Approximate Optimal Trajectories for Flexible-Link Manipulator Slewing Using Recursive Quadratic Programming

This article presents a method for computation of a unified inverse dynamics and hydrodynamics of a serial link manipulator, completely submerged in water using Lagrangian formulation. The derivation is based on recurrence relation for the velocities, accelerations and generalized forces including hydrodynamic forces. In dealing with the fluid dynamic effects of both uniform and accelerated motion of a body submerged in water, this paper makes use of empirical formulations/relations available in standard literature. As an exemplar implementation, the recursive formulation for a two-link planar underwater manipulator, moving in a vertical plane against gravity, is presented using the proposed algorithm to obtain the motion equations. A free-fall experiment of the chosen two-link manipulator is carried out in simulation through solving the equations of motion numerically with initial conditions set at rest. The two-link manipulator is physically built with straight cylindrical links and free joints (on antifriction bearings). The free-fall experiment same as the simulation experiment is again carried out physically, keeping the whole assembly completely submerged underwater in a glass tank. The time-varying evolution of manipulator configurations is recorded using high-speed motion capture and then analyzed to obtain time evolution of manipulator configurations and kinematic states. The paper concludes by stating the effectiveness of the proposed recursive procedure for inverse dynamics formulation through comparative study of the simulation and experimental results.KeywordsUnderwater manipulatorAdded inertiaHydrodynamic dragBuoyancyInverse dynamics

Robo-analyzer (RA) is open-source software that uses a 3D representation of a robot manipulator to carry out various analytical studies. It was created primarily to assist instructors and students in getting started with robotics teaching and learning utilizing framework-based skeleton models or computer aided design (CAD) software designs of serial robots i.e., articulated robot. The RA software is used in this work to simulate and examine a two-degree of freedom (DOF) robot with two link and two revolute joints respectively. The joint length is kept constant at 0.2m, and the joint velocity is varied from 0 to 180 degrees per second. The two-link manipulator is permitted to carry out forward kinematics after generating and establishing the input parameters for the simulation of the 2DOF model, which results in simulating the joint acceleration values, and that is the primary prerequisite for the machine learning (ML) process. The model tends to deduce the relationship between the input and output parameters in this study, which further aids in the deduction of a linear relationship between the two parameters, especially input and output parameter i.e., link length coordinates, joint velocity, and joint acceleration. The experimentation was then carried out on the basis of RA data to apply linear regression machine learning technique (LRMLT), which will assist in the prediction of an output, namely joint acceleration. The model tends to pave way for future research which can be carried out for joint vibration which is solely based on the basis of the acceleration present at joint.

The passive dynamic control (PDC) is a mechanical system control method which places the most importance on safety. It positively uses brakes having variable characteristics. In this paper, the PDC is applied to an antagonistic two-link pneumatic artificial muscle manipulator set on a vertical plane. Since the original PDC has limitations of capacity, the authors propose an improved PDC which introduces the PID control into the basic PDC, and verify the effectiveness of the improved PDC through positioning control experiments.

Ultra-deep azimuthal resistivity (UDAR) tools are frequently deployed to map resistivity boundaries in 3D around the wellbore. The high depth of investigation allows mapping of resistivity bodies over 100ft away. However, in thinner reservoirs, deep azimuthal resistivity (DAR) tools are deployed. To date these only depict a vertical inversion plane to approximately 30ft, ignoring lateral variability. This paper presents high resolution 3D inversion of DAR data to increase reservoir understanding. Deep azimuthal Resistivity tools measure the full electromagnetic (EM) field surrounding the wellbore as they rotate. The single collar transmitter to receiver spacing is smaller than multi collar UDAR tools and the transmission frequencies are higher, resulting in a decreased depth of investigation but increased resolution. Resistivity boundary mapping in the vertical plane allows these tools to display the subsurface geology and optimise well placement, but this ignores the lateral component of the EM field. A full 3D inversion of this data bridges this gap, providing deeper reservoir understanding while having increased resolution when compared to UDAR 3D inversions. A standard one-dimensional EM inversion of the target well showed a sand channel sequence with a complex morphology with 5 to 15ft thick sand units. Detailed investigation of the azimuthal resistivity and density images show that when considering geology to the sides of the reservoir there is lateral heterogeneity as well as the variability in boundary positions displayed along the well path, but it is unclear exactly what this heterogeneity is representing. 3D EM inversion clearly shows this lateral heterogeneity to be a series of oblique delineations resulting in thinning of the reservoir. Inversion quality control is critical to validate this new technology. Independent verification of the defined structures with density image log dip picks and qualitative assessment of the azimuthal resistivity images provides additional support for the results to backup statistical assessment of misfit in the inversion. Formation and fluid boundaries can show variability in 3D driven by the depositional environment and post deposition deformation. 3D inversion of EM data for UDAR and now deep azimuthal resistivity tools allows assessment of this variability away from the wellbore, improving well optimization and geological models of the reservoir.

Minimum-Time Trajectory for Multiple Manipulators Handling a Common Object

An exact dynamic model of a constrained two-link manipulator with a flexible forearm moving in a horizontal plane is derived using Hamilton's principle. A new variable is introduced before the procedure of modal expansion in order to convert the non-homogeneous boundary condition into a homogeneous one in the model formulation. The static tip deflection of the flexible link is allowed in order to maintain the contact force between the end-effector and the constrained surface and this tip deflection is considered in both the inverse kinematics and the order reduction procedures. The state vector of the reduced model for controller design consists of joint angle of the rigid link, its derivative and integral, the first deflection mode and its derivative, and the integral of contact force. A multivariable controller is proposed for a simultaneous control of end point position and contact force of the manipulator. The controller consists of a feedforward term which contributes the torque for the expected joint angles and the contact force, and a feedback term with the time varying optimal gains obtained from the matrix Riccati equation. Computer simulation results show that this proposed controller is capable of performing the straight line tracking task satisfactorily under three different conditions.

This paper presents a systematic approach for computing local solutions to motion planning problems in nonconvex environments using numerical optimal control techniques. It extends the range of use of state-of-the-art numerical optimal control tools to problem classes where these tools have previously not been applicable. Today these problems are typically solved using motion planners based on randomized or graph search. The general principle is to define a homotopy that transforms, or preferably relaxes, the original problem to an easily solved problem. In this work, it is shown that by combining a Sequential Quadratic Programming (SQP) method with a homotopy approach that gradually transforms the problem from a relaxed one to the original one, practically relevant locally optimal solutions to the motion planning problem can be computed. The approach is demonstrated in motion planning problems in challenging 2D and 3D environments, where the presented method significantly outperforms both a state-of-the-art numerical optimal control method and a state-of-the-art open-source optimizing sampling-based planner commonly used as benchmark.

Dynamics analysis and time-optimal motion planning for unmanned quadrotor transportation systems

In this study, the impact of misalignments on root stresses of hypoid gear sets is investigated experimentally and theoretically. An experimental set-up designed to allow operation of a hypoid gear pair under loaded quasi-static conditions with various types of tightly controlled misalignments is introduced. These misalignments include the position errors (V and H) of the pinion along the vertical and horizontal directions, the position error (G) of the gear along its axis, and the angle error (γ) between the two gear axes. For example, face-hobbed hypoid gear pair from an automotive axle application is instrumented via a set of strain gauges positioned at the roots along the faces of multiple teeth to measure root strains within a range of input torque. These root strain measurements at different V, H, G, and γ values are presented. A computational model is also proposed to predict the root stresses of face-milled and face-hobbed hypoid gear pairs under various loading and misalignment conditions. The model employs an automated finite elements mesh generator based on a predefined template for a general and computationally efficient treatment of the problem. Model predictions are compared to measurements at the end to assess the accuracy of the model and describe the measured sensitivities.

We present an efficient structure for the computation of robot dynamics in real time. The fundamental characteristic of this structure is the division of the computation into a high-priority synchronous task and low-priority background tasks, possibly sharing the resources of a conventional computing unit based on commercial microprocessors. The background tasks compute the inertial and gravitational coefficients as well as the forces due to the velocities of the joints. In each control sample pe riod, the high-priority synchronous task computes the product of the inertial coefficients by the accelerations of the joints and performs the summation of the torques due to the velocities and gravitational forces. Kircanski et al. (1986) have shown that the bandwidth of the variation of joint angles and of their velocities is an order of magnitude less than the variation of the joint accelerations. This result agrees with the experiments that we have carried out using a PUMA 260 robot. Two main strategies contribute to reduce the computational burden associated with the evaluation of the dynamic equa tions. The first involves the use of efficient algorithms for the evaluation of the equations. The second is aimed at reducing the number of dynamic parameters by identifying beforehand the linear dependencies among these parameters, as well as carrying out a significance analysis of the parameters' contri bution to the final joint torques. We selected an iterative procedure for the computation of the inertial and gravitational coefficients (Featherstone 1984; Renaud 1985; Izaguirre and Paul 1986), and a recursive iter ation for the computation of the velocity torques (Khalil et al. 1986). In our experiments with a PUMA 260, we obtained a set of 52 linearly independent parameters from an initial set of 78 parameters. Identification of the parameters revealed only 23 parameters to be significant. These reductions permit the calculation of the inertias and gravitational coefficients, for the PUMA 260 without load, with 98 multiplications and 70 additions and calculation of the ve lacity torques with 140 multiplications and 110 additions. In the case of an arbitrary load at the end effector, calculation of the inertias and gravitational coefficients requires 190 multi plications and 150 additions and that of the velocity torques, 200 multiplications and 170 additions. Velocity torques, inertial coefficients, and gravitational coefficients can be computed in the background in 20 ms using an Intel 8087 microprocessor. The synchronous task requires only six multiplications and six additions per joint. The actual code used to evaluate this dynamic model is entirely computer generated from experimental data, requiring no other manual intervention than performing a campaign of measurements.

Disturbance compensation control of a free-flying space robot is considered in this paper. In the method proposed here, disturbances imposed on a nominal dynamic model are estimated and compensated by utilizing a combination of joint torque input and acceleration signals. The dynamics of the equivalent manipulator with a fixed base is treated as the nominal model, noting that the mass of the base satellite is usually much larger than that of the manipulator. The attitude of the base satellite changes because of the reaction force generated by the manipulator. However, the influence of the change is estimated and compensated as a disturbance based on a combination of the joint torque and the acceleration of the end-effector in the operational coordinate frame. Computation of the proposed control method is as simple as the control of a manipulator with a fixed base. The proposed method is robust against unknown disturbances and modeling errors. This method can also be extended to the case of a space robot with multiple manipulators and attitude control of the base satellite. The effectiveness of the method is demonstrated by computer simulations.

Producing a high-performance motorcycle prototype entails extensive engineering in which virtual prototyping plays an important role by reducing the number of physical tests that need to be performed during the design process. High-performance motorcycle maneuvering required in racing competitions is discussed. Various constraints that limit the performance of a motorcycle are focused upon. Motorcycle features - including engine power, tire forces, and wheelie and stoppie maneuvers - are reviewed. An algorithm for finding the minimum-time trajectory for a constrained 1DOF vehicle model is developed. This model is a point-mass vehicle constrained to follow a given path and subject to accelerations representative of more general vehicles. Examination of the idealized situation clarifies the dynamic features needed to find the minimum-time velocity profile. A detailed nonholonomic motorcycle model capturing gross vehicle motion and the associated contact forces is presented. A quasi-steady technique for approximating the velocity constraint and acceleration limits that are in play for the vehicle at each location along the desired path is developed. From the information obtained, an approximately optimal velocity profile is constructed and used to build an approximate motorcycle trajectory

In space application, robot system are subject to unknown or unmodeled dynamics, for example, in the tasks of transporting an unknown payload or catching an unmodeled moving object. We discuss the parameterization problem in dynamic structure and adaptive control of a space robot system with an attitude-controlled base to which the robot is attached. We first derive the system kinematic and dynamic equations based on Lagrangian dynamics and the linear momentum conservation law. Based on the dynamic model developed, we discuss the problem of linear parameterization in term of dynamic parameters, and find that in joint space, the dynamics can be linearized by a set of combined dynamic parameters; however, in inertial space linear parameterization is impossible in general. Then we propose an adaptive control scheme in joint space, and present a simulation study to demonstrate its effectiveness and computational procedure. Because most takes are specified in inertial space instead of joint space, we discuss the issues associated to adaptive control in inertial space and identify two potential problem: unavailability of joint trajectory because the mapping from inertial space trajectory is dynamic-dependent and subject to uncertainty; and nonlinear parameterization in inertial space. We approach the problem by making use of the proposed joint space adaptive controller and updating the joint trajectory by the estimated dynamic parameters and given trajectory in inertial space.

In this paper, a novel methodology for estimating the parameters of robotic manipulator systems is proposed. It can be seen that, for the purpose of parameter estimation, the input torque to each joint motor is designed as a linear combination of sinusoids. After the transient responses of joint angles exponentially converge to zero, the steady states of joint angle outputs can be extracted. Since the steady states of joint angles are the equivalent finite Fourier series, the coefficients of the steady state components of joint angles can be further extracted in a fundamental period. With the amazing finding that the steady states contain all dynamic information of manipulator systems, all unknown parameters of the system model can be accurately estimated with the extracted coefficients in finite frequency bands. The simulation results for a two-link manipulator are carried out to illustrate the effectiveness and robustness against measurement noise of the proposed method.

In the real world, the tracking controllers designed for ideal scenarios will be inaccurate due to presence of noise. This paper deals with trajectory tracking control of a two-link manipulator using three different tracking controllers namely, Proportional Integral Derivative (PID), Adaptive Neuro-Fuzzy Inference System (ANFIS), and Back-stepping controller in a noisy environment. Here, the PID controller is designed using the singular perturbation technique, it helps in dealing with external noise. However, its performance is not good with variable noise. Thus, the ANFIS controller is developed in which the rules are based on data collected from previously designed PID controller. Lastly, the back-stepping controller based on the virtual control signal using Lyapunov for zero error tracking is developed. The three controllers for the manipulator have been tested with the introduction of variable random noise and a fixed noise quantity. Performance analysis of these controllers is based on ISE (Integral Square Error), IAE (Integral Absolute Error), ITSE (Integral Time Squared Error), and ITAE (Integral Time Absolute Error). The simulation results illustrate the accuracy of the ANFIS controller which has better tracking in comparison to the other two control schemes with comparable torque inputs.