Zexiang Li

Grasping and Coordinated Manipulation by a Multifingered Robot Hand

A new avenue of progress in the area of robotics is the use of multifingered robot hands for fine motion manipulation. This paper treats two fundamental problems in the study of multi fingered robot hands: grasp planning and the determination of coordinated control laws with point contact models. First, we develop the dual notions of grasp stability and grasp manipulability and propose a procedure for task modeling. Using the task model, we define the structured grasp quality measures, and using these measures we then devise a grasp planning algorithm. Second, based on the assumption of point contact models, we develop a computed torque-like con trol algorithm for the coordinated manipulation of a multi fingered robot hand. This control algorithm, which takes into account both the dynamics of the object and the dynamics of the hand, will realize simultaneously both the position trajec tory of the object and any desired value of internal grasp force. Moreover, the formulation of the control scheme can be easily extended to allow rolling and sliding motion of the fingers with respect to the object.

Motion of two rigid bodies with rolling constraint

The motion of two rigid bodies under rolling constraint is considered. In particular, the following two problems are addressed: (1) given the geometry of the rigid bodies, determine the existence of an admissible path between two contact configurations; and (2) assuming that an admissible path exists, find such a path. First, the configuration space of contact is defined, and the differential equations governing the rolling constraint are derived. Then, a generalized version of Frobeniuss theorem, known as Chows theorem, for determining the existence of motion is applied. Finally, an algorithm is proposed that generates a desired path with one of the objects being flat. Potential applications of this study include adjusting grasp configurations of a multifingered robot hand without slipping, contour following without dissipation or wear by the end-effector of a manipulator, and wheeled mobile robotics. >

Nonholonomic Motion Planning

Nonholonomic kinematics and the role of elliptic functions in constructive controllability, R.W. Brockett and L. Dai steering nonholonomic control systems using sinusoids, R.M. Murray and S. Shakar Sastry smooth time-periodic feedback solutions for nonholonomic motion planning, L. Gurvits and Zexiang Li lie bracket extensions and averaging - the single-bracket case, H.J. Sussmann and Wensheng Liu singularities and topological aspects in nonholonomic motion planning, J.-P. Laumond motion planning for nonholonomic dynamic systems, M. Reyhanoglu et al a differential geometric approach to motion planning, G. Lafferriere and H.J. Sussmann planning smooth paths for mobile robots, P. Jacobs and J. Canny nonholonomic control and gauge theory, R. Montgomery optimal nonholonomic motion planning for a falling cat, C. Fernandes et al nonholonomic behaviour in free-floating space manipulators and its utilization, E.G. Papadopoulos.

Near-optimal nonholonomic motion planning for a system of coupled rigid bodies

How does a falling cat change her orientation in midair without violating angular momentum constraint? This has become an interesting problem to both control engineers and roboticists. In this paper, we address this problem together with a constructive solution. First, we show that a falling cat problem is equivalent to the constructive nonlinear controllability problem. Thus, the same principle and algorithm used by a falling cat can be used for space robotic applications, such as reorientation of a satellite using rotors and attitude control of a space structure using internal motion, and other robotic tasks, such as dextrous manipulation with multifingered robotic hands and nonholonomic motion planning for mobile robots. Then, using ideas from Ritz approximation theory, we develop a simple algorithm for motion planning of a falling cat. Finally, we test the algorithm through simulation on two widely accepted models of a falling cat. It is interesting to note that one set of simulation results closely resembles the real trajectories employed by a falling cat. >

Control of seismic-excited buildings using active variable stiffness systems

Abstract It has been demonstrated that active variable stiffness (AVS) systems may be effective for response control of buildings subjected to earthquake excitations. The applications of active variable stiffness systems involve nonlinear control in which control theories for linear systems are not applicable. Based on the theory of variable structure system (VSS) or sliding mode control (SMC), control methods are presented in this paper for applications of active variable stiffness systems to seismic-excited buildings. In addition to full-state feedback controllers, general static output feedback controllers as well as simple output feedback controllers using only collocated sensors are presented. The principle of active variable stiffness control is interpreted based on the concept of the dissipation of hysteretic energies. Simulation results indicate that the control methods presented are robust and the performance of static output feedback controllers is comparable to that of the fullstate feedback controllers. Simulation results further indicate that the active variable stiffness systems, using locking and unlocking devices, are effective in reducing the interstorey drifts of seismicexcited buildings. However, the floor acceleration of the building may increase significantly, depending on the structure design and earthquake excitation.

A Geometric Theory for Analysis and Synthesis of Sub-6 DoF Parallel Manipulators

Mechanism synthesis is mostly dependent on the designers experience and intuition and is difficult to automate. This paper aims to develop a rigorous and precise geometric theory for analysis and synthesis of sub-6 DoF (or lower mobility) parallel manipulators. Using Lie subgroups and submanifolds of the special Euclidean group SE(3), we first develop a unified framework for modelling commonly used primitive joints and task spaces. We provide a mathematically rigorous definition of the notion of motion type using conjugacy classes. Then, we introduce a new structure for subchains of parallel manipulators using the product of two subgroups of SE(3) and discuss its realization in terms of the primitive joints. We propose the notion of quotient manipulators that substantially enriches the topologies of serial manipulators. Finally, we present a general procedure for specifying the subchain structures given the desired motion type of a parallel manipulator. The parallel mechanism synthesis problem is thus solved using the realization techniques developed for serial manipulators. Generality of the theory is demonstrated by systematically generating a large class of feasible topologies for (parallel or serial) mechanisms with a desired motion type of either a Lie subgroup or a submanifold.

Geometric algorithms for workpiece localization

We present a unified geometric theory for localization of three types of workpieces: 1) general three-dimensional (3D) workpieces where points from the finished surfaces fully constrain the rigid motions of the workpieces; 2) symmetric workpieces; 3) partially machined workpieces where points from the finished surfaces are inadequate to fully constrain the rigid motions of the workpieces. Applications of the study include workpiece setup, refixturing and dimensional inspections in a flexible manufacturing environment. First, we formulate the localization problem for a general 3D workpiece and study the mathematical properties of the underlying problem. We discuss an iterative approach for solving the general localization problem and show how different considerations in updating the Euclidean transformation lead to various geometric algorithms. Then, we extend the localization techniques to symmetric workpieces and partially machined workpieces and present a simple algorithm for each of the problems. Finally, we present simulation results showing convergence and robustness properties of the various geometric algorithms.

A Novel Contour Error Estimation for Position Loop-Based Cross-Coupled Control

Reduction of contour error is the main control objective in contour-following applications. A common approach to this objective is to design a controller based on the contour error directly. In this case, the contour error estimation is a key factor in the contour-following operation. Contour error can be approximated by the linear distance from the actual position to the tangent line or plane at the desired position. This approach suffers from a significant error due to linear approximation. A novel approach to contour error calculation of an arbitrary smooth path is proposed in this paper. The proposed method is based on coordinate transformation and circular approximation. In this method, the contour error is represented by the coordinate of the actual position with respect to a specific virtual coordinate frame. The method is incorporated in a position loop-based cross-coupled control structure. An equivalent robust control system is used to establish stability of the closed-loop system. Experimental results demonstrate the efficiency and performance of the proposed contour error estimation algorithm and the motion control strategy.

Smooth Time-Periodic Feedback Solutions for Nonholonomic Motion Planning

In this paper, we present an algorithm for computing time-periodic feedback solutions for nonholonomic motion planning with collision-avoidance. For a first-order Lie bracket system, we begin by computing a holonomic collision-free path using the potential field method. Then, we compute a nonholonomic path approximating the collision-free path within a predetermined bound. For this we first solve for extended inputs of an extended system using Lie bracket completion vectors. We then use averaging techniques to calculate the asymptotic trajectory of the nonholonomic system under application of a family of highly-oscillatory inputs. Comparing the limiting trajectories with the extended system we obtain a system of nonlinear equations from which the desired admissible control inputs can be solved. For higher-order Lie bracket systems we use multi-scale averaging and apply recursively the algorithm for first-order Lie bracket systems. Based on averaging techniques we also provide error bounds between a nonholonomic system and its averaged system.

Singularities of parallel manipulators: a geometric treatment

A parallel manipulator is naturally associated with a set of constraint functions defined by its closure constraints. The differential forms arising from these constraint functions completely characterize the geometric properties of the manipulator. In this paper, using the language of differential forms, we provide a thorough geometric study on the various types of singularities of a parallel manipulator, their relations with the kinematic parameters and the configuration spaces of the manipulator, and the role redundant actuation plays in reshaping the singularities and improving the performance of the manipulator. First, we analyze configuration space singularities by constructing a Morse function on some appropriately defined spaces. By varying key parameters of the manipulator, we obtain homotopic classes of the configuration spaces. This allows us to gain insight on configuration space singularities and understand how to choose design parameters for the manipulator. Second, we define parametrization singularities which include actuator and end-effector singularities (or other equivalent definitions) as their special cases. This definition naturally contains the closure constraints in addition to the coordinates of the actuators and the end-effector and can be used to search a complete set of actuator or end-effector singularities including some singularities that may be missed by the usual kinematics methods. We give an intrinsic classification of parametrization singularities and define their topological orders. While a nondegenerate singularity poses no problems in general, a degenerate singularity can sometimes be a source of danger and should be avoided if possible.