Robust Learning Control for Manipulators with Uncertainty Disturbances Based on Internal Model

In this paper, a disturbance controller is designed for making robotic system behave as a decoupled linear system according to the concept of internal model. Based on the linear system, the paper presents an iterative learning control algorithm to robotic manipulators. A sufficient condition for convergence is provided. The selection of parameter values of the algorithm is simple and easy to meet the convergence condition. The simulation results demonstrate the effectiveness of the algorithm..

Compliance and Force Control for Computer Controlled Manipulators

Compliant motion occurs when the manipulator position is constrained by the task geometry. Compliant motion may be produced either by a passive mechanical compliance built in to the manipulator, or by an active compliance implemented in the control servo loop. The second method, called force control, is the subject of this report. In particular, this report presents a theory of force control based on formal models of the manipulator, and the task geometry. The ideal effector is used to model the manipulator, and the task geometry is modeled by the ideal surface, which is the locus of all positions accessible to the ideal effector. Models are also defined for the goal trajectory, position control, and force control.

Effects of Constraint Errors on Parallel Manipulators with Decoupled Motion

From perspective of structure synthesis, certain special geometric constraints, such as joint axes intersecting at one point or perpendicular to each other, are necessary in realizing the end-effector motion of kinematically decoupled parallel manipulators (PMs) along individual motion axes. These requirements are difficult to achieve in the actual system due to assembly errors and manufacturing tolerances. Those errors that violate the geometric constraint requirements are termed “constraint errors”. The constraint errors usually are more troublesome than other manipulator errors because the decoupled motion characteristics of the manipulator may no longer exist and the decoupled kinematic models will be rendered useless due to these constraint errors. Therefore, identification and prevention of these constraint errors in initial design and manufacturing stage are of great significance. In this article, three basic types of constraint errors are identified, and an approach to evaluate the effects of constraint errors on decoupling characteristics of PMs is proposed. This approach is illustrated by a 6-DOF PM with decoupled translation and rotation. The results show that the proposed evaluation method is effective to guide design and assembly.

Workspace evaluation of manipulators through finite-partition of SE(3)

Workspace analysis and optimization are important in a manipulator design. As the complete workspace of a 6-DOF manipulator is embedded into a 6-imensional space, it is difficult to quantify and qualify it. Most literatures only considered the 3-D sub workspaces of the complete 6-D workspace. In this paper, a finite-partition approach of the Special Euclidean group SE(3) is proposed based on the topology properties of SE(3), which is the product of Special Orthogonal group SO(3) and R^3. It is known that the SO(3) is homeomorphic to a solid ball D^3 with antipodal points identified while the geometry of R^3 can be regarded as a cuboid. The complete 6-D workspace SE(3) is at the first time parametrically and proportionally partitioned into a number of elements with uniform convergence based on its geometry. As a result, a basis volume element of SE(3) is formed by the product of a basis volume element of R^3 and a basis volume element of SO(3), which is the product of a basis volume element of D^3 and its associated integration measure. By this way, the integration of the complete 6-D workspace volume becomes the simple summation of the basis volume elements of SE(3). Two new global performance indices, i.e., workspace volume ratio Wr and global condition index GCI, are defined over the complete 6-D workspace. A newly proposed 3 RPPS parallel manipulator is optimized based on this finite-partition approach. As a result, the optimal dimensions for maximal workspace are obtained, and the optimal performance points in the workspace are identified.

An intelligent configuration-sampling based local motion planner for robotic manipulators

Manipulator motion planning is a task which relies heavily on the construction of a configuration space prior to path planning. However when fast real-time motion is needed, the full construction of the manipulator's high-dimensional configu-ration space can be too slow and expensive. Alternative planning methods, which avoid this full construction of the manipulator's configuration space are needed to solve this problem. Here, one such existing local planning method for manipulators based on configuration-sampling and subgoal-selection has been extended. Using a modified Artificial Potential Fields (APF) function, goal-configuration sampling and a novel subgoal selection method, it provides faster, more optimal paths than the previously proposed work. Simulation results show a decrease in both runtime and path lengths, along with a decrease in unexpected local minimum and crashing issues.

Self-Feedback Motion Control for Cable-Driven Parallel Manipulators

This article proposes a closed-loop control scheme based on joint-angle feedback for cable-driven parallel manipulators (CDPMs), which is able to overcome various difficulties resulting from the flexible nature of the driven cables to achieve higher control accuracy. By introducing a unique structure design that accommodates built-in encoders in passive joints, the seven degrees of freedom (7-DOF) CDPM can obtain joint angle values without external sensing devices, and it is used for feedback control together with a proper closed-loop control algorithm. The control algorithm has been derived from the time differential of the kinematic formulation, which relates the joint angular velocities to the time derivative of cable lengths. In addition, the Lyapunov stability theory and Monte Carlo method have been used to mathematically verify the self-feedback control law that has tolerance for parameter errors. With the aid of co-simulation technique, the self-feedback closed-loop control is applied on a 7-DOF CDPM and it shows higher motion accuracy than the one with an open-loop control. The trajectory tracking experiment on the motion control of the 7-DOF CDPM demonstrated a good performance of the self-feedback control method.

Topology synthesis of three-legged spherical parallel manipulators employing Lie group theory

Driven by the requirements of the bionic joint or tracking equipment for the spherical parallel manipulators (SPMs) with three rotational degrees-of-freedom (DoFs), this paper carries out the topology synthesis of a class of three-legged SPMs employing Lie group theory. In order to achieve the intersection of the displacement subgroups, the subgroup characteristics and operation principles are defined in this paper. Mainly drawing on the Lie group theory, the topology synthesis procedure of three-legged SPMs including four stages and two functional blocks is proposed, in which the assembly principles of three legs are defined. By introducing the circular track, a novel class of three-legged SPMs is synthesized, which is the important complement to the existing SPMs. Finally, four typical examples are given to demonstrate the finite displacements of the synthesized three-legged SPMs.

A multi-objective approach for the motion planning of redundant manipulators

Kinematic redundancy occurs when a manipulator possesses more degrees of freedom than those required to execute a given task. Several kinematic techniques for redundant manipulators control the gripper through the pseudo-inverse of the Jacobian, but lead to a kind of chaotic inner motion with unpredictable arm configurations. Such algorithms are not easy to adapt to optimization schemes and, moreover, often there are multiple optimization objectives that can conflict between them. Unlike single optimization, where one attempts to find the best solution, in multi-objective optimization there is no single solution that is optimum with respect to all indices. Therefore, trajectory planning of redundant robots remains an important area of research and more efficient optimization algorithms are needed. This paper presents a new technique to solve the inverse kinematics of redundant manipulators, using a multi-objective genetic algorithm. This scheme combines the closed-loop pseudo-inverse method with a multi-objective genetic algorithm to control the joint positions. Simulations for manipulators with three or four rotational joints, considering the optimization of two objectives in a workspace without and with obstacles are developed. The results reveal that it is possible to choose several solutions from the Pareto optimal front according to the importance of each individual objective.

A fractional approach for the motion planning of redundant and hyper-redundant manipulators

The trajectory planning of redundant robots through the pseudoinverse control leads to undesirable drift in the joint space. This paper presents a new technique to solve the inverse kinematics problem of redundant manipulators, which uses a fractional differential of order α to control the joint positions. Two performance measures are defined to examine the strength and weakness of the proposed method. The positional error index measures the precision of the manipulator's end-effector at the target position. The repeatability performance index is adopted to evaluate if the joint positions are repetitive when the manipulator execute repetitive trajectories in the operational workspace. Redundant and hyper-redundant planar manipulators reveal that it is possible to choose in a large range of possible values of α in order to get repetitive trajectories in the joint space.