Motoji Yamamoto

Trajectory control of incompletely restrained parallel-wire-suspended mechanism based on inverse dynamics

This paper discusses parallel wire mechanisms where an end-effector of the mechanism is suspended by multiple wires. The mechanisms enable not only three-dimensional (3-D) positioning but also 3-D orienting of the end-effector, unlike typical wire suspension-type mechanisms such as overhead crane. To discuss the parallel-wire-suspended mechanisms generally, two forms of basic dynamic equations are presented. Then the parallel wire mechanisms are classified into two types based on the basic equations. Dynamical properties of the two types of wire-suspended positioning mechanism are discussed. In this paper, one of the wire-suspended mechanism, incompletely restrained-type parallel wire mechanism, is mainly discussed on its inverse dynamics problem and its trajectory control problem. The inverse dynamics problem for the incompletely restrained-type mechanism plays an important role on its control problem, because the mechanism has low stiffness based on incomplete constraints on the suspended object which is governed by its dynamics. The paper proposes an antisway control method for the suspended object. In the method, the inverse dynamics calculation is used for nonlinear dynamics compensation to control the suspended object of the incompletely restrained parallel wire mechanism.

Proxy-Based Sliding Mode Control: A Safer Extension of PID Position Control

High-gain proportional-integral-derivative (PID) position control involves some risk of unsafe behaviors in cases of abnormal events, such as unexpected environment contacts and temporary power failures. This paper proposes a new position-control method that is as accurate as conventional PID control during normal operation, but is capable of slow, overdamped resuming motion without overshoots from large positional errors that result in actuator-force saturation. The proposed method, which we call proxy-based sliding mode control (PSMC), is an alternative approximation of a simplest type of sliding mode control (SMC), and also is an extension of the PID control. The validity of the proposed method is demonstrated through stability analysis and experimental results.

Trajectory planning of mobile manipulator with stability considerations

This paper presents methods of trajectory planning for a mobile manipulator with stability considerations. The proposed trajectory planning method is to generate a trajectory for the mobile manipulator from a given path of the end-effector considering stability. Then, we derive a dynamics model of the mobile manipulator considering it as the combined system of the manipulator and the mobile platform. ZMP criterion is used as an index for the system stability. The trajectory planning problem is formulated as an optimal control problem with some constraints. To solve the problem, we use a hierarchical gradient method which synthesizes the gradient function in a hierarchical manner based on the order of priority. The simulation results of the 2-link planar nonholonomic mobile manipulator are given to show the effectiveness of the proposed algorithm.

Quasi-time-optimal motion planning of mobile platforms in the presence of obstacles

This paper addresses a problem of optimal motion planning of mobile platforms amidst obstacles, considering the mobile platform dynamics. Due to nonholonomic constraints, actuator constraints, and state constraints by obstacle avoidance, the planning problem of mobile platform with two independently driven wheels is a complicated one. In this study, a dynamical model for the mobile platform is presented, including nonholonomic kinematic constraints. The idea of a path parameter is introduced to simplify the planning problem by considering the dynamics and nonholonomic constraints. Using the path parameter, the optimal motion planning problem is divided into two sub-problems: 1) time-optimization of trajectory along specified path, and 2) search for optimal path. Then two methods are proposed the solve the problems using the path parameter and parametrization by B-spline function. Finally, quasi-time-optimal solution for the original problem are planned by combining the two methods. Numerical examples show effectiveness of the motion planner.

Inverse dynamics and control of crane-type manipulator

This paper discusses an inverse dynamics problem for a parallel wire mechanism with multi-degrees of freedom. Firstly, a crane-type parallel wires mechanism which has three trolleys and three wires is proposed for handling heavy objects. This handling mechanism enables not only three dimensional positioning but also orientating of objects, unlike typical crane mechanism. A dynamical model using wire force vector is derived. Based on the dynamical model with wire force vector, inverse dynamics problem is analytically solved by a linear equation in terms of the wire force vector. The trajectory of end-effector of the crane-type manipulator can be transformed into the trajectory of wire length and trolley position by the calculation method. Using the trajectory of wire length and trolley position, the end-effector of the crane-type manipulator is controlled. Two dimensional experimental crane-type manipulator is also developed to verify an effectiveness of the inverse dynamics calculation and the trajectory control method.

An edge-based computationally efficient formulation of Saint Venant-Kirchhoff tetrahedral finite elements

This article describes a computationally efficient formulation and an algorithm for tetrahedral finite-element simulation of elastic objects subject to Saint Venant-Kirchhoff (StVK) material law. The number of floating point operations required by the algorithm is in the range of 15% to 27% for computing the vertex forces from a given set of vertex positions, and 27% to 38% for the tangent stiffness matrix, in comparison to a well-optimized algorithm directly derived from the conventional Total Lagrangian formulation. In the new algorithm, the data is associated with edges and tetrahedron-sharing edge-pairs (TSEPs), as opposed to tetrahedra, to avoid redundant computation. Another characteristic of the presented formulation is that it reduces to that of a spring-network model by simply ignoring all the TSEPs. The technique is demonstrated through an interactive application involving haptic interaction, being combined with a linearized implicit integration technique employing a preconditioned conjugate gradient method.

Trajectory planning of mobile manipulator with end-effector's specified path

In this paper, a trajectory planning method of a mobile manipulator with the end-effectors specified path is presented. We derive the dynamics of the mobile manipulator considering it as the combined system of the manipulator and the mobile platform. The planning problem is formulated as an optimal control problem. To solve the problem, we use the concept of the order of priority. A gradient-based iterative algorithm which synthesize the gradient function in a hierarchical manner based on the order of priority is used. The simulation results of the 2-link planar nonholonomic mobile manipulator are given to show the effectiveness of the proposed algorithm.

On the dynamic model and motion planning for a spherical rolling robot actuated by orthogonal internal rotors

The paper deals with the dynamics of a spherical rolling robot actuated by internal rotors that are placed on orthogonal axes. The driving principle for such a robot exploits nonholonomic constraints to propel the rolling carrier. A full mathematical model as well as its reduced version are derived, and the inverse dynamics are addressed. It is shown that if the rotors are mounted on three orthogonal axes, any feasible kinematic trajectory of the rolling robot is dynamically realizable. For the case of only two rotors the conditions of controllability and dynamic realizability are established. It is shown that in moving the robot by tracing straight lines and circles in the contact plane the dynamically realizable trajectories are not represented by the circles on the sphere, which is a feature of the kinematic model of pure rolling. The implication of this fact to motion planning is explored under a case study. It is shown there that in maneuvering the robot by tracing circles on the sphere the dynamically realizable trajectories are essentially different from those resulted from kinematic models. The dynamic motion planning problem is then formulated in the optimal control settings, and properties of the optimal trajectories are illustrated under simulation.

Sub-optimal trajectory planning of mobile manipulator

A trajectory planning method of a mobile manipulator is presented. We derive the dynamics of the mobile manipulator considering it as the combined system of the manipulator and the mobile platform. The planning problem is formulated as an optimal control problem. To solve the problem, we use the concept of the order of priority. A gradient-based iterative algorithm which synthesize the gradient function in a hierarchical manner based on the order of priority is used. The simulation results of the 2-link planar nonholonomic mobile manipulator are given to show the effectiveness of the proposed algorithm.

Anti-sway control for wire-suspended mechanism based on dynamics compensation

Proposes a feedback control method for wire-suspended mechanisms. The wire-suspended mechanisms are classified into two types, which are completely restrained type mechanisms and incompletely restrained type mechanisms. The paper discusses mainly incompletely restrained type mechanisms form the viewpoint of actual control. The incompletely restrained type wire-suspended mechanism has the merit that it enables three dimensional positioning and orientation of suspended object with simple mechanism using a small number of wires. However it also has the drawback that the manipulated object is easy to swing as seen in overhead crane which is a simple incompletely restrained type mechanism. For this reason, an anti-sway control method for incompletely restrained type mechanisms is needed. To resolve the problem of swing, inverse dynamics for general incompletely restrained type wire-suspended mechanism is discussed, then a feedback control method based on dynamics compensation is presented.