On minimum-fuel control of affine nonlinear systems

The minimum-fuel control problem is investigated for a class of multiinput affine nonlinear systems whose associated Lie algebra is nilpotent. After preliminary notions and definitions are presented, emphasis is on the solution to the optimal control problem of the Lie algebra generated by certain system vector fields is nilpotent. Consequences of the maximum principle are deduced for such systems     

Robust Hybrid Control of Constrained Robot Manipulators via Decomposed Equations

Basing on a constraint Jacobian induced orthogonal decomposition of the task space and by requiring the force controller to be orthogonal to the constraint manifold, the dynamics of the constrained robots under hybrid control is decomposed into a set of two equations. One describes the motion of robots moving on the constraint manifold, while the other relates the constraint force with the hybrid controller. This decomposition does not require the solution of the constraint equation in partition form. In this setting, the hybrid control of constrained robots can be essentially reduced to robust stabilization of uncertain nonlinear systems whose uncertainties do not satisfy the matching condition. A continuous version of the sliding-mode controller (from Khalil [12]) is employed to design a position controller. The force controller is designed as a proportional force error feedback of high gain type. The coordination of the position controller and the force controller is shown to achieve ultimately bounded position and force tracking with tunable accuracy. Moreover, an estimate of the domain of attraction is provided for the motion on the constraint manifold. Simulation for a planar two-link robot constraining on an ellipse is given to show the effectiveness of a hybrid controller. In addition, the friction effect, viewed as external disturbance to the system, is also examined through simulations.     

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

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.     

On tracking control for affine nonlinear systems by sliding mode

The stability problem of output tracking of a bounded time-varying reference by decouplable affine nonlinear systems using sliding mode control is investigated. It is shown that when the error dynamics on the sliding surface is chosen to be linear time-invariant, closed loop stability of systems under the presented sliding mode control can be guaranteed only if the systems are minimum phase.     

Hybrid position/force tracking for a class of constrained mechanical systems

We study the hybrid tracking problem for a class of mechanical systems, described by Euler-Lagrange equations of motion, subject to a set of holonomic and/or nonholonomic constraints in a unified fashion. Based on a QR-like decomposition of the constraint Jacobian, it is shown that the constraint-force free and reduced constrained motions of constrained mechanical systems can be naturally separated. A new hybrid control is proposed for the decomposed motions to achieve simultaneous, independent position and force tracking. Some comments about the applicability of main tracking result are given.     

A Recursive Algorithm for On-line Clustering Obstacles Cluttered in Dynamic Environments

In some applications of industrial robots, the robot manipulator must traverse a pre-specified Cartesian path with its hand tip while links of the robot safely move among obstacles cluttered in the robot's scene (environment). In order to reduce the costs of collision detection, one approach is to reduce the number of collision checks by enclosing a few real obstacles with a larger (artificial) bounding volume (a cluster), e.g., by their convex hull [4, 14], without cutting the specified path.In this paper, we propose a recursive algorithm composed of four procedures to tackle the problem of clustering convex polygons cluttered around a specified path in a dynamic environment. A key fact observed is that the number k of clusters is actually determined by the specified path not by any criterion used in clustering. Based on this fact, an initial set of k clusters could be rapidly generated. Then, the initial set of clusters and its number is further refined for satisfying the minimum Euclidean distance criterion imposed in clustering. Compared to the heuristic algorithm in [14], complexity of the proposed algorithm is reduced by one order with respect to the number n of obstacles. Simulation are performed in both static and dynamic environments, which show that the recursive algorithm is very efficient and acquires less number k of clusters.     

Decoupling of continuous-time linear time-invariant systems using generalized sampled-data hold functions

We investigate the possibility of input-output decoupling without stability a square continuous-time LTI plant (C, A, B) by designing discrete devices, the generalized sampled-data hold functions. By adopting sequential design procedures for the resulting diagonalizing problem, two cases are found to be solvable and yield nontrivial solutions: (1) CB nonsingular; (2) mn2m, rk(CB)=n-m where n, m are the number of states and inputs (outputs) respectively; C=I_n-C^T(CC^T)⁻¹C.     

Real-time Velocity Alteration Strategy for Collision-free Trajectory Planning of Two Articulated Robot Manipulators

Two articulated robots working in a shared workspace can be programmed by planning the tip trajectory of each robot independently. To account for collision avoidance between links, a real-time velocity alteration strategy based on fast and accurate collision detection is proposed in this paper to determine the step of next motion of slave (low priority) robot for collision-free trajectory planning of two robots with priorities. The effectiveness of the method depends largely on a newly developed method of accurate estimate of distance between links. By using the enclosing and enclosed ellipsoids representations of polyhedral models of links of robots, the minimum distance estimate and collision detection between the links can be performed more efficiently and accurately. The proposed strategy is implemented in an environment where the geometric paths of robots are pre-planned and the preprogrammed velocities are piecewise constant but adjustable. Under the control of the proposed strategy, the master robot always moves at a constant speed. The slave robot moves at the selected velocity, selected by a tradeoff between collision trend index and velocity reduction in one collision checking time, to keep moving as far as possible and as fast as possible while avoid possible collisions along the path. The collision trend index is a fusion of distance and relative velocity between links of two robots to reflect the possibility of collision at present and in the future. Graphic simulations of two PUMA560 robot arms working in common workspace but with independent goals are conducted. Simulations demonstrate the collision avoidance capability of the proposed approach as compared to the approach based on bounding volumes. It shows that advantage of our approach is less number of speed alterations required to react to potential collisions.