You-Liang Gu

Dynamic model for industrial robots based on a compact Lagrangian formulation

A compact Lagrangian formulation has been developed and discussed to deal with the highly coupled non-linear dynamic equations of robotic manipulators. It bridges the dynamic and kinematic problems of robotics closely together by means of Jacobian and subjacobian matrices. Its numeric computational complexity has been reduced to O(n2) time. When n<6, the number of operations required for computing all joint torques is almost close to that of Newton-Euler approach. Due to its significant insight of the robot behavior, it is concluded that the compact Lagrangian formulation offers a convenient approach to building up a feasible real-time adaptive control strategy for computer-based manipulators. Finally, it has been found that all information required for solving the dynamic equation and the adaptive control problems is concentrated in Hessian matrix of the kinetic energy for a given robotic manipulator.

A direct adaptive control scheme for under-actuated dynamic systems

This paper presents a class of under-actuated dynamic systems and the adaptive control methodology. A system is said to be under-actuated if it has at least one passive joint (i.e. not driven by actuators). The under-actuated dynamic systems have found many meaningful applications in either space explorations or advanced manufacturing operations. Due to the passive joints, input channels become deficient, and dynamic characteristics fundamentally differ from a full-actuated system. The dynamic parameter-linearity is destroyed by the under-actuated nature. To overcome the difficulty, an extended dynamic model and a normal-form augmentation approach are proposed. Using the normal-form augmentation approach, the parameter-linearity can be recovered, and a direct adaptive control scheme can be developed to stabilize the system against parameter uncertainty.<<ETX>>

Under-actuated robot systems: dynamic interaction and adaptive control

An under-actuated robot manipulator is a serial mechanism, in which the number of joints is greater than the number of actuators. Making use of the dynamic interaction between the passive joints and actuated joints, the robot can provide desirable motion and forces dynamically. In comparison to a fully actuated robot, the under-actuated system will be more compact in size and lower in weight due to less actuators, and more efficient due to less energy consumption. In this paper, we deal with the following two problems: 1) the dynamic coupling of the system and the control problem of the system by using its dynamic coupling; and 2) when the dynamic parameters are uncertain/unknown in practice, and the kinematics relationship is thus not accurate, the feasible application of adaptive control scheme for this nonlinear system where the linear parameterization does not hold and linear structured adaptive control scheme is not valid, is considered.<<ETX>>

A fuzzy learning algorithm for kinematic control of a robotic system

In this paper, a new control algorithm called fuzzy learning control is proposed as a method of trajectory tracking control for a robotic system. Fuzzy learning control is an extension of differential motion control which utilizes the robotic Jacobian equations. The principles of fuzzy set theory and fuzzy regression analysis are applied to these kinematic equations. This is accomplished by treating the inverse of the Jacobian matrix as a matrix of fuzzy numbers, subsequently transforming the kinematic equations of the manipulator into a linear possibility system with fuzzy coefficients, which is solved for the fuzzy coefficients using fuzzy regression. In this way, the fuzzy Jacobian inverse is found and used to update the desired joint positions on each sampling interval. The algorithm is augmented with a PD type control law to guarantee convergence to the desired trajectory. A simulation study is performed using the 6-joint Stanford Arm. The results show that the fuzzy learning control augmented with a PD control law can converge to the desired trajectory. More significantly, it does so without the need for modeling the robotic kinematics, as would normally be required for differential motion control. Some disadvantage of the fuzzy learning control algorithm and the future work for improvement are also addressed in the paper.<<ETX>>

Modeling and simplification for dynamic systems with testing procedures and metric decomposition

The author discusses a general simplification method for arbitrary dynamic systems which follow the Euler-Lagrange equation. The discussion includes some directions to systems modeling and simplification, system metric testing procedures, metric decomposition approaches, and their geometrical and physical interpretations. Since the study is mathematically based on several concepts from classical differential geometry, such as Riemannian metric space, covariant derivative, differential connection, geodesic equation, the Riemann curvature tensor, and geodesic deviation and stability, a brief overview of these fundamental definitions and properties is given. A metric testing problem and a metric decomposition procedure are considered. The geodesic deviation as well as computer iterations to assess Euclidean metrics for given dynamic systems are outlined. The physical and geometrical interpretation of the metric decomposition is described.<<ETX>>

Imaginary robot: Concept and application to robotic system modeling

A new dynamic model which represents an exact linearization scheme with a simplified nonlinear feedback is presented in this paper. To realize this model for robotic systems, the output function should be chosen so that a special decomposition of the total inertial matrix is satisfied. The concept of an imaginary robot is introduced to achieve the formulation and to solve the realization problem. Two illustrative examples are given in the paper, one for the Stanford arm and the other for a PUMA type of robots.

A fuzzy learning algorithm for redundant manipulators using nonlinear programming

The fuzzy learning algorithm is a control algorithm which has been developed for the kinematic control of redundant robotic manipulators without any modelling of the manipulator itself. It is based on conventional kinematic control methods for manipulators combined with the techniques of fuzzy regression and fuzzy inferencing to learn the appropriate kinematic models based on actual trajectory data. In this paper, we modify the fuzzy regression formulation itself, which is a linear programming problem, to learn a fuzzy generalized inverse of the manipulator Jacobian, which is normally a non-unique matrix. However, we impose additional constraints in the fuzzy regression formulation, and modify the cost function to maximize the effect of the additional constraints, such that the matrix that is learned is one which optimizes the subtask as well as executing the main task of trajectory tracking. The modification of the cost function results in the fuzzy regression formulation being transformed into a nonlinear programming problem.<<ETX>>

Control by exact linearization with a simplified nonlinear feedback for robotic systems

A control strategy by exact linearization with simplified nonlinear feedback for robotic systems is proposed. Through the Hamiltonian canonical transformation, it is possible to find an equivalent but linearized robotic system as well as a compact relation between the original and transformed input control functions. The realization of the proposed control scheme requires the construction of an imaginary robot to accomplish a decomposition for the inertial matrix of robot. An overall control system block diagram based on the Hamiltonian canonical transformation and the design method of the controller are also presented.

Redundant robot control utilizing an imaginary robot model

The concept and theory of an imaginary robot model with applications to the design of redundant robot control systems are presented. This model offers quite an effective way for simplifying nonlinear feedback while preserving the already linearized system equation. A redundant robot main-frame having three revolute joints plus a prismatic joint is used to illustrate the design procedure based on the imaginary robot model. A double-PD control law and a learning control law are explored and discussed.<<ETX>>

Computation methods in design of robotic orientation control

The design of robotic orientation control is relatively difficult due to its representation problem. A number of conventional orientation representation methods are reviewed. A detailed analysis, formulations, design procedures and computation methods in robotic orientation control, particularly for a class of trajectory-tracking control problems, are developed. A computer simulation study of orientation control for a robotic wrist system is discussed.<<ETX>>