In this paper, we propose a robust controller for the tracking of robot motion. This controller is a nonlinear-based controller that compensates for the uncertainties present in the manipulator dynamic equation. The main result of this paper is that we explicitly show how the response of the tracking error can be modified by adjusting the control parameters. The corresponding stability result for the tracking error is Global Exponential Stability (GES). We then illustrate how similar control approaches are related to the proposed controller. Finally, simulation and experimental results are utilized to illustrate the performance of the robust controller.

This paper proposes a fast tracking error control method for a mobile robot with two differentially driven wheels. The tracking error between reference state and current state is transformed to the required displacement changes of each drive wheel by a wheel Jacobian. The major objective of this paper is to propose a control method for eliminating the tracking error quickly by controlling two independent driving wheels at the same time. To avoid long computational requirements of a Cartesian-based control, a kinematic model of the vehicle and co-ordinate system are introduced. Several simulation results are presented using this method. The fast tracking error control method proposed is mainly hardware-independent and Hence can be applied to various kinds of mobile robots which have two differentially driven wheels. The method was implemented on an experimental vehicle, WCVS, The experimentation shows a performance suitable for practical applications.

A modeling method for robots is proposed, in which a convex polyhedron is represented as a set of inequalities and a robot is represented as a union of convex polyhedrons. With this method, collision between robots can be detected by solving a set of linear programming problems at every sampling instant. By detecting possible collision at every sampling instant, a directed graph for robots is created. The motion planning problem of robots is then transformed into a path searching problem in the directed graph and can be solved by exisiting searching algorithms.

It is shown that if one comes back to the formulation of the Hamilton's variational principle, it is then possible to obtain new viewpoints on the tracking control of robot manipulators. First, the Lagrange multiplier associated to the sliding surface can be interpretated in terms of control effort and/or forces of reaction of the mechanical system. Secondly, one can use the Taylor expansion of the mechanical Lagrangian, combined with a neighbour- ing Hamilton's principle, to obtain control schemes via sliding surfaces. Thirdly, a perturbation approach combined with the neighbouring Hamilton's principle provides results on the robustness of the control.

In this paper, we investigate the crab gaits of a quadruped. Some important characteristics that simplify the analysis of crab gaits are presented, and several formulas for optimizing the longitudinal gait stability margin of a quadruped crab gait are derived by incorporating the time weighting factor. The analysis and implementation of the gait have been simplified by employing a pseudo-world coordinate frame as a reference frame for describing footholds and vehicle's motion. We also suggest a unique gait which optimizes gait stability margin according to the range of crab angle. Finally, we consider the effects of variations of footholds on stability and maximum permissible stroke in terms of support boundary angle. The results derived in this paper contain previous works on the forward walking gait as a special case of the crab gait.

A method is presented to perform path planning in the Cartesian space. The motion velocity and acceleration are continuous. This is the first polynomial path planning algorithm in the Cartesian space working in real-time; it does not need an advanced knowledge of the trajectory and can be used when knot points are provided on-line by a sensor. The Bézier representation is used to compute a fifth degree polynomial path. It has been tested on an industrial robot controller.

In this study, highly practical and reliable methods are proposed to determine arm solutions for a six-link robot manipulator. Based on a typical mathematical structure of minimizing an objective function, the optimization theory is applied to solve a reduced system of kinematic equations. The performance tests show that three different approaches are superior to a conventional method and of sufficiently practical use. Especially, the use of an algorithm presented in a linear search is promising.

A method is presented for generating the path which significantly reduces residual vibration. The desired path is optimally designed so that the system completes the required move with minimum residual vibration. The dynamic model and optimal path are effectively formulated and computed by using special moving coordinates, called virtual rigid link coordinates, to represent the link flexibilities. Also joint compliances are included in the model. Characteristics of residual vibration are identified from the linearized equations of motion. From these results, the performance index is selected to reduce residual vibration effectively. The path to be designed is developed by a combined Fourier series and polynomial function to satisfy both the convergence and boundary condition matching problems. The concept of correlation coefficients is used to select the minimum number of design variables, i.e. Fourier coefficients, the only ones which have a considerable effect on the reduction of residual vibration. A two-link manipulator is used to evaluate this method. Results show that residual vibration can be drastically reduced by selecting an appropriate manipulator path.

Present study on industrial manipulator control either completely neglects structural flexibility or only considers manipulator link flexibility. Ignoring joint flexibility may cause significant errors in gross motion control if the joint elastic effect is predominant. This paper presents an effective control scheme which can compensate for the motion errors generated by simultaneous existence of both link and joint flexibility. The manipulator dynamics is formulated comprehensively by a superposition of two models, namely, an assumed modes of vibration model for links and a torsional spring model.for joints. Then, a nonlinear feedback rate servo control system is developed that compensates for the gross motion errors introduced by both joint elasticity and link flexibility. Motion simulation results show that the proposed formulation can effectively describe the dynamic behavior of a flexible-link, elastic-joint robot. They also verify that the proposed controller is robust in that it can satisfactorily suppress the manipulator end oscillations and yield an accurate gross motion.