vector, or a specific arrangement of accelerometer orientations, it can be easily applied to many impact investigations in which accurate kinematics need to be extracted from single-axis accelerometer data.

ACTION WITH ACCELERATION I: EUCLIDEAN HAMILTONIAN AND PATH INTEGRAL

An action having an acceleration term in addition to the usual velocity term is analyzed. The quantum mechanical system is directly defined for Euclidean time using the path integral. The Euclidean Hamiltonian is shown to yield the acceleration Lagrangian and the path integral with the correct boundary conditions. Due to the acceleration term, the state space depends on both position and velocity — and hence the Euclidean Hamiltonian depends on two degrees of freedom. The Hamiltonian for the acceleration system is non-Hermitian and can be mapped to a Hermitian Hamiltonian using a similarity transformation; the matrix elements of the similarity transformation are explicitly evaluated.

RINDLER TYPE ACCELERATION IN f(R) GRAVITY

By choosing a fluid source in f(R) gravity, defined by f(R) = R-12aξ ln |R|, where a (Rindler acceleration) and ξ are both constants, the field equations correctly yield the Rindler acceleration term in the metric. We identify domains in which the weak energy conditions (WEC) and the strong energy conditions (SEC) are satisfied.

Computation of the Output Torque, Power and Work of the Driving Motor for a Redundant Parallel Manipulator

Inverse dynamic analysis of the 8-PSS redundant parallel manipulator is carried out in the exhaustive decoupled way. The required output of the torque, the power and the work of the driving motor are achieved. The whole actuating torque is divided into four terms which are caused by the acceleration, the velocity, the gravity, and the external force. It is also decoupled into the components contributed by the moving platform, the strut, the slider, the lead screw, the motor rotor-coupler, and the external force. The required powers contributed by the component of torque caused by the acceleration term, the velocity term, the gravity term, the external force term, and the powers contributed by the moving platform, the strut, the slider, the lead screw, and the motor rotor-coupler are computed respectively. For a prescribed trajectory, the required output work generated by the ith driving motor is obtained by the presented numerical integration method. Simulation for the computation of the driving motor’s output torque, power and work is illustrated.

Modelling nonlinear thermoacoustic instability in an electrically heated Rijke tube

An analysis of thermoacoustic instability is performed for a horizontal Rijke tube with an electrical resistance heater as the heat source. The governing equations for this fluid flow become stiff and are difficult to solve by the computational fluid dynamics (CFD) technique, as the Mach number of the steady flow and the thickness of the heat source (compared to the acoustic wavelength) are small. Therefore, an asymptotic analysis is performed in the limit of small Mach number and compact heat source to eliminate the above stiffness problem. The unknown variables are expanded in powers of Mach number. Two systems of governing equations are obtained: one for the acoustic field and the other for the unsteady flow field in the hydrodynamic zone around the heater. In this analysis, the coupling between the acoustic field and the unsteady heat release rate from the heater appears from the asymptotic analysis. Furthermore, a non-trivial additional term, referred to as the global-acceleration term, appears in the momentum equation of the hydrodynamic zone, which has serious consequences for the stability of the system. This term can be interpreted as a pressure gradient applied from the acoustic onto the hydrodynamic zone. The asymptotic stability of the system with the variation of system parameters is presented using the bifurcation diagram. Numerical simulations are performed using the Galerkin technique for the acoustic zone and CFD techniques for the hydrodynamic zone. The results confirm the importance of the global-acceleration term. Bifurcation diagrams obtained from the simulations with and without the above term are different. Acoustic streaming is shown to occur during the limit cycle and its effect on the unsteady heat release rate is discussed.

Computation of the Output Torque, Power and Work of the Driving Motor for a Redundant Parallel Manipulator

Inverse dynamic analysis of the 8-PSS redundant parallel manipulator is carried out in the exhaustive decoupled way. The required output of the torque, the power and the work of the driving motor are achieved. The whole actuating torque is divided into four terms which are caused by the acceleration, the velocity, the gravity, and the external force. It is also decoupled into the components contributed by the moving platform, the strut, the slider, the lead screw, the motor rotor-coupler, and the external force. The required powers contributed by the component of torque caused by the acceleration term, the velocity term, the gravity term, the external force term, and the powers contributed by the moving platform, the strut, the slider, the lead screw, and the motor rotor-coupler are computed respectively. For a prescribed trajectory, the required output work generated by the ith driving motor is obtained by the presented numerical integration method. Simulation for the computation of the driving motor’s output torque, power and work is illustrated.