Jing-Sin Liu

Practical and flexible path planning for car-like mobile robot using maximal-curvature cubic spiral

Abstract This paper presents a nonholonomic path planning method, aiming at taking into considerations of curvature constraint, length minimization, and computational demand, for car-like mobile robot based on cubic spirals. The generated path is made up of at most five segments: at most two maximal-curvature cubic spiral segments with zero curvature at both ends in connection with up to three straight line segments. A numerically efficient process is presented to generate a Cartesian shortest path among the family of paths considered for a given pair of start and destination configurations. Our approach is resorted to minimization via linear programming over the sum of length of each path segment of paths synthesized based on minimal locomotion cubic spirals linking start and destination orientations through a selected intermediate orientation. The potential intermediate configurations are not necessarily selected from the symmetric mean circle for non-parallel start and destination orientations. The novelty of the presented path generation method based on cubic spirals is: (i) Practical: the implementation is straightforward so that the generation of feasible paths in an environment free of obstacles is efficient in a few milliseconds; (ii) Flexible: it lends itself to various generalizations: readily applicable to mobile robots capable of forward and backward motion and Dubins’ car (i.e. car with only forward driving capability); well adapted to the incorporation of other constraints like wall-collision avoidance encountered in robot soccer games; straightforward extension to planning a path connecting an ordered sequence of target configurations in simple obstructed environment.

Collision-free curvature-bounded smooth path planning using composite Bezier curve based on Voronoi diagram

In this paper, we present an obstacle avoiding smooth path planning method based on Voronoi diagram and composite Bezier curve algorithm which obtains the curvature bounded path with small length. In our algorithm, a Voronoi diagram is constructed according to the global environment. The piecewise linear rough path in the Voronoi diagram which keeps away from the obstacles is obtained by performing Dijkstras shortest path algorithm. Dynamic programming is employed to subdivide the nodes on the piecewise linear path into control point subsequences to generate a collision free composite Bezier curve which satisfies the curvature constraint and approaches minimal path length.

Robust nonlinear control of robotic manipulators

Abstract A robust nonlinear control strategy is proposed to deal with the control problem of robotic manipulators with second order nonlinear actuator dynamics. The control scheme is composed of two stages: the nominal dynamics stage and the perturbed dynamics stage. The control at the nominal dynamics stage and the perturbed dynamics stage. The control at the nominal dynamics stage is aimed at exact linearization and input/output decoupling of the nonlinear actuator‐manipulator system in the task space by nonlinear feedback and nonlinear state space diffeomorphic transformations. The resulting closed‐loop nominal system is capable of precise trajectory following in a desired second‐order linear behavior. To compensate uncertainties in a practical situation, an optimal error correcting compensator is designed to achieve some robustness at the perturbed dynamics stage. Simulation study of a cylindrical robot is given to illustrate the effectiveness of the proposed scheme.

Robust neuro-fuzzy control of multivariable systems by tuning consequent membership functions

A robust neuro-fuzzy controller with tuning mechanism of membership functions and neural weights to achieve the tracking control of composite multivariable systems is proposed. The control strategy is developed to facilitate robust property by self-tuning the consequent membership functions of the fuzzy controllers. By an on-line tuning mechanism, the fuzzy system can effectively deal with the equivalent uncertainties that may appear in the subsystems due to plant uncertainty, function approximation error, or external disturbance. By using Lyapunov stability theory, the overall system with the proposed controller has been proved to be uniform ultimate bounded. Simulation results of a two-link robot control demonstrate the effectiveness and robustness of the design.

On-line multi-criteria based collision-free posture generation of redundant manipulator in constrained workspace

The manipulator with a large degree of redundancy is useful for realizing multiple tasks such as maneuvering the robotic arms in the constrained workspace, e.g. the task of maneuvering the end-effector of the manipulator along a pre-specified path into a window. This paper presents an on-line technique based on a posture generation rule to compute a null-space joint velocity vector in a singularity-robust redundancy resolution method. This rule suggests that the end of each link has to track an implicit trajectory that is indirectly resulted from the constraint imposed on tracking motion of the end-effector. A proper posture can be determined by sequentially optimizing an objective function integrating multiple criteria of the orientation of each link from the end-effector toward the base link as the secondary task for redundancy resolution, by assuming one end of the link is clamped. The criteria flexibly incorporate obstacle avoidance, joint limits, preference of posture in tracking, and connection of posture to realize a compromise between the primary and secondary tasks. Furthermore, computational demanding of the posture is reduced due to the sequential link-by-link computation feature. Simulations show the effectiveness and flexibility of the proposed method in generating proper postures for the collision avoidance and the joint limits as a singularity-robust null-space projection vector in maneuvering redundant robots within constrained workspaces.

A novel collision detection method based on enclosed ellipsoid

The paper introduces an efficient collision detection method for convex polyhedra in a three-dimensional workspace. In cooperation with the enclosing and the enclosed ellipsoids of convex polyhedra, potential collisions can be detected more accurate than those methods using only bounding ellipsoids for object representation, and more efficient than the polyhedral methods. An approach for computing the enclosed ellipsoid of a convex polyhedron by compressing, stretching and scaling operations on its best-fit enclosing ellipsoid is also introduced in this content. Graphical simulation of two robot manipulators moving in a share workspace was conducted to demonstrate the effectiveness of the proposed algorithm for collision detection.

A P-type iterative learning controller for robust output tracking of nonlinear time-varying systems

A P-type iterative learning controller using the concept of the forgetting factor and current error modification is proposed in this paper for a class of uncertain nonlinear time-varying systems. The robustness, convergence and performance of this P-type learning control scheme are completely studied. It is shown that the uniformly boundedness between the system output and the desired output is achieved in each iterate. Under some conditions on the uncertainties, the residual set of the tracking error on the final iterate can be shown to be a class K function of the forgetting factor. When all the uncertainties and the forgetting factor tend to zero, the system output will converge uniformly to the desired one.

Estimate of minimum distance between convex polyhedra based on enclosed ellipsoids

A tight estimate of upper and lower bounds of the distance between convex polyhedra based on the best ellipsoid fit is proposed. Estimated distance is mainly based on enclosed ellipsoids, instead of minimum volume enclosing ellipsoids. We provide an algorithm for computing the enclosed ellipsoid of a convex polyhedron by the use of its best fit enclosing ellipsoid. By this estimate, the collision-free region could be much larger than enclosing ellipsoids and the detection of potential collisions can be more accurate than that of using enclosing ellipsoids. A numerical example is presented to show the tightness of upper and lower distance estimates based on enclosed ellipsoids.

A Robotic Indoor 3D Mapping System Using a 2D Laser Range Finder Mounted on a Rotating Four-Bar Linkage of a Mobile Platform

This paper describes our work in developing a 3D robotic mapping system composed by an experimental mobile platform equipped with a rotating laser range finder (LRF). For the purpose of obtaining more complete 3D scans of the environment, we design, construct and calibrate a crank-rocker four-bar linkage so that a LRF mounted on it could undergo repetitive rotational motion between two extreme positions, allowing both horizontal and vertical scans. To reduce the complexity of map representation suitable for optimization later, the local map from the LRF is a grid map represented by a distance-transformed (DT) matrix. We compare the DT-transformed maps and find the transformation matrix of a robot pose by a linear simplex-based map optimization method restricted to a local region allows efficient alignment of maps in scan matching. Several indoor 2D and 3D mapping experiments are presented to demonstrate the consistency, efficiency and accuracy of the 3D mapping system for a mobile robot that is stationary or in motion.

Fast and accurate collision detection based on enclosed ellipsoid

A fast and accurate method for detecting the collisions of convex polyhedra in a graphical simulation environment based on a newly developed method of distance estimate is presented. By the simultaneous use of the enclosing and the enclosed ellipsoids of convex polyhedra, potential collisions can be detected more accurate than those methods using only bounding volume for object representation, and more efficient than the polyhedral methods. An approach for computing the enclosed ellipsoid of a convex polyhedron by compressing, stretching and scaling operations on its best-fit enclosing ellipsoid is introduced. Graphical simulations of two case studies (moving polyhedral objects in three-dimensional space and multiple robot arms undergoing straight line motions) are conducted to demonstrate the accuracy of the proposed algorithm for collision detection.