Suguru Arimoto

Dynamic object manipulation using a virtual frame by a triple soft-fingered robotic hand

This paper proposes a novel object manipulation method to regulate the position and attitude of an object in the task space with dynamic stability by using a triple soft-fingered robotic hand system. In our previous works, a dynamic object grasping method without use of any external sensing, called “the Blind Grasping”, has been proposed. Although stable grasping in a dynamic sense has been realized by the method, a simultaneous object position and attitude control has not yet been treated, so far. In this paper, instead of using any information of the real object position and attitude, virtual data of object position and attitude are introduced by defining a virtual frame. By using the virtual information, a control signal to regulate the virtual object position and attitude without use of any external sensing is designed. The usefulness of our proposed control method even under the existence of nonholonomic rolling constraints is illustrated through a numerical simulation result.

A riemannian-geometry approach for dynamics and control of object manipulation under constraints

A Riemannian-geometry approach for control and stabilization of dynamics of object manipulation under holonomic or non-holonomic (but Pfaffian) constraints is presented. First, position/force hybrid control of an endeffector of a multi-joint redundant (or nonredundant) robot under a nonholonomic constraint is reinterpreted in terms of “submersion” in Riemannian geometry. A force control signal constructed in the image space spanned from the constraint gradient can be regarded as a lifting in the direction orthogonal to the kernel space. By means of the Riemannian distance on the constraint submanifold, stability on a manifold for a redundant system under holonomic constraints is discussed. Second, control and stabilization of dynamics of two-dimensional object grasping and manipulation by using a pair of multi-joint robot fingers are tackled, when a rigid object is given with arbitrary shape. Then, it is shown that rolling contact constraint induce the Euler equation of motion in an implicit function form, in which constraint forces appear as wrench vectors affecting on the object. The Riemannian metric can be introduced in a natural way on a constraint submanifold induced by rolling contacts. A control signal called “blind grasping” is defined and shown to be effective in stabilization of grasping without using the details of information of object shape and parameters or external sensing. The concept of stability of the closed-loop system under constraints is renewed in order to overcome the degrees-of-freedom redundancy problem. An extension of Dirichlet-Lagranges stability theorem to a system of DOF-redundancy under constraints is presented by using a Morse-Lyapunov function.

Modeling and Control of Multi-Body Mechanical Systems: Part I A Riemannian Geometry Approach

Control problems of motion of multi-body mechanical systems under constraints and/or with redundancy in system’s degrees-of-freedom (DOF) are treated from the standpoint of Riemannian geometry. A multi-joint reaching problem with excess DOF is tackled and it is shown that a task space PD feedback with damping shaping in joints maneuvers the endpoint of the robot arm to reach a given target in the sense of exponentially asymptotic convergence. An artificial potential inducing the position feedback in task space can be regarded as a Morse-Bott function introduced in Riemannian geometry, from which the Lagrange stability theorem can be directly extended to this redundant case. The speed of convergence of both the orbit of the endpoint in task space and the trajectory of joint vector in joint space can be adjusted by damping shaping and adequately choosing a single stiffness parameter. In the case that the endpoint is constrained on a hypersurface in E 3, the original Lagrange dynamics expressed in an implicit form by introducing a Lagrange multiplier is decomposed into two partial dynamics with the aid of decomposition of the tangent space into the image of the endpoint Jacobian matrix and the kernel orthogonally complemented to the image. The stability problem of point-to-point endpoint movement on the constraint surface is reduced to the former case without constraint.

Modeling and control of a pair of robot fingers with saddle joint under orderless actuations

A new robot hand dynamics model with rolling constraints and with a saddle joint at one finger is proposed, where two saddle-joint actuations are considered to be orderless. Spinning motion around the opposition axis connecting two center points of each finger-tip contact area with an object is faithfully treated, and a viscosity model for damping rotational motion of the object is proposed. A class of control signals without referring to object kinematics or using external sensing is proposed. Finally, numerical simulation results show the stability of motion of the overall closed-loop dynamics supplied with the proposed control input.

Evaluation of gait with trans-femoral prosthesis based on Riemannian distance

This paper presents a method to quantify the goodness of gait with a trans-femoral prosthesis in order to evaluate walking skill with the prosthesis and its application to its design. Advancements in the mechanism and the control method of trans-femoral prostheses have drastically improved the gait of amputees. However, realization of a natural gait has not been investigated in detail even though such smooth gait is important to increase the amputees activities of daily living (ADL). Inertia of the prosthesis plays an important role in natural and smooth gaits during the swing phase. We suppose that goodness of gait or easiness of walking is strongly related to effective use of the prosthesis inertia. Recently, inertia-induced measure has been proposed as a measure to quantify inertia-induced motion of a multi-body system based on the Riemannian distance. In this paper, we will attempt to evaluate the goodness or easiness of walking with a prosthesis leg by quantifying the effective use of the prosthesis inertia based on the Riemannian distance. Gaits with several different inertia properties will be measured. The results will then demonstrate the strong relevance between subjective evaluation of easiness of walking and effective use of inertia evaluated based on the Riemannian distance.

Stability of two-dimensional blind grasping under the gravity effect and rolling constraints

This paper aims to show a sensory-motor coordination control scheme that realizes stable pinching of rigid objects with parallel or nonparallel flat surfaces movable in 2-dimensional vertical plane by a pair of robot fingers with hemispherical ends. The proposed control signal is composed of gravity compensation for fingers, damping shaping, exertion of forces to the object from opposite directions, generation of moments for balancing of rotational moments, and regressors for estimating unknown steady-state terms, all of which neither need the knowledge of object parameters nor use any object sensing data. In other words, stable grasping can be realized by using only finger-joint sensing in a blind manner without using force sensors or tactile sensing. Stability of pinching motion with convergence to the state of force/torque balance is shown through computer simulations and is also proved theoretically.

Pinching 2D object with arbitrary shape by two robot fingers under rolling constraints

Modeling of pinching an object with arbitrary shape by a pair of robot fingers with hemispherical ends in a horizontal plane is proposed in a mathematical and computational manner. Since the curvature of an object contour with an arbitrary curve is variable according to the change of the contact point between the object surface and the rigid finger tip, the arclength paremeter “s” explicitly appears in the overall fingers-object dynamics. It is shown that the overall fingers-object system should be accompanied with the first-order differential equation of the parameter “s” that includes the curvatures of both the object contour and finger-tip curve. A control input, which is of the same category as the control input called “blind grasping” appeared in our former papers, is utilized for the realization of stable grasp. The control input does neither need to use the kinematic information of the object nor use any external sensing. Finally, numerical simulations are carried out in order to confirm the effectiveness of our proposed model and control input.

A Riemannian-Geometry Approach for Modeling and Control of Dynamics of Object Manipulation under Constraints

A Riemannian-geometry approach for modeling and control of dynamics of object manipulation under holonomic or non-holonomic constraints is presented. First, position/force hybrid control of an endeffector of a multijoint redundant (or nonredundant) robot under a holonomic constraint is reinterpreted in terms of “submersion” in Riemannian geometry. A force control signal constructed in the image space of the constraint gradient is regarded as a lifting (or pressing) in the direction orthogonal to the kernel space. By means of the Riemannian distance on the constraint submanifold, stability of position control under holonomic constraints is discussed. Second, modeling and control of two-dimensional object grasping by a pair of multijoint robot fingers are challenged, when the object is of arbitrary shape. It is shown that rolling contact constraints induce the Euler equation of motion, in which constraint forces appear as wrench vectors affecting the object. The Riemannian metric is introduced on a constraint submanifold characterized with arclength parameters. An explicit form of the quotient dynamics is expressed in the kernel space with accompaniment of a pair of first-order differential equations concerning the arclength parameters. An extension of Dirichlet-Lagranges stability theorem to redundant systems under constraints is suggested by introducing a Morse-Lyapunov function.

Task-Space Iterative Learning for Redundant Robots: Simultaneous Acquirements of Desired Motion and Force Trajectories under Constraints

Abstract This paper focuses on iterative learning control (ILC) for multi-joint robots with redundancy in degrees of freedom (DOFs) when task descriptions are given only in task-space. The specified task is of precise tracking of both endpoint position and force trajectories given on the plane by a five-DOF robot arm whose endpoint contacts with a plane during motion. Even in the case of twice continuously differentiable desired motion and force trajectories given only in task-space, it is possible to construct a learning update law in task-space by using the desired trajectories together with measured data correspond to them. The convergence of trajectory tracking under constraints by the proposed task space ILC is proved theoretically on the basis of nonlinear robot dynamics with DOF-redundancy.

Modeling and Control of 2D Grasping under Rolling Contact Constraints between Arbitrary Shapes: A Riemannian-Geometry Approach

Modeling, control, and stabilization of dynamics of two-dimensional object grasping by using a pair of multijoint robot fingers are investigated under rolling contact constraints and arbitrariness of the geometry of the object and fingertips. First, modeling of rolling motion between 2D rigid bodies with arbitrary shape is treated under the assumption that the two contour curves coincide at the contact point and share the same tangent. The rolling constraints induce the Euler equation of motion that is parameterized by a pair of arclength parameters and constrained onto the kernel space as an orthogonal complement to the image space spanned from all the constraint gradients. Furthermore, it is shown that all the Pfaffian forms of the rolling constraints are integrable in the sense of Frobenius and therefore the rolling contacts are regarded as a holonomic constraint. The Euler-Lagrange equation of motion of the overall fingers/object system is rederived together with a couple of first-order differential equations that express evolution of contact points in terms of quantities of the second fundamental form. A control signal called “blind grasping” is defined and shown to be effective in maintenance or stabilization of grasping without using the details of object shape and parameters or external sensing. An extension of the Dirichlet-Lagrange stability theorem to a system of DOF-redundancy under constraints is discussed by introducing a Morse-Bott function and deriving its Hessian, in a special case that the object to be grasped is a parallelepiped.