The purpose of this paper is to design a stabilizing controller for a car with n connected trailers. The proposed control algorithm is constructed on the Lyapunov theory. In this paper, the purpose of navigating the system toward the desired point considering the slip phenomenon as a main source of uncertainty is analyzed. First mathematical models are presented. Then, a stabilizing control approach based on the Lyapunov theory is presented. Subsequently, an uncertainty estimator is taken into account to overcome the wheel slip effects. Obtained results show the convergence properties of the proposed control algorithm against the slip phenomenon.

A mobile manipulator system (MMS) consists of a robotic arm mounted on a mobile platform that is used in rescue and relief, space exploration, warehouse automation, etc. As the total system has 14 Degrees of Freedom (DOF), it does not have a closed-form inverse kinematics (IK) solution. A learning-based method is proposed, which uses the forward kinematics data to learn the IK relation for motion of an MMS on a rough terrain, using a one-class support vector machine (SVM) framework. Once trained, the model estimates the joint probability distribution of the MMS configuration and end-effector position. This distribution is used to find the MMS configuration for a given desired end-effector path. Past research using a Kohonen Self organizing map (KSOM) neural network-based open-loop control method has shown that the MMS deviates from its desired path while moving on an uneven terrain due to unknown disturbances such as wheel slip, slide, and terrain deformation. Therefore, a new sequential two-stage SVM-based end-effector path-tracking control scheme is proposed to control the end-effector path. In this scheme, the error in the end-effector path is continuously tracked with the help of a Microsoft Kinect 2.0 (Microsoft Regional Sales, Singapore 119968) and is sent as a feedback to the controller. Once the error reaches a threshold value, the error correction step of the controller gets activated to correct the error until the desired accuracy is reached. The effectiveness of the proposed approach is proved through extensive simulations and experiments conducted on 3D terrain in which it is shown that the end effector can follow the desired path with an average experimental error of around 2 cm between the desired and final corrected path.

With rapid development of methods for dynamic systems modeling, those with less computation effort are becoming increasingly attractive for different applications. This paper introduces a new form of Kane's equations expressed in the matrix notation. The proposed form can efficiently lead to equations of motion of multi-body dynamic systems particularly those exposed to large number of nonholonomic constraints. This approach can be used in a recursive manner resulting in governing equations with considerably less computational operations. In addition to classic equations of motion, an efficient matrix form of impulse Kane formulations is derived for systems exposed to impulsive forces.

This paper considers a problem of tracking control design for different types of nonholonomic mobile manipulators. The mobile platform is in form of a unicycle. In the first step, an input–output decoupling controller is developed. The proposed selection of output functions is in more general form than the output functions previously introduced by others [Yamamoto and Yun]. It makes possible to move simultaneously, the mobile platform and the manipulator built on it. Regularity conditions that guarantee the existence of the input–output decoupling control law are presented. In the second step, trajectory and path tracking controllers are formulated and presented. Theoretical considerations are illustrated with simulations for the mobile manipulator consisting of a vertical, three degree of freeedom (DOF) pendulum (with holonomic or nonholonomic drives) mounted atop of a unicycle.