A Double-Layered Artificial Delay-Based Approach for Maneuvering Control of Planar Snake Robots

This paper considers path following control of planar snake robots using virtual holonomic constraints. We first derive the Euler-Lagrange equations of motion of the snake robot. Moreover, we integrate the effects of friction forces into these equations. Subsequently, we define geometric relations among the generalized coordinates of the system, using the method of virtual holonomic constraints. These appropriately defined constraints shape the geometry of a constraint manifold for the system, which is a submanifold of the configuration space of the robot. In particular, we show that the constraint manifold can be made invariant by a suitable choice of feedback. Furthermore, we analytically design a smooth feedback control law to render the constraint manifold exponentially stable for the controlled system. We show that enforcing the appropriately defined virtual holonomic constraints implies that the robot converges to and follows a desired geometric path. Numerical simulations are presented to support the theoretical design.

The problem of making a bicycle trace a strictly convex Jordan curve with bounded roll angle and bounded speed is investigated. The problem is solved by enforcing a virtual holonomic constraint which specifies the roll angle of the bicycle as a function of its position along the curve. It is shown that virtual holonomic constraints can be generated as periodic solutions of a scalar periodic differential equation. Finally, it is shown that if the mean curvature of the path is sufficiently small the virtual holonomic constraint can be asymptotically stabilised and the speed of the bicycle is asymptotically periodic.

In this paper, the time-delayed control (TDC) scheme with a sliding mode controller for a robot manipulator is presented. Since TDC suffers from the selection of an inertia matrix of a robot manipulator, the effect of the constant matrix on the performance is investigated. TDC is designed with the sliding mode controller (SMC) to improve the control performance. For the performance comparison between several control schemes, PD control, SMC, TDC, and TDC-SMC are presented. The performances are compared by simulating the same trajectory tracking task of a three link robot manipulator u nder different control schemes.

Virtual constraints are functional relations (i.e., constraints) on the state variables of a robot's model that are achieved through the action of actuators and feedback control instead of physical contact forces. They are called virtual because they can be re-programmed on the fly without modifying any physical connections among the links of the robot or its environment. Previous analytical and experimental work has established that vector relative degree two virtual holonomic (i.e., only configuration dependent) constraints are a powerful means to synchronize the links of a bipedal robot so as to achieve walking and running motions over a variety of terrain profiles. This paper introduces a class of virtual nonholonomic constraints that depend on velocity through (generalized) angular momentum while maintaining the property of being relative degree two. This additional freedom is shown to yield control solutions that handle a wider range of gait perturbations arising from terrain variations and exogenous forces. Moreover, including angular momentum in the virtual constraints allows foot placement control to be rigorously designed on the basis of the full dynamic model of the biped, instead of on the basis of an inverted pendulum approximation of its center of mass, as is commonly done in the bipedal robotics literature. This new class of control laws is shown in simulation to be robust to a variety of common gait disturbances.

This paper presents a method for designing a dynamic compensator based on artificial neural networks (ANN). The ANN is trained to give the proper compensator parameters (X, Tz) so as to always assign certain eigenvalues to desired locations in the output feedback system. The eigenvalues of concern are those associated with the angle /spl delta/ and speed /spl omega/. These eigenvalues are to be assigned to the specified locations under variations in several system parameters [static nonlinear load parameters A/sub p/ and A/sub q/, transmission line reactance, x/sub e/, and generated real power, P/sub G/]. The exact and ANN's results of compensator's parameters are plotted. In addition speed response is provided for the compensated and uncompensated systems. Results show that the ANN can be used on line once the off line training is performed to determine the compensator data so as to maintain the desired response of the system under variations in system parameters.

Gait Control of a Fully Actuated Walking Robot

Synthesis of virtual holonomic constraints for obtaining stable constraint dynamics

An Active Disturbance Rejection Control based on Generalized Proportional Integral observer (ADRC with GPI observer) was developed to control the gait of a bipedal robot with five degrees of freedom. The bipedal robot used is a passive point feet which produces an underactuated dynamic walking. A virtual holonomic constraint is imposed to generate online smooth trajectories which were used as references of the control system. The proposed control strategy is tested through numerical simulation on a task of forward walking with the robot exposed to external disturbances. The performance of ADRC with GPI observer strategy is compared with a feedback linearization with proportional-derivative control. A stability test consisting on analyzing the existence of limit cycles using the Poincare's method revealed that asymptotically stable walking was achieved. The proposed control strategy effectively rejects the external disturbances and keeps the robot in a stable dynamic walking.

The snake robot can be used to monitor and maintain underwater structures and environments. The motion of a snake robot is achieved by lateral undulation which is called the gait pattern of the snake robot. The parameters of a gait pattern need to be adjusted for compensating environmental uncertainties. In this work, 3D motion dynamics of a snake robot for the underwater environment is proposed with vertical motion using the buoyancy variation technique and horizontal motion using lateral undulation. “The neutral buoyant snake robot motion in hypothetical plane and added mass effect is negligible”, these previous assumptions are removed in this work. Two different control algorithms are designed for horizontal and vertical motions. The existing super twisting sliding mode control (STSMC) is used for the horizontal serpentine motion of the snake robot. The control law is designed on a reduced-ordered dynamic system based on virtual holonomic constraints. The vertical motion is achieved by controlling the mass variation using a pump. The water pumps are controlled using the event-based controller or Proportional Derivative (PD) controller. The results of the proposed control technique are verified with various external environmental disturbances and uncertainties to check the robustness of the control approach for various path following cases. Moreover, the results of STSMC scheme are compared with SMC scheme to check the effectiveness of STSMC. The practical implementation of the work is also performed using Simscape Multibody environment where the designed control algorithm is deployed on the virtual snake robot.

We consider a special benchmark mechanical system with two degrees of freedom and underactuation degree one. Furuta pendulum consists of an arm, rotating in the horizontal plane, and a pendulum, attached to the end of the arm freely and moving in the vertical plane. Our goal is to create and partially shape stable oscillations of the pendulum. The approach is based on the idea of stabilization of a particular virtual holonomic constraint, imposed on the configuration coordinates. We describe here a step-by-step design procedure in details. Our approach is illustrated through successful experimental tests

Traditional digital distance relaying scheme is used to protect the transmission lines against various abnormal conditions/faults. In this paper, the authors have discussed the adverse effects of fault and system parameters, such as fault resistance, fault location, power transfer angle etc., on the performance of the protection scheme. Further, a modified protection algorithm is developed to mitigate the effect of weak sources/non-homogeneous network on the protection of shunt-compensated doubly-fed transmission line. It also improves the performance of the protection scheme during all the aforesaid variations in system and fault parameters. The modified protection scheme is based on the mathematical analysis of the sequence components of voltage, current and impedance of the network components. An equivalent impedance vector for each of the above-stated fault and system parameters is obtained and the relationship between these vectors is represented in vectorial form. With the help of this vector diagram and the mathematical analysis, the actual impedance of faulted part of the line is calculated. Since the algorithm is derived mathematically, it is simple to understand and user-friendly. A negligible error is observed while simulating the modified protection algorithm considering all the severe variations in fault and system parameters. MATLAB/Simulink software is used to verify the developed algorithm using 50 Hz frequency of the power system.

The implementation of SMC-based techniques in Chap. 2 strictly required the uncertainties in the system to be bounded [1, 2]. However, considering these state-dependent uncertainties to be bounded can be regarded as a conservative assumption for practical scenarios. Furthermore, these approaches depend upon the viscous friction model to compute the nominal friction forces which is essential for determining the control effort. For situations where this analytical friction model doesn’t hold, tracking accuracy would eventually be further compromised. Hence, to relax such assumptions and circumvent the dependence on the friction model, an artificial-delay-based methodology has been proposed in this chapter to solve the tracking problem for a planar snake robot. Time-Delayed Control (TDC) is a robust control method applied to solve the trajectory tracking problem for systems with model as well as parametric uncertainties and disturbances without assuming them to be bounded, utilizing input and output measurements from a delayed time. The implementation of TDC is based on the assumption that the uncertainties should vary slowly over time. As practical snake robots are known to travel slowly through their surroundings, the uncertainty in the ground condition or the frictional forces, do evolve at a slow rate making TDC a natural and fitting choice to accomplish satisfactory tracking performance for a snake robot.

In this paper, a high accuracy linear positioning system with linear force actuator and magnetic levitation is proposed. By locating a permanently magnetized rod inside a current-carrying solenoid, the axial force is achieved by boundary effect of magnet poles and utilized to power the linear motion. While the force for levitation is governed by Ampere's law supplied with the same solenoid. With the levitation in radial direction, there is hardly any friction between the rod and the solenoid. The high speed motion can hence be achieved. Besides, the axial force act on the rod is a smooth function of rod position, so the system can provide nanometer resolution linear positioning to the molecule size. Since the force-position relation is highly nonlinear, and mathematical model is derived according to some assumptions, such as equivalent solenoid of the permanently magnetized rod, so there exists unknown dynamics in practical application. Thus robustness is an important issue in controller design. Meanwhile the load effect reacts directly on the servo system without transmission elements, so the capability of rejection is also required. With above consideration, a time-delay control scheme is chosen and applied. By comparing the input-output relation and the mathematical model, the time-delay controller calculates an estimation of unmodelled dynamics and disturbance then composes the desired compensation into the system. Effectiveness of the linear positioning system and control scheme are illustrated with simulation results.

Virtual holonomic output constraints define a set in the output space of a robot to which the end-effector should be confined. We propose the use of set stabilization for implementing virtual constraints, conducting analyses and experimental comparisons between existing control schemes and a set stabilization controller to justify our choice. The existing methods combine geometric projections and PD control, which ignores the higher-order properties of the constraint like curvature. The set stabilization method inherently incorporates constraint curvature information, allowing it to decouple the dynamics towards and along the set. It is shown that the two methods are equivalent on a line constraint, but that only the set stabilization method simultaneously guarantees asymptotic stability on a circle.

Implementation of Adaptive Controllers Using Digital Signal Processor Chips