An underactuated mechanical system is generally a good test bed for advanced nonlinear controllers and can be applied to design a novel mechanical system with better energy efficiency and good controllability. It has been shown that the dynamics of many underactuated mechanical systems could be transformed into the chained canonical form. To improve the performance of the controllers presented in the literature, a novel controller design method is proposed in this paper. It is shown that the set-point stabilization problem of the second-order chained form systems can be changed into a trajectory-tracking problem based on the nonsmooth Hölder continuous feedback. By designing the tracked trajectory, the presented controller permits the achievement of exponential stability. Some numerical simulations demonstrate the stability of the proposed controller for an underactuated Hovercraft system.

In this paper, a new sensor-based approach called nonholonomic random replanner (NRR) is presented for motion planning of car-like mobile robots. The robot is incrementally directed toward its destination using a nonholonomic rapidly exploring random tree (RRT) algorithm. At each iteration, the robot's perceived map of the environment is updated using sensor readings and is used for local motion planning. If the goal was not visible to the robot, an approximate path toward the goal is calculated and the robot traces it to an extent within its sensor range. The robot updates its motion to goal through replanning. This procedure is repeated until the goal lies within the scope of the robot, after which it finds a more precise path by sampling in a tighter Goal Region for the nonholonomic RRT. Three main replanning strategies are proposed to decide when to perform a visibility scan and when to replan a new path. Those are named Basic, Deliberative and Greedy strategies, which yield different paths. The NRR was also modified for motion planning of Dubin's car-like robots. The proposed algorithm is probabilistically complete and its effectiveness and efficiency were tested by running several simulations and the resulting runtimes and path lengths were compared to the basic RRT method.

The dynamic model of an articulated vehicle consisting of one tractor and two semi-trailers is derived according to a systematic approach available in the literature. The model is produced on the assumption of no slippage, which enforces nonholonomic constraints. The resulting equations encompass a number of significant special cases.

Motion Planning and control of mobile vehicles with nonholonomic constraints are in their infancy. A systematic approach for modeling and base; motion control of a mobile vehicle is presented. A nonlinear coordinate transformation that takes into account the complete dynamics with nonholonomic constraints is used in order to obtain a linear system in space coordinates. An input-output feedback linearization inner loop is subsequently designed to transform this system into a linear-point mass system in the coordinates corresponding to the control objectives. A rigorous yet simple approach to motion planning through optimization techniques is presented for these mobile vehicles. The resulting Cartesian trajectory generated from the motion planning algorithm is employed as the reference trajectory in the outer loop, which is designed based on a Lyapunov function candidate. The net result is a base motion controller that gives capabilities to these mobile vehicles not only for tracking a Cartesian trajectory but also to achieve a desired final orientation (docking angle).

This paper is to investigate inherent oscillations problems of Potential Field Methods (PFMs) for nonholonomic robots in dynamic environments. In prior work, we proposed a modification of Newton's method to eliminate oscillations for omnidirectional robots in static environment. In this paper, we develop control laws for nonholonomic robots in dynamic environment using modifications of Newton's method. We have validated this technique in a multirobot search-and-forage task. We found that the use of the modifications of Newton's method, which applies anywhere C2 continuous navigation functions are defined, can greatly reduce oscillations and speed up robot's movement, when compared to the standard gradient approaches.

In this paper, we focus on the development of a quantitative performance analysis framework for a cooperative system of multiple wheeled mobile manipulators physically transporting a common payload. Each mobile manipulator module consists of a differentially driven wheeled mobile robot (WMR) with a mounted planar three-degree-of-freedom (DOF) revolute-jointed manipulator. A composite cooperative system is formed when a payload is placed at the end-effectors of many such modules. The system possesses the ability to change its relative configuration as well as to accommodate relative positioning errors of the wheeled agents. However, the combination of nonholonomic constraints due to the mobile bases, holonomic constraints due to the closed kinematic loops, and the different joint-actuation schema (active/passive/locked) within the system requires careful quantitative evaluation to efficiently realize the payload manipulation task. Hence, in this paper, we extend the differential kinematic model for treatment of constrained articulated mechanical systems to formulate a framework to include both the mixture effect of holonomic/nonholonomic constraints and the different possible joint-actuation schema in our system. The system-level performance is then examined quantitatively by the manipulability measure in terms of isotropy index with representative case studies.

This paper presents a recursive approach for solving kinematic and dynamic problems in snake-like robots using Kane's equations. An n-link model with n-nonholonomic constraints is used as the snake robot model in our analysis. The proposed algorithm which is used to derive kinematic and dynamic equations recursively, enhances the computational efficiency of our analysis. Using this method we can determine the number of additions and multiplications as a function of n. The proposed method is compared with the Lagrange and Newton-Euler's method in three different aspects: Number of operations, CPU time and error in the computational procedures.

This paper presents a novel time-optimal motion planning strategy for a mobile robot with kinematic constraints. The method works in environments in presence of obstacles, without needing to generate the configuration space for the robot. Further, it derives a minimum time first derivative smooth path, as opposed to a minimum distance path which is commonly given by various present solution techniques. The problem is solved in three stages: (i) A reduced visibility graph for a point object is obtained. (ii) The reduced visibility graph is converted into a feasible reduced visibility graph accounting for the size and kinematic constraints of the robot. (iii) The A* algorithm is used to search the feasible reduced visibility graph with the cost function being the time of travel, to obtain a safe, time-optimal, smooth path. The algorithm runs in polynomial time. The method has been tested in computer simulations and test results are presented