Nonprehensile Manipulation of an Underactuated Mechanical System With Second-Order Nonholonomic Constraints: The Robotic Hula-Hoop

A mechanical system consisting of a hoop and a pole is considered, for which the corresponding dynamic model represents an underactuated system subject to second-order nonholonomic constraints. The pursued goal is to simultaneously track a trajectory in the unactuated coordinates and to stabilize the actuated ones. For the model under consideration, the well-known noncollocated partial feedback linearization algorithm fails since the corresponding zero dynamics is unstable. In this work, we show that the actuated coordinates, i.e., the pole can be stabilized by exploiting the null space of the coupling inertia matrix without affecting the performance in the underactuated coordinates tracking. We present a formal mathematical analysis, which guarantees ultimate boundedness of all coordinates. Performed simulations bolster the proposed approach

Nonholonomic Hybrid Zero Dynamics for the Stabilization of Periodic Orbits: Application to Underactuated Robotic Walking

This brief addresses zero dynamics associated with relative degree one and two nonholonomic outputs for exponential stabilization of given periodic orbits for hybrid models of bipedal locomotion. Zero dynamics manifolds are constructed to contain the orbit while being invariant under both the continuous- and discrete-time dynamics. The associated restriction dynamics are termed the hybrid zero dynamics (HZD). Prior results on the HZD have mainly relied on input–output linearization of holonomic outputs and are referred to as holonomic HZD (H-HZD). This brief presents reduced-order expressions for the HZD associated with nonholonomic output functions referred to as nonholonomic HZD (NH-HZD). This brief systematically synthesizes NH-HZD controllers to stabilize periodic orbits based on a reduced-order stability analysis. A comprehensive study of H-HZD and NH-HZD is presented. It is shown that NH-HZD can stabilize a broader range of walking gaits that are not stabilizable through traditional H-HZD. The power of the analytical results is finally illustrated on a hybrid model of a bipedal robot through numerical simulations

Trajectory stabilization for a planar carangiform robot fish

Considers the task of trajectory stabilization for a fish-like robot by means of feedback. We use oscillatory control inputs and apply correction signals at the endpoints of each periodic input signal. Such a strategy can be proven to cause the system to converge to a desired trajectory. We present a specific model of a planar carangiform fish, and verify the stabilization results with simulations and with experiment on a planar robotic fish system that is propelled using carangiform-like movements

Dynamics and Control of Higher-order Nonholonomic Systems

A theoretical framework is established for the control of higher-order nonholonomic systems, defined as systems that satisfy higher-order nonintegrable constraints. A model for such systems is developed in terms of differential-algebraic equations defined on a higher-order tangent bundle. A number of control-theoretic properties such as nonintegrability, controllability, and stabilizability are presented. Higher-order nonholonomic systems are shown to be strongly accessible and, under certain conditions, small time locally controllable at any equilibrium. There are important examples of higher-order nonholonomic systems that are asymptotically stabilizable via smooth feedback, including space vehicles with multiple slosh modes and Prismatic-Prismatic-Revolute (PPR) robots moving open liquid containers, as well as an interesting class of systems that do not admit asymptotically stabilizing continuous static or dynamic state feedback. Specific assumptions are introduced to define this class, which includes important examples of robotic systems. A discontinuous nonlinear feedback control algorithm is developed to steer any initial state to the equilibrium at the origin. The applicability of the theoretical development is illustrated through two examples: control of a planar PPR robot manipulator subject to a jerk constraint and control of a point mass moving on a constant torsion curve in a three dimensional space

Control Based on Linear Algebra for Trajectory Tracking and Positioning of Second-Order Chained Form System

The development of controllers for underactuated systems with nonholonomic constraints has been a topic of significant interest for many researchers in recent years. These systems are hard to control because their linearization transform them into uncontrollable systems. The proposed approaches involve the use of a permanent excitation in the reference trajectory; coordinate transformation; discontinuities; or complex calculations. This paper proposes the design of the controller of the second-order chained form system for trajectory tracking by using a simpler approach based on linear algebra. Up to the present time, no controllers based on this approach have been designed for that system. The control problem is solved by setting two of the three systems variables as a reference, while the remaining variable is calculated imposing the condition that the equations system has an exact solution to ensure that tracking errors go to zero. The stability of the proposed controller is theoretically demonstrated, and simulations results show a suitable control system performance. Also, no coordinate transformation is necessary.Fil: Rodriguez Aguilar, Leandro Pedro Faustino. Universidad Nacional de San Juan. Facultad de Ingeniería. Instituto de Ingeniería Química; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; ArgentinaFil: Serrano, Mario Emanuel. Universidad Nacional de San Juan. Facultad de Ingeniería. Instituto de Ingeniería Química; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; ArgentinaFil: Sanchez, Mabel Cristina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; ArgentinaFil: Scaglia, Gustavo Juan Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentina. Universidad Nacional de San Juan. Facultad de Ingeniería. Instituto de Ingeniería Química; Argentin

Control Strategy Based on Fourier Transformation and Intelligent Optimization for Planar Pendubot

This paper presents a new control strategy based on Fourier transformation and intelligent optimization for a planar Pendubot with a passive second link, which can be treated as a second-order nonholonomic system whose control has been an open and challenging issue. A controller acting within a time corresponding to the frequency of its fundamental harmonic term is designed to realize the system control objective, which is to move the system from its initial position to the target position. By employing Fourier transformation, a general expression of the controller composed of a constant term and harmonic terms is obtained. Next, the constant term is obtained by the angular momentum theorem, and the particle swarm optimization algorithm is employed to obtain the harmonic terms of the controller. A feedback control strategy based on a nonlinear disturbance observer is then applied to overcome the uncertainties/disturbances in the system. Finally, simulation results prove the validity of this control method

Formation Control of Underactuated Bio-inspired Snake Robots

This paper considers formation control of snake robots. In particular, based on a simplified locomotion model, and using the method of virtual holonomic constraints, we control the body shape of the robot to a desired gait pattern defined by some pre-specified constraint functions. These functions are dynamic in that they depend on the state variables of two compensators which are used to control the orientation and planar position of the robot, making this a dynamic maneuvering control strategy. Furthermore, using a formation control strategy we make the multi-agent system converge to and keep a desired geometric formation, and enforce the formation follow a desired straight line path with a given speed profile. Specifically, we use the proposed maneuvering controller to solve the formation control problem for a group of snake robots by synchronizing the commanded velocities of the robots. Simulation results are presented which illustrate the successful performance of the theoretical approach.© ISAROB 2016. This is the authors' accepted and refereed manuscript to the article. Locked until 2017-07-27

Robust control of underactuated wheeled mobile manipulators using GPI disturbance observers

This article describes the design of a linear observer–linear controller-based robust output feedback scheme for output reference trajectory tracking tasks in the case of nonlinear, multivariable, nonholonomic underactuated mobile manipulators. The proposed linear feedback scheme is based on the use of a classical linear feedback controller and suitably extended, high-gain, linear Generalized Proportional Integral (GPI) observers, thus aiding the linear feedback controllers to provide an accurate simultaneous estimation of each flat output associated phase variables and of the exogenous and perturbation inputs. This information is used in the proposed feedback controller in (a) approximate, yet close, cancelations, as lumped unstructured time-varying terms, of the influence of the highly coupled nonlinearities, and (b) the devising of proper linear output feedback control laws based on the approximate estimates of the string of phase variables associated with the flat outputs simultaneously provided by the disturbance observers. Simulations reveal the effectiveness of the proposed approach

Operational Space Control for Planar PAN–1 Underactuated Manipulators Using Orthogonal Projection and Quadratic Programming

In this paper, we propose an operational space control formulation for a planar N-link underactuated manipulator (PA N–1 ) 1 with a passive first joint subject to actuator constraints (N ⩾ 3), covering both stabilization and tracking tasks. Such underactuated manipulators have an inherent first-order nonholonomic constraint, allowing us to project their dynamics to a space consistent with the nonholonomic constraint. Based on the constrained dynamics, we can design operational space controllers with respect to tasks assuming that all joints of the manipulator are active. Due to underactuation, we design a Quadratic Programming (QP) based controller to minimize the error between the desired torque commands and available motor torques in the null space of the constraint, as well as involve the constraint of motor outputs. The proposed control framework was demonstrated by stabilization and tracking tasks in simulations with both planar PA 2 and PA 3 manipulators. Furthermore, we verified the controller experimentally using a planar PA 2 robot

Nonlinear Control for Dual Quaternion Systems

The motion of rigid bodies includes three degrees of freedom (DOF) for rotation, generally referred to as roll, pitch and yaw, and 3 DOF for translation, generally described as motion along the x, y and z axis, for a total of 6 DOF. Many complex mechanical systems exhibit this type of motion, with constraints, such as complex humanoid robotic systems, multiple ground vehicles, unmanned aerial vehicles (UAVs), multiple spacecraft vehicles, and even quantum mechanical systems. These motions historically have been analyzed independently, with separate control algorithms being developed for rotation and translation. The goal of this research is to study the full 6 DOF of rigid body motion together, developing control algorithms that will affect both rotation and translation simultaneously. This will prove especially beneficial in complex systems in the aerospace and robotics area where translational motion and rotational motion are highly coupled, such as when spacecraft have body fixed thrusters. A novel mathematical system known as dual quaternions provide an efficient method for mathematically modeling rigid body transformations, expressing both rotation and translation. Dual quaternions can be viewed as a representation of the special Euclidean group SE (3). An eight dimensional representation of screw theory (combining dual numbers with traditional quaternions), dual quaternions allow for the development of control techniques for 6 DOF motion simultaneously. In this work variable structure nonlinear control methods are developed for dual quaternion systems. These techniques include use of sliding mode control. In particular, sliding mode methods are developed for use in dual quaternion systems with unknown control direction. This method, referred to as self-reconfigurable control, is based on the creation of multiple equilibrium surfaces for the system in the extended state space. Also in this work, the control problem for a class of driftless nonlinear systems is addressed via coordinate transformation. It is shown that driftless nonlinear systems that do not meet Brockett\u27s conditions for coordinate transformation can be augmented such that they can be transformed into the Brockett\u27s canonical form, which is nonholonomic. It is also shown that the kinematics for quaternion systems can be represented by a nonholonomic integrator. Then, a discontinuous controller designed for nonholonomic systems is applied. Examples of various applications for dual quaternion systems are given including spacecraft attitude and position control and robotics