Nonholonomic Behavior Research Articles

A Staged Finite‐Time Control Strategy for Formation of Underactuated Unmanned Surface Vehicles

The formation control issue for a group of underactuated unmanned surface vehicles (USVs) is discussed in the paper, and a staged finite‐time control strategy for the USVs is proposed. Firstly, we try to steer each USV to its own starting point in the formation for a limited time, under the initial condition that each of these vehicles is parked at random. To deal with the nonholonomic behavior of the system, the dynamics of the USV is transformed into cascade systems. Then, the finite‐time controller is designed for each vehicle based on homogeneity theory. After each USV reaches its own starting point with desired orientation, the model of the vehicle is decomposed into two subsystems under the Serret‐Frenet frame. In order to maintain the formation pattern, two finite‐time distributed controllers are developed for the surge subsystem and the yaw subsystem, respectively. The settling time for the staged control strategy is limited. Numerical simulations are carried out to illustrate the effectiveness of the proposed formation control strategy.

Dynamic Compensation Based Control of a Comprehensive Model of Wheeled Mobile Robots

This paper uses the general framework of dynamic feedback linearization for stabilization of mobile robots. Instead of using unicycle model for control design, this paper uses a comprehensive model which is based on the physics of differential drive robots. The model used in the paper describes nonholonomic underactuated behavior of robot in terms of the physical dimensions and velocities of the wheels. Next, the proposed control is applied to this model and it is theoretically proven that dynamic feedback linearization can successfully solve the stabilization problem. To evaluate the performance of proposed control, another controller is designed based on the Lyapunov's method. The performance of the two controllers and the complexity of control gain tuning process are compared. Next, the robustness of the proposed control against uncertainties is studied. The results of analysis and simulations show that the proposed control has very good performance against parametric uncertainties.

Dual Arm Free Flying Space Robot Trajectory Planning Using Polynomial

The paper presents path planning of dual arm free flying space robot using smooth functions of time. Kinematic and dynamic modeling of dual arm free flying space robot is presented first. Using kinematic model, the Jacobian of the system has been derived, and using dynamic model, equations of motion are derived. A path planning methodology for planar system is developed using smooth function of time such as polynomials. Due to nonholonomic behaviour of the manipulator in the zero gravity environment linear and angular momentum is conserved. The proposed method yields input trajectories that drive both the manipulator and the base to a desired configuration. Joint torque curves can be obtained by introducing this joint trajectory curves in equation of motion of the space robot.

On the use of free-floating space robots in the presence of angular momentum

Free-floating space manipulator systems include at least one manipulator mounted on an unactuated spacecraft. It is known that such systems exhibit nonholonomic behavior due to angular momentum conservation. In this paper, the initial angular momentum of the system is not assumed to be zero and its influence on system behavior is studied. In contrast to the case of zero initial momentum, in the presence of momentum, the manipulator end effector in general cannot remain at a given location for indefinite time. The paper studies the conditions under which this is possible, rendering the end-effector immune to angular momentum accumulation. The relevant kinematics and dynamics are studied in 2D and 3D systems, and workspace subsets, where the end effector can remain fixed, are identified. Examples illustrate the validity of the results.

An Optimal Control-Based Formulation to Determine Natural Locomotor Paths for Humanoid Robots

In this paper we explore the underlying principles of natural locomotion path generation of human beings. The knowledge of these principles is useful to implement biologically inspired path planning algorithms on a humanoid robot. By 'locomotion path' we denote the motion of the robot as a whole in the plane. The key to our approach is to formulate the path planning problem as an optimal control problem. We propose a single dynamic model valid for all situations, which includes both non-holonomic and holonomic modes of locomotion, as well as an appropriately designed unified objective function. The choice between holonomic and non-holonomic behavior is not accomplished by a switching model, but it appears in a smooth way, along with the optimal path, as a result of the optimization by efficient numerical techniques. The proposed model and objective function are successfully tested in six different locomotion scenarios. The resulting paths are implemented on the HRP-2 robot in the simulation environment OpenHRP as well as in the experiment on the real robot.

On point-to-point motion planning for underactuated space manipulator systems

In free-floating mode, space manipulator systems have their actuators turned off, and exhibit nonholonomic behavior due to angular momentum conservation. The system is underactuated and a challenging problem is to control both the location of the end effector and the attitude of the base, using manipulator actuators only. Here a path planning methodology satisfying this requirement is developed. The method uses high order polynomials, as arguments in cosine functions, to specify the desired path directly in joint-space. In this way, the accessibility of final configurations is extended drastically, and the free parameters are determined by optimization techniques. It was found that this approach leads always to a path, provided that the desired change in configuration lies between physically permissible limits. Physical limitations, imposed by system’s dynamic parameters, are examined. Lower and upper bounds for base rotation, due to manipulator motions, are estimated and shown in the implementation section. The presented method avoids the need for many small cyclical motions, and uses smooth functions in the planning scheme, leading to smooth configuration changes in finite and prescribed time.

Nonholonomic behavior in redundant robots under kinematic control

We analyze the behavior of redundant robots when the joint motion is generated by inverting task velocity commands through a kinematic control scheme. Depending on the chosen inversion scheme, the robot motion is subject to differential constraints that may or may not be integrable. Accordingly, we give a classification in terms of holonomic, partially nonholonomic, and completely nonholonomic behavior, pointing out also the relationship with the so-called cyclicity property. This general classification is illustrated by means of several examples. When the kinematic control scheme is nonholonomic, the whole configuration space of the robot is accessible by a proper choice of the task input commands. Under this assumption, we address the joint reconfiguration problem, namely the design of end-effector velocity commands that drive the robot to a desired joint configuration. To solve this problem, it is possible to borrow existing methods for motion planning of nonholonomic mechanical systems, such as the sinusoidal steering technique for chained-form systems.

Free-floating closed-chain planar robots: Kinematics and path planning

The study of free-floating manipulators is important for the success of robotics program in space and in the design of innovative robot systems which can operate over a large workspace. In order to study the fundamental theoretical and experimental issues encountered in space robotics, a closed-chain planar manipulator was built at Ohio University (OU) which floats on a flat table using air bearings. Due to the absence of external forces in the plane of the table and couples normal to this plane, the linear momentum in the plane and the angular momentum normal to this plane are conserved. It is well known that the linear momentum equations are holonomic while the angular momentum equation is nonholonomic. Due to this nonholonomic behavior, the path-planning schemes commonly used for fixed-base manipulators do not directly apply to free-floating manipulators. In this paper, we present an algorithm for motion planning of planar free-floating manipulators based on the inverse position kinematics of the mechanism. It is demonstrated that the inverse position kinematics algorithms, commonly used for fixed-base manipulators, can be successfully applied to free-floating manipulators using an iterative search procedure to satisfy the nonholonomic angular momentum constraints. This procedure results in paths identical to those predicted by inverse rate kinematics. The inverse position kinematics algorithm is then used to avoid singularities during motion to result in successful paths. The results of the simulation of this algorithm using parameter estimates of the OU free-floating robot are presented.

A developed algorithm for the inelastic analysis of reinforced concrete frames

A mathematical algorithm is developed and presented for use in conjunction with the Imposed Rotation Method as reformulated by Kaneko as a ( n ∗ 2n) linear complementarity problem. The inelastic tri-linear moment rotation law which is modelled to reflect behaviour at critical sections is adjusted during the incremental analysis in order to adhere to the non-holonomic behaviour of reinforced concrete when stress unloading occurs. The developed algorithm also incorporates the two relevant failure criteria, namely local failure and failure by the formation of a collapse mechanism. A typical reinforced concrete frame is analyzed under different load combinations to show the features of the developed algorithm.

Optimal control of a satellite-robot system using direct collocation with non-linear programming

The non-holonomic behavior of a satellite-robot system is used to develop the system's equations of motion. The resulting non-linear differential equations are transformed into a non-linear programming problem using direct collocation. The link rates of the robot are minimized along optimal reorientations. Optimal solutions to several maneuvers are obtained and the results are interpreted to gain an understanding of the satellite-robot dynamics.

The swing up control problem for the Acrobot

Underactuated mechanical systems are those possessing fewer actuators than degrees of freedom. Examples of such systems abound, including flexible joint and flexible link robots, space robots, mobile robots, and robot models that include actuator dynamics and rigid body dynamics together. Complex internal dynamics, nonholonomic behavior, and lack of feedback linearizability are often exhibited by such systems, making the class a rich one from a control standpoint. In this article the author studies a particular underactuated system known as the Acrobot: a two-degree-of-freedom planar robot with a single actuator. The author considers the so-called swing up control problem using the method of partial feedback linearization. The author gives conditions under which the response of either degree of freedom may be globally decoupled from the response of the other and linearized. This result can be used as a starting point to design swing up control algorithms. Analysis of the resulting zero dynamics as well as analysis of the energy of the system provides an understanding of the swing up algorithms. Simulation results are presented showing the swing up motion resulting from partial feedback linearization designs.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Optimal design of reinforced concrete frames based on inelastic analysis

A new algorithm is presented for use in conjunction with the imposed rotation method as reformulated by Kaneko as a ( n × 2 n) linear complementarity problem. The inelastic trilinear moment rotation law, which is modelled to reflect behaviour at critical sections, is adjusted during the incremental analysis in order to adhere the non-holonomic behaviour of reinforced concrete (RC) when stress unloading occurs. The algorithm is utilized in performing inelastic analysis for the optimal design of RC frames. Optimum concrete dimensions and reinforcement are evaluated for minimum cost. Optimization, following the multilevel approach, is carried out on typical frames using SUMT and Rosenbrock minimization methods.

Nonuniqueness in Elastoplastic Frames

Lack of uniqueness of the kinematic solution of elastoplastic flexural frames is studied by deriving a general solution for nonholonomic behavior. A singular hinge set is defined as a collection of plastic hinges that would form a mechanism if they were replaced by mechanical hinges. It is shown that whenever singular subsets can be found among active plastic hinges, the kinematic solution may become nonunique. The rate of work done by the load rates on the contributing mechanisms must be zero if a prevailing nonuniqueness is to sustain.