Local joint control in cooperating manipulator systems - force distribution and global stability

A closed kinematic chain, like an arm that operates a crank, has a constrained movement space. A meaningful movement of the chain's endpoint is only possible along the free movement directions which are given implicitly by the contour of the object that confines the movement of the chain. Many technical solutions for such a movement task, in particular those used in robotics, use central controllers and force-torque sensors in the arm's wrist or a leg's ankle to construct a coordinate system (task frame formalism) at the local point of contact the axes of which coincide with the free and constrained movement directions. Motivated by examples from biology, we introduce a new control system that solves a constrained movement task. The control system is inspired by the control architecture that is found in stick insects like Carausius morosus. It consists of decentral joint controllers that work on elastic joints (compliant manipulator). The decentral controllers are based on local positive velocity feedback (LPVF). It has been shown earlier that LPVF enables contour following of a limb in a compliant motion task without a central controller. In this paper we extend LPVF in such a way that it is even able to follow a contour if a considerable counter force drags the limb away along the contour in a direction opposite to the desired. The controller extension is based on the measurement of the local mechanical power generated in the elastic joint and is called power-controlled relaxation LPVF. The new control approach has the following advantages. First, it still uses local joint controllers without knowledge of the kinematics. Second, it does not need a force or torque measurement at the end of the limb. In this paper we test power-controlled relaxation LPVF on a crank turning task in which a weight has to be winched up by a two-joint compliant manipulator.

Multiple coordinated robot arms are modeled by considering the arms as closed kinematic chains and as a force-constrained mechanical system working on the same object simultaneously. In both formulations, a novel dynamic control method is discussed. It is based on feedback linearization and simultaneous output decoupling technique. By applying a nonlinear feedback and a nonlinear coordinate transformation, the complicated model of the multiple robot arms in either formulation is converted into a linear and output decoupled system. The linear system control theory and optimal control theory are used to design robust controllers in the task space. The first formulation has the advantage of automatically handling the coordination and load distribution among the robot arms. In the second formulation, it was found that by choosing a general output equation it became possible simultaneously to superimpose the position and velocity error feedback with the force-torque error feedback in the task space. >

Robust adaptive control of a class of nonlinear mechanical systems with unbounded and fast-varying uncertainties

Nonlinear Attitude Control for Large and Fast Maneuvers

Recently, R. E. Udwadia (2003) suggested to derive tracking controllers for mechanical systems using a generalization of Gauss' principle of least constraint. This method allows us to reformulate control problems as a special class of optimal control. We take this line of reasoning one step further and demonstrate that well-known and also several novel nonlinear robot control laws can be derived from this generic methodology. We show experimental verifications on a Sarcos Master Arm robot for some of the derived controllers. We believe that the suggested approach offers a promising unification and simplification of nonlinear control law design for robots obeying rigid body dynamics equations, both with or without external constraints, with over-actuation or underactuation, as well as open-chain and closed-chain kinematics.

We have proposed two different digital control methods, where the controlled variables are joint torque and joint angular velocity, of space robot manipulators using the transpose of Generalized Jacobian Matrix. These methods are developed in discrete time domain so that the stability of system can be guaranteed when digital computers are used as controllers. The relation between the two methods, however, is not reported, although the basic concepts of these methods ar similar. This paper presents a novel digital control method, which integrates joint torque control with joint velocity control, of nonredundant space robot manipulators using the transpose of Generalized Jacobian Matrix. The merit of this new control law is to be applicable to both joint's torque controller and joint's velocity controller by only tuning the controller gains. Furthermore, computer simulation of a 6-DOF space robot manipulator is performed. Simulation result demonstrates the effectiveness of the proposed method.

This article addresses the problem regarding power regulation in classical DC-DC second-order converters by means of a nonlinear control technique based on inverse optimal control theory. There are few papers that describe inverse optimal control for DC-DC converters in the literature. Therefore, this study constitutes a contribution to the state of the art on nonlinear control techniques for DC-DC converters. In this vein, the main objective of this research was to implement inverse optimal control theory with integral action to the typical DC-DC conversion topologies for power regulation, regardless of the load variations and the application. The converter topologies analyzed were: (i) Buck; (ii) Boost; (iii) Buck-Boost; and (iv) Non-Inverting Buck-Boost. A dynamical model was proposed as a function of the state variable error, which helped to demonstrate that the inverse optimal control law with proportional-integral action implemented in the different converters ensures stability in each closed-loop operation via Lyapunov’s theorem. Numerical validations were carried out by means of simulations in the PSIM software, comparing the established control law, the passivity-based PI control law, and an open-loop control. As a conclusion, it was possible to determine that the proposed model is easier to implement and has a better dynamical behavior than the PI-PBC, ensuring asymptotic stability from the closed-loop control design.

The structure of the time-optimal control law for multiple robot arms cooperatively moving a common object along a specified path with the control torque constraints is addressed. The overall mechanical system is modeled by considering the arms as closed kinematic chains using the Lagrange formulation. This results in a reduced-order dynamic model of the multi-arm system. By parameterizing the resulting dynamic model along a given path, the original higher order optimal control problem with state constraints (path constraints) is transformed into a problem of a double integrator system with state-dependent control constraints that are determined by a linear programming approach. It is then shown that the number of saturated actuators on any finite time interval along the optimal trajectory is (1+3(D-1)(m-1)), where D=2 in 2-dimensional Cartesian space, D=3 in 3-dimensional space, and m is the number of robot arms in the system. The theoretical result is validated by a numerical example.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In this paper, the construction of CLFs for nonlinear systems and a new inverse optimal control law are presented. The construction of a CLF for an affine nonlinear system is reduced to the construction of a CLF for a simpler system, and a new L g V type control law with respect to a CLF is provided. This control law is a generalization of Sontag’s formula and contains a design parameter. Tuning this parameter gives many suboptimal solutions for the optimization problem. Also, the gain margin and sector margin of the control law are calculated. Examples are provided to illustrate the main theoretical results of the paper.

Nonlinear Inverse and Predictive End Point Trajectory Control of Flexible Macro-Micro Manipulators

This paper deals with the torque control of multi-phase permanent magnet synchronous machines. The dynamic model of these motors is obtained using the Power-Oriented Graphs technique. This graphical modeling technique allows to write the dynamic equations of the system in a very compact form. Starting from the dynamic equations, a torque control law with saturated input voltages is proposed based on a new current vector approach for describing the voltage constraint. Some simulation results validate the proposed control law.

In this paper, a novel methodology is introduced for the inverse optimal control of non-affine, nonlinear and discrete-time systems. Although inverse optimal control of affine systems is studied in detail in technical literature, there is no adequate research about its implementation on non-affine systems. here are two main contributions of this work. Firstly using the input–output data of the system to be controlled its NARMA-L2 model is obtained using a multi-layer feedforward neural network, this step provides a conversion from a non-affine to affine system model. After the affine system model is obtained, the inverse optimal control law is applied. The second contribution of this paper is the computation of the inverse optimal control signal. The selection of the P matrix in the control law is crucial since its value directly affects the control performance. Here a novel method is proposed where an adaptive and optimal P matrix is computed online using a recurrent neural network to minimize a predefined cost function. The performance of the proposed control method is evaluated by simulations performed on benchmark problems. The robustness of the method is also tested by additional simulations where noise and disturbance is imposed on the system. The obtained results justify the applicability of the proposed approach.

In this paper, the authors propose a particle swarm optimization (PSO) for a discrete-time inverse optimal control scheme of a doubly fed induction generator (DFIG). For the inverse optimal scheme, a control Lyapunov function (CLF) is proposed to obtain an inverse optimal control law in order to achieve trajectory tracking. A posteriori, it is established that this control law minimizes a meaningful cost function. The CLFs depend on matrix selection in order to achieve the control objectives; this matrix is determined by two mechanisms: initially, fixed parameters are proposed for this matrix by a trial-and-error method and then by using the PSO algorithm. The inverse optimal control scheme is illustrated via simulations for the DFIG, including the comparison between both mechanisms.

The cable sagging problem of cable-driven parallel robots (CDPRs) is very complicated, because several models for calculating cable sag based on the well-known catenary equation have been studied, but time and computational efficiency are a problem to be solved. There is still no simple mathematical model to calculate cable sag by considering all relevant conditions due to the complexity and nonlinearity of the cable sagging model, which involves many dominant variables and their influence on the position accuracy of CDPRs. In this study, we proposed an ANFIS (adaptive neuro-fuzzy inference system) architecture to estimate cable sag for large-sized CDPRs. The ANFIS model can be used to solve nonlinear functions and detect nonlinear factors online in the control system; this characteristic is consistent with the nonlinear model of cable sag. The trained data for ANFIS models were taken from calculation results by Trust-Region-Dogleg algorithm based on two cable tension calculation algorithms as Dual Simplex Algorithm and Force Distribution in Closed Form. Cable sagging data obtained from ANFIS and Trust-Region-Dogleg algorithm are compared and evaluated by statistical factors of evaluations consisting of root-mean-square error, correlation coefficients, and scatter index. The analytical results show that the ANFIS gave computed results with small errors and can be applied to predict cable sagging for any CDPR configuration, with the advantage of fast calculation time and high precision. The results of these models are also applied on a CDPR that contains two redundant actuators.

Regional source contributions to fine particulate matter of less studied cities in Beijing-Tianjin-Hebei region in 2017