Optimal Motion Planning for Differentially Flat Underactuated Mechanical Systems

Underactuated mechanical system has less independent inputs than the degrees of freedom（DOF） of the mechanism. The energy efficiency of this class of mechanical systems is an essential problem in practice. On the basis of the sufficient and necessary condition that concludes a single input nonlinear system is differentially flat, it is shown that the flat output of the single input underactuated mechanical system can be obtained by finding a smooth output function such that the relative degree of the system equals to the dimension of the state space. If the flat output of the underactuated system can be solved explicitly, and by constructing a smooth curve with satisfying given boundary conditions in fiat output space, an energy efficiency optimization method is proposed for the motion planning of the differentially flat underactuated mechanical systems. The inertia wheel pendulum is used to verify the proposed optimization method, and some numerical simulations show that the presented optimal motion planning method can efficaciously reduce the energy cost for given control tasks.

Adaptive Proportional-Derivative Sliding Mode Control Law With Improved Transient Performance for Underactuated Overhead Crane Systems

In this paper, an adaptive proportional-derivative sliding mode control(APD-SMC) law, is proposed for 2D underactuated overhead crane systems. The proposed controller has the advantages of simple structure, easy to implement of PD control, strong robustness of SMC with respect to external disturbances and uncertain system parameters, and adaptation for unknown system dynamics associated with the feedforward parts. In the proposed APD-SMC law, the PD control part is used to stabilize the controlled system, the SMC part is used to compensate the external disturbances and system uncertainties,and the adaptive control part is utilized to estimate the unknown system parameters. The coupling behavior between the trolley movement and the payload swing is enhanced and, therefore, the transient performance of the proposed controller is improved.The Lyapunov techniques and the La Salle's invariance theorem are employed in to support the theoretical derivations. Experimental results are provided to validate the superior performance of the proposed control law.

Second-order Sliding Mode Approaches for the Control of a Class of Underactuated Systems

In this paper, first-order and second-order sliding mode controllers for underactuated manipulators are proposed. Sliding mode control(SMC) is considered as an effective tool in different studies for control systems. However, the associated chattering phenomenon degrades the system performance. To overcome this phenomenon and track a desired trajectory, a twisting, a supertwisting and a modified super-twisting algorithms are presented respectively. The stability analysis is performed using a Lyapunov function for the proposed controllers. Further, the four different controllers are compared with each other. As an illustration, an example of an inverted pendulum is considered. Simulation results are given to demonstrate the effectiveness of the proposed approaches.

Swing Suppression and Accurate Positioning Control for Underactuated Offshore Crane Systems Suffering From Disturbances

Offshore cranes are widely applied to transfer largescale cargoes and it is challenging to develop effective control for them with sea wave disturbances. However, most existing controllers can only yield ultimate uniform boundedness or asymptotical stability results for the system's equilibrium point, and the state variables' convergence time cannot be theoretically guaranteed. To address these problems, a nonlinear sliding mode-based controller is suggested to accurately drive the boom/rope to their desired positions. Simultaneously, payload swing can be eliminated rapidly with sea waves. As we know, this paper firstly presents a controller by introducing error-related bounded functions into a sliding surface, which can realize boom/rope positioning within a finite time, and both controller design and analysis based on the nonlinear dynamics are implemented without any linearization manipulations. Moreover, the stability analysis is theoretically ensured with the Lyapunov method. Finally, we employ some experiments to validate the effectiveness of the proposed controller.

Differential flatness-based distributed control of underactuated robot swarms

This paper proposes a distributed control method based on the differential flatness(DF) property of robot swarms. The swarm DF mapping is established for underactuated differentially flat dynamics, according to the control objective. The DF mapping refers to the fact that the system state and input of each robot can be derived algebraically from the flat outputs of the leaders and the cooperative errors and their finite order derivatives. Based on the proposed swarm DF mapping, a distributed controller is designed. The distributed implementation of swarm DF mapping is achieved through observer design. The effectiveness of the proposed method is validated through a numerical simulation of quadrotor swarm synchronization.

MOTION CONTROL OF A CLASS OF UNDERACTUATED MECHANICAL SYSTEMS: THE ACROBOT EXAMPLE

Presents a control strategy for underactuated mechanical system: the acrobot example, which combines fuzzy control and linear quadratic control. The fuzzy controller designed for the upswing ensures that the energy of the acrobot increases with each swing. After the acrobot enters a neighborhood of the unstable straight up equilibrium position, a linear quadratic regulator is designed to balance it.

A Systematic Approach for Designing Analytical Dynamics and Servo Control of Constrained Mechanical Systems

A systematic approach for designing analytical dynamics and servo control of constrained mechanical systems is proposed. Fundamental equation of constrained mechanical systems is first obtained according to Udwadia-Kalaba approach which is applicable to holonomic and nonholonomic constrained systems no matter whether they satisfy the D’Alember’s principle.The performance specifications are modeled as servo constraints.Constraint-following servo control is used to realize the servo constraints. For this inverse dynamics control problem, the determination of control inputs is based on the Moore-Penrose generalized inverse to complete the specified motion. Secondorder constraints are used in the dynamics and servo control.Constraint violation suppression methods can be adopted to eliminate constraint drift in the numerical simulation. Furthermore,this proposed approach is applicable to not only fully actuated but also underactuated and redundantly actuated mechanical systems. Two-mass spring system and coordinated robot system are presented as examples for illustration.

An Anthropomorphic Robot Hand Developed Based on Underactuated Mechanism and Controlled by EMG Signals

When developing a humanoid myo-control hand,not only the mechanical structure should be considered to afford a high dexterity,but also the myoelectric (electromyography,EMG) control capability should be taken into account to fully accomplish the actuation tasks.This paper presents a novel humanoid robotic myocontrol hand (AR hand Ⅲ) which adopted an underac- tuated mechanism and a forearm myocontrol EMG method.The AR hand Ⅲ has five fingers and 15 joints,and actuated by three embedded motors.Underactuation can be found within each finger and between the rest three fingers (the middle finger,the ring finger and the little finger) when the hand is grasping objects.For the EMG control,two specific methods are proposed:the three-fingered hand gesture configuration of the AR hand Ⅲ and a pattern classification method of EMG signals based on a statistical learning algorithm-Support Vector Machine (SVM).Eighteen active hand gestures of a testee are recognized ef- fectively,which can be directly mapped into the motions of AR hand Ⅲ.An on-line EMG control scheme is established based on two different decision functions:one is for the discrimination between the idle and active modes,the other is for the recog- nition of the active modes.As a result,the AR hand Ⅲ can swiftly follow the gesture instructions of the testee with a time delay less than 100 ms.

Optimal reorientation of underactuated spacecraft using genetic algorithm with wavelet approximation

The optimal attitude control of an underactuated spacecraft is investigated in this paper. The flywheels of the spacecraft can somehow only provide control inputs in two independent directions. The dynamic equations are formulated for the spacecraft under a nonholonomic constraint resulting from the constant time-rate of the total angular momentum of the system. The reorientation of such underactuated spacecraft is transformed into an optimal control problem. A genetic algorithm is proposed to derive the control laws of the two flywheels angle velocity inputs. The control laws are approximated by the discrete orthogonal wavelets. The numerical simulations indicate that the genetic algorithm with the wavelet approximation is an effective approach to deal with the optimal reorientation of underactuated spacecraft.

SELF-RECONFIGURATION OF UNDERACTUATED REDUNDANT MANIPULATORS WITH OPTIMIZING THE FLEXIBILITY ELLIPSOID

The multi-modes feature, the measure of the manipulating flexibility, andself-reconfiguration control method of the underactuated redundant manipulators are investigatedbased on the optimizing technology. The relationship between the configuration of the joint spaceand the manipulating flexibility of the underactuated redundant manipulator is analyzed, a newmeasure of manipulating flexibility ellipsoid for the underactuated redundant manipulator withpassive joints in locked mode is proposed, which can be used to get the optimal configuration forthe realization of the self-reconfiguration control. Furthermore, a time-varying nonlinear controlmethod based on harmonic inputs is suggested for fulfilling the self-reconfiguration. A simulationexample of a three-DOFs underactuated manipulator with one passive joint features some aspects ofthe investigations.

A New Grasping Mode Based on a Sucked-type Underactuated Hand

Robot hands have been developing during the last few decades. There are many mechanical structures and analyti?cal methods for di erent hands. But many tough problems still limit robot hands to apply in homelike environment. The ability of grasping objects covering a large range of sizes and various shapes is fundamental for a home service robot to serve people better. In this paper, a new grasping mode based on a novel sucked?type underactuated(STU) hand is proposed. By combining the flexibility of soft material and the e ect of suction cups, the STU hand can grasp objects with a wide range of sizes, shapes and materials. Moreover, the new grasping mode is suitable for some situations where the force closure is failure. In this paper, we deduce the e ective range of sizes of objects which our hand using the new grasping mode can grasp. Thanks to the new grasping mode, the ratio of grasping size between the biggest object and the smallest is beyond 40, which makes it possible for our robot hand to grasp diverse objects in our daily life. For example, the STU hand can grasp a soccer(220 mm diameter, 420 g) and a fountain pen(9 mm diameter, 9 g). What’s more, we use the rigid body equilibrium conditions to analysis the force condition. Experiment evaluates the high load capacity, stability of the new grasping mode and displays the versatility of the STU hand. The STU hand has a wide range of applications especially in unstructured environment.

Adaptive robust dissipative designs on straight path control for underactuated ships

An adaptive robust control algorithm for ship straight path control system in the presence of both modeling uncertainties and the bounded disturbances is proposed. Motivated by the backstepping approach, the algorithm is developed by using the dissipation theory, such that the resulting dosed-loop system is both strictly dissipative and asymptotically adaptively stable for all admissible uncertainties. Also, it is able to steer an underactuated ship along a prescribed straight path with ultimate bounds under external disturbances induced by wave, wind and ocean current. When there are no disturbances, the straight path control can be implemented in a locally asymptotically stable manner. Simulation results on an ocean-going training ship ‘YULONG＇ are presented to validate the effectiveness of the algorithm.

Path following control of underactuated ships based on nonswitch analytic model predictive control

A path following controller is developed for underactuated ships with only surge force and yaw moment available to follow a predefined path.The proposed controller is based on nonswitch analytic model predictive control.It is shown that the optimal control law for a nonlinear path following system with ill-defined relative degree is continuous and nonsingular.The problem of ill-defined relative degree is solved.The path-following ability of the nonlinear system is guaranteed.Numerical simulations are provided to demonstrate the effectiveness of the proposed control law.

Design Considerations for an Underactuated Robotic Finger Mechanism

A design approach is presented in this paper for underactuation in robotic finger mechanisms. The characters of underactuated finger mechanisms are introduced as based on linkage and spring systems. The feature of self-adaptive enveloping grasp by underactuated finger mechanisms is discussed with feasible in grasping unknown objects. The design problem of robotic fingers is analyzed by looking at many aspects for an optimal functionality. Design problems and requirements for underactuated mechanisms are formulated as related to human-like robotic fingers. In particular, characteristics of finger mechanisms are analyzed and optimality criteria are summarized with the aim to formulate a general design algorithm. A general multi-objective optimization design approach is applied as based on a suitable optimization problem by using suitable expressions of optimality criteria. An example is illustrated as an improvement of finger mechanism in Laboratory of Robotics and Mechatronics （LARM） Hand. Results of design outputs and grasp simulations are reported with the aim to show the practical feasibility of the proposed concepts and computations.

Controllability of an underactuated spacecraft with one thruster under disturbance

For an underactuated spacecraft using only one thruster, the attitude controllability with respect to the or- bit frame is studied in the presence of periodical oscillation disturbance, which provides a preconditional guide on de- signing control law for underactuated attitude control sys- tem. Firstly, attitude dynamic model was established for an underactuated spacecraft, and attitude motion was described using the special orthogonal group （SO （3））. Secondly, Liou- ville theorem was used to confirm that the flow generated by the drift vector of the underactuated attitude control system is volume-preserving. Furthermore, according to Poincar6＇s re- currence theorem, we draw conclusions that this drift field is weakly positively poisson stable （WPPS）. Thirdly, the suffi- cient and necessary condition of controllability was obtained on the basis of lie algebra rank condition （LARC）. Finally, the controllable conditions were analyzed and simulated in different cases of inertia matrix with the installed position of thruster.

Bottom-following control for an underactuated unmanned undersea vehicle using integral-terminal sliding mode control

The bottom-following problem of an underactuated unmanned undersea vehicle(UUV) is addressed. A robust nonlinear controller is developed by using integral-terminal sliding mode control(ITSMC), which can exponentially drive an UUV onto a predefined path at a constant forward speed. The kinematic error equations are first derived in the Serret-Frenet frame. Using the line of sight(LOS) method, Lyapunov's direct technique and tracking differentiator, the guidance law is established. Then, the kinematic controller, the guidance law, is expanded to cope with vehicle dynamics by resorting to introduce two integral-terminal sliding surfaces. Robustness to parameter perturbation is addressed by incorporating the reaching laws associated with the upper bound of the parameter perturbation. The proposed control law can guarantee that all error signals globally exponentially converge to the origin. Finally, a series of numerical simulation results are presented and discussed. In these simulations, wave, constant unknown ocean currents(for the purposes of the controller) and the parameter perturbation are added to illustrate the robustness and effectiveness of the bottom-following control scheme.

A Cascade Approach for Global Trajectory Tracking Control of Underactuated AUVs

A global trajectory tracking controller is presented for underactuated AUVs with only surge force and yaw moment in the horizontal plane. A transformation is introduced to represent the tracking error system into a cascade form. The global and uniform asymptotic stabilization problem of the resulting cascade system is reduced to the stabilization problem of two subsystems by use of the cascade approach. For the stabilization of the subsystem involving the yaw moment, a control law is proposed based on the feedback linearization method. Another subsystem is stabilized by designing a fuzzy sliding mode controller which can offer a systematical means of constructing a set of shrinking-span and dilating-span membership functions. In order to demonstrate the practicability of the proposed controller, control constraints, parameter uncertainties, and external disturbances are considered according to practical situation of AUVs. Simulation results show very good tracking performance and robustness of the proposed control schemes.

Exponential Set-Point Stabilization of Underactuated Vehicles Moving in Three-Dimensional Space

This paper investigates the stabilization of underactuated vehicles moving in a three-dimensional vector space.The vehicle’s model is established on the matrix Lie group SE(3),which describes the configuration of rigid bodies globally and uniquely.We focus on the kinematic model of the underactuated vehicle,which features an underactuation form that has no sway and heave velocity.To compensate for the lack of these two velocities,we construct additional rotation matrices to generate a motion of rotation coupled with translation.Then,the state feedback is designed with the help of the logarithmic map,and we prove that the proposed control law can exponentially stabilize the underactuated vehicle to the identity group element with an almost global domain of attraction.Later,the presented control strategy is extended to set-point stabilization in the sense that the underactuated vehicle can be stabilized to an arbitrary desired configuration specified in advance.Finally,simulation examples are provided to verify the effectiveness of the stabilization controller.

Control for Underactuated Reentry Aircraft in Small Angle of Attack

The control problem for under-actuated reentry vehicle like HTV-2 is considered with small angle of attack.The control strategy for an aircraft with positive lateral control departure parameter relies on strong lateral stability,which declines with the decrease of the angle of attack.Thus,to control the lateral-directional motion in a stable state is hard and even impossible in some scenarios where the under-actuated reentry vehicle,like HTV-2,flies in a low angle of attack.To address this problem,the lateral-directional open-loop motion characteristics are analyzed.The results show that in an uncontrolled state,the lateral-directional motion can automatically converge to stabilization thanks to the aerodynamic damping effect.Therefore,a method of turning-off the lateral-directional control and inviting aerodynamic damping to control can achieve stability.The six-degree-of-freedom simulation show that the lateral-directional motion can be stabilized by the aerodynamic damping,and the lateral position error caused by the bank angle deviation is limited near the zero-rise angle of attack.The control strategy is effective.

Nonlinear dynamic model and control of three-axis stabilized liquid-filled spacecraft attitude system

The fuel slosh in the storage tanks affects the attitude dynamics of the liquid-filled spacecraft during orbit transferring. To describe the interactions between the fuel slosh dynamics and the spacecraft attitude dynamics, a novel nonlinear dynamic model for three-axis liquid-filled spacecraft is presented, and in this paper, the multi-body dynamics method is utilized. In this model, the fuel slosh is represented by the motions of an equivalent sphere pendulum, and the fuel slosh is underactuated. The proposed dynamics model meets the demand of attitude controller design of liquid-filled spacecraft. Then, a nonlinear proportional-plus-derivative (PD) type controller is designed for the proposed model based on the Lyapunov direct approach. This controller can suppress the fuel slosh and stabilize the attitude of the liquid-filled spacecraft. Numerical simulations are presented to verify the effectiveness of the proposed nonlinear dynamic model and the designed underactuated controller when compared with the conventional control scheme.