Tetsuji Shimogawa

Improvement of trajectory tracking for industrial robot arms by learning control with B-spline

This paper describes that a learning control algorithm with B-spline is effective to improve the trajectory tracking accuracy of an industrial robot and shows the results of simulation and experiment. The learning control method consists of two processes: Global Learning (GL) and Local Learning (LL). GL estimates the dynamics of a robot control system and obtains a learning gain matrix used in LL. LL decreases the tracking errors by iterative trial movements and acquires satisfactory tracking accuracy. The learning algorithm needs only measuring of position errors from a desired trajectory and does not require any derivatives of them. As the input trajectories after the convergence of learning are expressed by B-spline curves, they are easily memorized as input patterns corresponding to specified works.

Generation and optimality of trajectory described by B-spline

This paper discusses about the generation and optimality of the trajectory described by B-spline. In the trajectory generation values of B-spline control points are optimized by the complex method. The algorithm has following advantages: 1) it only needs computation of a performance index for the optimization but requires no computation of the gradient; 2) it is applicable to the problem of an arbitrary performance index to evaluate trajectories; 3) it can generate trajectories with continuous time derivative curves; and 4) it needs less memory to store the generated trajectories. For checking the optimality of the trajectories, it is applied to four types of trajectory generation: a manipulator trajectory generation, a solution of ordinary differential equation, a minimal time control problem, and a movement curve generation such as a cam curve one.

Control of mechatronic systems by learning actuator reference trajectories described by B-spline curves

Two algorithms are proposed for learning actuator reference trajectories to control mechatronic systems. The first algorithm uses the nominal dynamics and specified trajectories of the controlled systems. The algorithm is applicable to linear control systems. In the second algorithm the learning process does not require knowledge of the dynamics of the controlled system but only uses the performance index to evaluate motion of the system. This algorithm does not require specification of a trajectory. It is effective in the case that the system is nonlinear or difficult to identify. Two algorithms are obtained and applied to two systems: one involving trajectory tracking control for a one-link flexible arm and the other for learning the swing trajectory of an inverted pendulum.

A feedback control gain tuning for mechatronic systems by iterative trials

A feedback gain tuning method is proposed to control mechatronic systems which have the characteristic applicable to iterative trial movements. The tuning algorithm is composed of an optimization procedure based on the complex method and has the following features: (1) it does not require any dynamic model of controlled systems; (2) it tunes the feedback gain under an arbitrary performance index and is applicable to both linear and nonlinear control laws; (3) the algorithm is concise and has a few adjusting parameters; and (4) the tuning process proceeds well and the on-site tuning for actual systems is possible. It is also confirmed by the experiments using both simulations and actual systems that the proposed tuning method is effective to the stabilization control of an inverted pendulum.

Learning Control of a Flexible Arm by B-spline Curves in Consideration of Time Scaling

A learning control method using B-spline curves is extended to be applied to the tracking of specified spatial paths at arbitrary speed. This tracking control means the tracking of time scaled trajectories with geomemc path constraints. The proposed method obtains following results : (1) By using Time Scale Factor, dynamics of controlled system is described by two separate terms, a part defining a spatial path and the other one scaling time. (2) An algorithm is proposed to estimat coefficients describing the dynamics. (3) A gain matrix for learning control is expressed as a function of Time Scale Factor. (4) The learning control method is effectively applied to the control of a one-link flexible arm to track arbitrary trajectories which are determined by specifying spatial paths and scaling time.

Comparison of Collision-Free Trajectory Generation Methods of a Manipulator with Dynamic Constraints in Consideration of Working Time.

Three algorithms are proposed by using Complex Method to generate a collision-free trajectory for a robot manipulator in consideration of working time, under complete constraint conditions of dynamics, kinematics and obstacle avoidance. Each method has its advantage. Method 1 is that join spatial paths are specified and Time Scale Factor is used to satisfy constraint conditions. Method 2 is that working time is a variable and simultaneously optimized with join trajectories. Method 3 is that join paths are not specified and Time Scale Factor is also used. The three methods are compared by applying to a trajectory generation of a manipulator with three links.