Robot dynamics: A recursive algorithm for efficient calculation of Christoffel symbols

Christoffel symbols of the first kind are very important in robot dynamics. They are used for tuning various proposed robot controllers, for determining the bounds on Coriolis/Centrifugal matrix, for mathematical formulation of optimal trajectory calculation, among others. In the literature of robot dynamics, Christoffel symbols of the first kind are calculated from Lagrangian dynamics using an off-line generated symbolic formula. In this study we present a novel and efficient recursive, non-symbolic, method where Christoffel symbols of the first kind are calculated on-the-fly based on the inertial parameters of robot’s links and their transformation matrices. The proposed method was analyzed in terms of execution time, computational complexity and numerical error. Results show that the proposed algorithm compares favorably with existing methods

A Modified DLS Scheme With Controlled Cyclic Solution for Inverse Kinematics in Redundant Robots

Redundancy in robotic manipulators has many advantages. It is successfully used to achieve better dexterity, and to avoid obstacles, singularities, or the kinematic limitations. However, redundancy makes the inverse kinematics (IK) problem harder to solve. The damped least squares (DLS) is a powerful method for calculating the IK of redundant robots, but it suffers from noncyclicity issue, where a closed curve motion in the Cartesian space of the end-effector (EEF) does not map into a closed curve in the joint space. This results in nonrepetitive motion in the joint space, even though the EEF motion is repetitive. In this article, we present a solution for the noncyclicity problem in the DLS method. The proposed scheme was successfully tested both in simulation (9 DoF robot) and on a real robotic manipulator (7 DoF robot)

Innovation of a Humanoid Robotic Wrist

Microbial Biotechnolog

Design, Simulation and Testing of a Controller And Software Framework for Automated Construction by a Robotic Manipulator

abstract: The construction industry is very mundane and tiring for workers without the assistance of machines. This challenge has changed the trend of construction industry tremendously by motivating the development of robots that can replace human workers. This thesis presents a computed torque controller that is designed to produce movements by a small-scale, 5 degree-of-freedom (DOF) robotic arm that are useful for construction operations, specifically bricklaying. A software framework for the robotic arm with motion and path planning features and different control capabilities has also been developed using the Robot Operating System (ROS). First, a literature review of bricklaying construction activity and existing robots’ performance is discussed. After describing an overview of the required robot structure, a mathematical model is presented for the 5-DOF robotic arm. A model-based computed torque controller is designed for the nonlinear dynamic robotic arm, taking into consideration the dynamic and kinematic properties of the arm. For sustainable growth of this technology so that it is affordable to the masses, it is important that the energy consumption by the robot is optimized. In this thesis, the trajectory of the robotic arm is optimized using sequential quadratic programming. The results of the energy optimization procedure are also analyzed for different possible trajectories. A construction testbed setup is simulated in the ROS platform to validate the designed controllers and optimized robot trajectories on different experimental scenarios. A commercially available 5-DOF robotic arm is modeled in the ROS simulators Gazebo and Rviz. The path and motion planning is performed using the Moveit-ROS interface and also implemented on a physical small-scale robotic arm. A Matlab-ROS framework for execution of different controllers on the physical robot is described. Finally, the results of the controller simulation and experiments are discussed in detail.Dissertation/ThesisMasters Thesis Mechanical Engineering 201

Control system design of spatial disorientation trainer

The spatial disorientation trainer (SDT) is a dynamic flight simulator used to enhance ability of pilots of modern combat aircrafts to deal with dangerous effects of spatial disorientation. This device can be modeled and controlled as 4DoF robot manipulator. In this paper, control system design of SDT based on a dynamic model is presented. Two control strategies are compared: 1) computed torque method with feedforward compensation of nonlinearities and cross-coupling effects in dynamic model; 2) single joint (decentralized) PD position controller. PD controller is designed for the actuator model which includes inertia reflected on rotor shafts (effective inertia). Position feedback design considers structural natural frequencies of the manipulator. Effective inertias of SDT for commanded motions are obtained from robot inverse dynamic model which is developed using recursive Newton-Euler equations. Simulation of position tracking for commanded motion is performed in Matlab Simulink

Decentralized Nonlinear Control of Redundant Upper Limb Exoskeleton with Natural Adaptation Law

The aim of this work is to utilize an adaptive decentralized control method called virtual decomposition control (VDC) to control the orientation and position of the end-effector of a 7 degrees of freedom (DoF) right-hand upper-limb exoskeleton. The prevailing adaptive VDC approach requires tuning of 13n adaptation gains along with 26n upper and lower parameter bounds, where n is the number of rigid bodies. Therefore, utilizing the VDC scheme to control high DoF robots like the 7-DoF upper-limb exoskeleton can be an arduous task. In this paper, a new adaptation function, so-called natural adaptation law (NAL), is employed to eliminate these burdens from VDC, which results in reducing all 13n gains to one and removing dependency on upper and lower bounds. In doing so, VDC-based dynamic equations are restructured, and inertial parameter vectors are made compatible with NAL. Then, the NAL adaptation function is exploited to design a new adaptive VDC scheme. This novel adaptive VDC approach ensures physical consistency conditions for estimated parameters with no need for upper and lower bounds. Finally, the asymptotic stability of the algorithm is proved with the virtual stability concept and the accompanying function. The experimental results are utilized to demonstrate the excellent performance of the proposed new adaptive VDC scheme.Comment: Manuscript is published in 2022 IEEE-RAS 21st International Conference on Humanoid Robots (Humanoids

End-to-End Learning of Hybrid Inverse Dynamics Models for Precise and Compliant Impedance Control

It is well-known that inverse dynamics models can improve tracking performance in robot control. These models need to precisely capture the robot dynamics, which consist of well-understood components, e.g., rigid body dynamics, and effects that remain challenging to capture, e.g., stick-slip friction and mechanical flexibilities. Such effects exhibit hysteresis and partial observability, rendering them, particularly challenging to model. Hence, hybrid models, which combine a physical prior with data-driven approaches are especially well-suited in this setting. We present a novel hybrid model formulation that enables us to identify fully physically consistent inertial parameters of a rigid body dynamics model which is paired with a recurrent neural network architecture, allowing us to capture unmodeled partially observable effects using the network memory. We compare our approach against state-of-the-art inverse dynamics models on a 7 degree of freedom manipulator. Using data sets obtained through an optimal experiment design approach, we study the accuracy of offline torque prediction and generalization capabilities of joint learning methods. In control experiments on the real system, we evaluate the model as a feed-forward term for impedance control and show the feedback gains can be drastically reduced to achieve a given tracking accuracy