Decentralized adaptive partitioned approximation control of high degrees-of-freedom robotic manipulators considering three actuator control modes

International audiencePartitioned approximation control is avoided in most decentralized control algorithms; however, it is essential to design a feedforward control term for improving the tracking accuracy of the desired references. In addition, consideration of actuator dynamics is important for a robot with high-velocity movement and highly varying loads. As a result, this work is focused on decentralized adaptive partitioned approximation control for complex robotic systems using the orthogonal basis functions as strong approximators. In essence, the partitioned approximation technique is intrinsically decentralized with some modifications. Three actuator control modes are considered in this study: (i) a torque control mode in which the armature current is well controlled by a current servo amplifier and the motor torque/current constant is known, (ii) a current control mode in which the torque/current constant is unknown, and (iii) a voltage control mode with no current servo control being available. The proposed decentralized control law consists of three terms: the partitioned approximation-based feedforward term that is necessary for precise tracking, the high gain-based feedback term, and the adaptive sliding gain-based term for compensation of modeling error. The passivity property is essential to prove the stability of local stability of the individual subsystem with guaranteed global stability. Two case studies are used to prove the validity of the proposed controller: a two-link manipulator and a six-link biped robot

Adaptive approximation control of biped robots: a low-level tracking control layer

The adaptive approximation control is a powerful tool for controlling robotic systems with unmodeled dynamics. The local (partitioned) approximation-based adaptive control includes representation of the uncertain matrices and vectors in the robot model as finite combinations of basis functions. Update laws for the weighting matrices are obtained by the Lyapunov-like design. However, one of the inherent limitations of this category of approximation is curse dimensionality associated with the approximation of uncertain matrix. There are three possible representations for the approximation of the uncertain matrix: Kronecker product, sparse matrices, and GL operator. Both Kronecker product and sparse matrices can grow exponentially with the dimension of the target matrix, whereas GL operator can grow linearly but without the use of conventional operations of matrices. In light of the above, this report proposes a simple representation for the approximation of the uncertain matrix. The proposed representation is directly linear concerning the dimension of the target matrix using the conventional operations of matrices. Two case studies are simulated which are: two-link manipulator and 6-link biped robots during the complete gait cycles (single support phase SSP and double support phase DSP). Biped robot has different configurations during the walking cycle; it is considered as an open-chain mechanism with a fixed-base stance foot during the SSP and as a closed constrained mechanism during the DSP.The results show that for low dimension robotic manipulators, all representations can be conducted equivalently. There is no large difference in simulation time, whereas for higher degrees of freedom robots the GL operator and the proposed representation are superior in simulation time

Adaptive Approximation Control of Robotic Manipulators: Centralized and Decentralized Control Algorithms

The regressor-based adaptive control is useful for controlling robotic systems with uncertain parameters but with known structure of robot dynamics. Unmodeled dynamics could lead to instability problems unless modification of control law is used. In addition, exact calculation of regressor for robots with more than 6 degrees of freedom is hard to be calculated, and the task could be more complex for robots. Whereas the adaptive approximation control is a powerful tool for controlling robotic systems with unmodeled dynamics. The local (partitioned) approximation-based adaptive control includes representation of the uncertain matrices and vectors in the robot model as finite combinations of basis functions. Update laws for the weighting matrices are obtained by the Lyapunov-like design. Therefore, this work is focused function approximation-based control algorithms considering centralized and decentralized approaches. In this work, the following control algorithms are designed: (1) Adaptive hybrid regressor-approximation control. This work attempts to combine the features of both the regressor and the approximation techniques in adaptive control. The regressor technique is a powerful tool for adaptive control of the known structure of modeling while the approximation is useful for estimation of time-varying uncertainty. Therefore, this work proposes adaptive hybrid regressor and approximation control for robots in both free and constrained spaces. The control law consists of three terms: (i) regressor term for initial estimation of the known structure of the robot dynamics, e.g. inertia matrix, Coriolis and centripetal matrix and gravity vector, and (ii) approximation term for estimation of internal and external disturbances resulted from the inexact calculation of regressor matrix and unknown modeling of friction, etc, and (iii) robust term consists of switching sgn(.) function. The control law is designed based on updating the uncertain parameters and the weighting coefficients corresponding to regressor and approximation respectively with position/force tracking purposes. The proposed controller is stable in the sense of Lyapunov stability.(2) Decentralized adaptive partitioned approximation control. Partitioned approximation control is avoided in most decentralized control algorithms; however, it is essential to design feedforward control with improved tracking accuracy. As a result, this work is focused on decentralized adaptive partitioned approximation control for complex robotic systems using the orthogonal basis functions as strong approximators. In essence, the partitioned approximation technique is intrinsically decentralized with some modifications. The proposed decentralized control law consists of three terms: the partitioned approximation-based feedforward term that is necessary for precise tracking, the high gain-based feedback term, and the adaptive sliding gain-based term for compensation of modeling error. The passivity property is essential to prove the stability of local stability of the individual subsystem with guaranteed global stability.Simulation experiments on 2-link robot and 6-link biped robot are performed to prove the effectiveness of the proposed algorithms

Dynamics of biped robots during a complete gait cycle: Euler-Lagrange vs. Newton-Euler formulations

The aim of this report is to derive the equations of motion for biped robot during different walking phases using two well-known formulations: Euler-Lagrange (E-L) and Newton-Euler (N-E) equations. The modeling problems of biped robots lie in their varying configurations during locomotion. They could be fully actuated during the single support phase (SSP) and overactuated during the double support phase (DSP). Therefore, first, the E-L equations of 6-link biped robot are described in some details for dynamic modeling during different walking phases with concentration on the DSP. Second, the detailed description of modified recursive Newton-Euler (N-E) formulation (which is very useful for modeling complex robotic system) is illustrated with a novel strategy for solution of the over-actuation/discontinuity problem. The derived equations of motion of the target biped for both formulations are suitable for control laws if the analyzer needs to deal with control problems. As expected, the N-E formulation is superior to the E-L concerning dealing with high degrees-of freedom (DOFs) robotic systems (larger than six DOFs)