This paper addresses the robust trajectory tracking problem for a redundantly actuated omnidirectional mobile manipulator in the presence of uncertainties and disturbances. The development of control algorithms is based on sliding mode control (SMC) technique. First, a dynamic model is derived based on the practical omnidirectional mobile manipulator system. Then, a SMC scheme, based on the fixed large upper boundedness of the system dynamics (FLUBSMC), is designed to ensure trajectory tracking of the closed-loop system. However, the FLUBSMC scheme has inherent deficiency, which needs computing the upper boundedness of the system dynamics, and may cause high noise amplification and high control cost, particularly for the complex dynamics of the omnidirectional mobile manipulator system. Therefore, a robust neural network (NN)-based sliding mode controller (NNSMC), which uses an NN to identify the unstructured system dynamics directly, is further proposed to overcome the disadvantages of FLUBSMC and reduce the online computing burden of conventional NN adaptive controllers. Using learning ability of NN, NNSMC can coordinately control the omnidirectional mobile platform and the mounted manipulator with different dynamics effectively. The stability of the closed-loop system, the convergence of the NN weight-updating process, and the boundedness of the NN weight estimation errors are all strictly guaranteed. Then, in order to accelerate the NN learning efficiency, a partitioned NN structure is applied. Finally, simulation examples are given to demonstrate the proposed NNSMC approach can guarantee the whole system's convergence to the desired manifold with prescribed performance.

Trajectory Tracking Control of Omnidirectional Wheeled Mobile Manipulators: Robust Neural Network-Based Sliding Mode Approach

We formulate control problems of mechanical systems as constraint following. The system contains uncertainty which is (possibly fast) time-varying. It is unknown but bounded. The bound is, however, unknown. The objective is to design control which renders approximate constraint following. Adaptive laws are constructed. The controls are then based on the adaptive parameters. We are able to demonstrate guaranteed system performance, regardless of the uncertainty.

Adaptive robust approximate constraint-following control for mechanical systems

Descriptions of real-life complex multibody mechanical systems are usually uncertain. Two sources of uncertainty are considered in this paper: uncertainties in the knowledge of the physical system and uncertainties in the “given” forces applied to the system. Both types of uncertainty are assumed to be time varying and unknown, yet bounded. In the face of such uncertainties, what is available in hand is therefore just the so-called “nominal system,” which is our best assessment and description of the actual real-life situation. A closed-form equation of motion for a general dynamical system that contains a control force is developed. When applied to a real-life uncertain multibody system, it causes the system to track a desired reference trajectory that is prespecified for the nominal system to follow. Thus, the real-life system’s motion is required to coincide within prespecified error bounds and mimic the motion desired of the nominal system. Uncertainty is handled by a controller based on a generalization of the concept of a sliding surface, which permits the use of a large class of control laws that can be adapted to specific real-life practical limitations on the control force. A set of closed-form equations of motion is obtained for nonlinear, nonautonomous, uncertain, multibody systems that can track a desired reference trajectory that the nominal system is required to follow within prespecified error bounds and thereby satisfy the constraints placed on the nominal system. An example of a simple mechanical system demonstrates the efficacy and ease of implementation of the control methodology. [DOI: 10.1115/1.4025399]

Control of Uncertain Nonlinear Multibody Mechanical Systems

This chapter presents a new approach for the tracking control of uncertain mechanical systems. Real-life multi-body systems are in general highly nonlinear and modeling them is intrinsically error prone due to uncertainties related to both their description and the description of the various forces that they may be subjected to. As such, in the modeling of such systems one only has in hand the so-called nominal system—a model based upon our best assessment of the system and our best assessment of the generalized forces acting on it. Uncertainties that are time-varying, unknown but bounded, are assumed in this chapter, and a new approach to the development of a closed-form controller is developed. The approach uses the concept of a generalized sliding surface. Its closed-form approach can guarantee, regardless of the uncertainty, that the uncertain system can track a desired reference trajectory that the nominal system is required to follow. An example of a simple multi-body system whose description is known only imprecisely is illustrated showing the simplicity of the approach and its efficacy in tracking the trajectory of the nominal system. The approach is easily implemented for a wide range of complex multi-body mechanical systems.

A New Approach to the Tracking Control of Uncertain Nonlinear Multi-body Mechanical Systems

This paper describes robot motion planning in a very dynamic environment, that is, a trajectory generation to attain a working purpose with redundancy freedom to use under the restriction of time and space. In particular, we focus on "juggling" as the typical example of such a task. We will describe a parametric representation of the robot motion which makes it easy to generate the appropriate trajectory of the end-effector for the "juggling" task. Also, we will describe a hierarchical learning control strategy which is effective in generating a desired motion pattern for juggling which has not been previously taught to the robot. For an actual robtot juggling several balls, we predict the location and time at which a ball is caught using sensory feedback signals and modify the end-tip trajectory. Experimental results obtained using a 2-d. o. f. direct-drive manipulator are also presented.

Robot Motion Planning and Control for Moving Objects.

This paper addresses the robust trajectory tracking problem for a general class of nonholonomic systems with velocity constraints in the presence of uncertainties. The development of the proposed algorithm is based on sliding mode control technique. First, for the purpose of designing controllers, the conservative upper-bounded function of dynamics model of nonholonomic systems is derived based on the dynamics structure properties. Then, a sliding mode control scheme is presented to guarantee trajectory tracking of closed-loop system. The asymptotical or exponential stability is obtained in the Lyapunov sense. Finally, simulation examples are given to demonstrate the proposed approach.

Zuozhi Song

Papers

Robust motion control for nonholonomic constrained mechanical systems: sliding mode approach