Sunil K. Agrawal

Differentially flat systems

Introduction Linear Time-Invariant SISO Systems Linear Time-Invariant MIMO Systems Time-Varying Linear Systems Discrete-Time Linear Systems Infinite Dimensional Linear Systems SISO Nonlinear Systems Multivariable Nonlinear Systems Mobile Robots Flatness and Optimal Trajectories Optimal Planning with Constraints Non-Differentially Flat Systems

Velocity and position control of a wheeled inverted pendulum by partial feedback linearization

In this paper, the dynamic model of a wheeled inverted pendulum (e.g., Segway, Quasimoro, and Joe) is analyzed from a controllability and feedback linearizability point of view. First, a dynamic model of this underactuated system is derived with respect to the wheel motor torques as inputs while taking the nonholonomic no-slip constraints into considerations. This model is compared with the previous models derived for similar systems. The strong accessibility condition is checked and the maximum relative degree of the system is found. Based on this result, a partial feedback linearization of the system is obtained and the internal dynamics equations are isolated. The resulting equations are then used to design two novel controllers. The first one is a two-level velocity controller for tracking vehicle orientation and heading speed set-points, while controlling the vehicle pitch (pendulum angle from the vertical) within a specified range. The second controller is also a two-level controller which stabilizes the vehicles position to the desired point, while again keeping the pitch bounded between specified limits. Simulation results are provided to show the efficacy of the controllers using realistic data.

Spherical rolling robot: a design and motion planning studies

Describes a prototype and analytical studies of a spherical rolling robot, a new design of a nonholonomic robot system. The spherical robot is driven by two remotely controlled, internally mounted rotors that induce the ball to roll and spin on a flat surface. It is tracked on the plane by an overhead camera. A mathematical model of the robots motion was developed using the nonholonomic constraints on its motion. For a number of simple motions, it is shown experimentally that the model agrees well with the results. Methods were developed for planning feasible, minimum time and minimum energy trajectories for the robot. These methods are illustrated both by mathematical simulation and hardware experiments.

Cable suspended planar robots with redundant cables: controllers with positive tensions

Cable-suspended robots are structurally similar to parallel actuated robots but with the fundamental difference that cables can only pull the end-effector but not push it. From a scientific point of view, this feature makes feedback control of cable-suspended robots more challenging than their counterpart parallel-actuated robots. In the case with redundant cables, feedback control laws can be designed to make all tensions positive while attaining desired control performance. This paper presents approaches to design positive tension controllers for cable suspended robots with redundant cables. Their effectiveness is demonstrated through simulations and experiments on a three degree-of-freedom cable suspended robots.

Trajectory Planning of Differentially Flat Systems with Dynamics and Inequalities

Trajectory planning of dynamic systems, in near real-time, is important for aerospace systems, specially, unmanned air vehicles and launched munitions. Trajectory plans that do not consider the governing dynamic equations, applicable path and actuator constraints may be unrealizable during execution. The purpose of this paper is to propose a trajectory planning scheme for a class of dynamic systems, referred to as differentially flat systems. The planner is motivated from on-line computations and is aimed to satisfy the state equations, path and actuator constraints, and given initial and terminal constraints. The essence of the approach is demonstrated by two examples: (i) a hardware implementation on a spring-mass-damper system to demonstrate real-time capabilities during pursuit; (ii) trajectory planning of a PVTOL to illustrate the application to nonlinear problems.

Design of a Cable-Driven Arm Exoskeleton (CAREX) for Neural Rehabilitation

Rehabilitation robots are, currently, being explored for training of neural impaired subjects or for assistance of those with weak limbs. Intensive training of neurally impaired subjects, with quantifiable outcomes, is the eventual goal of these robot exoskeletons. Conventional arm exoskeletons for rehabilitation are bulky and heavy. In recent years, the authors have proposed to make lightweight exoskeletons for rehabilitation by replacing the rigid links of the exoskeleton with lightweight cuffs fixed to the moving limb segments of the human arm. Cables are routed through these cuffs, which are driven by motors, to move the limb segments relative to each other. However, a scientific limitation of a cable-driven system is that each cable can only pull but not push. This paper is the first to demonstrate via experiments with cable-driven arm exoskeleton (CAREX) that it is possible to achieve desired forces on the hand, i.e., both pull and push, in any direction as required in neural training. In this research, an anthropomorphic arm was used to bench test the design and control concepts proposed in CAREX. As described in this paper, CAREX was attached to the limb segments of a five degree-of-freedom anthropomorphic arm instrumented with joint sensors. The cuffs of CAREX were designed to have adjustable cable routing points to optimize the “tensioned” workspace of the anthropomorphic arm. Simulation results of force field for training and rehabilitation of the arm are first presented. Experiments are conducted to show the performance of a CAREX force field controller when human subjects pull the end-effector of the anthropomorphic arm to travel on prescribed paths. The human-exoskeleton interface is also presented at the end of this paper to demonstrate the feasibility of CAREX on human arm.

Biologically Inspired Design Of Small Flapping Wing Air Vehicles Using Four-Bar Mechanisms And Quasi-steady Aerodynamics

In this paper, the energetics of a flapping wing micro air vehicle is analyzed with the objective of design of flapping wing air vehicles. The salient features of this study are: (i) design of an energy storage mechanism in the air vehicle similar to an insect thorax which stores part of the kinetic energy of the wing as elastic potential energy in the thorax during a flapping cycle; (ii) inclusion of aerodynamic wing models using blade element theory and inertia of the mechanism using rigid body modeling techniques; (iii) optimization of parameters of the energy storage mechanism using the dynamic models so that the peak power input from the external actuators during a flapping cycle is minimized. A series of engineering prototypes based on these studies have been fabricated which justify the use of these mathematical techniques.

Cable suspended robots: design, planning and control

Cable-suspended robots are structurally similar to parallel actuated robots, but with the fundamental difference that cables can only pull the end-effector but not push it. This feature makes the design, planning and control of cable-suspended robots a lot more challenging compared to their counterparts - parallel-actuated robots. This paper describes the kinematic and dynamic models, work-space, trajectory planning, and feedback controllers for these robots. These results are demonstrated through simulation and experiments on a six degree-of-freedom cable suspended robot.

Approaches for a tether-guided landing of an autonomous helicopter

In this paper, we address the design of an autopilot for autonomous landing of a helicopter on a rocking ship, due to rough sea. A tether is used for landing and securing a helicopter to the deck of the ship in rough weather. A detailed nonlinear dynamic model for the helicopter is used. This model is underactuated, where the rotational motion couples into the translation. This property is used to design controllers which separate the time scales of rotation and translation. It is shown that the tether tension can be used to couple the translation of the helicopter to the rotation. Two controllers are proposed in this paper. In the first, the rotation time scale is chosen much shorter than the translation, and the rotation reference signals are created to achieve a desired controlled behavior of the translation. In the second, due to coupling of the translation of the helicopter to the rotation through the tether, the translation reference rates are created to achieve a desired controlled behavior of the attitude and altitude. Controller A is proposed for use when the helicopter is far away from the goal, while Controller B is for the case when the helicopter is close to the ship. The proposed control schemes are proved to be robust to the tracking error of its internal loop and results in local exponential stability. The performance of the control system is demonstrated by computer simulations. Currently, work is in progress to implement the algorithm using an instrumented model of a helicopter with a tether.

Assessment of Motion of a Swing Leg and Gait Rehabilitation With a Gravity Balancing Exoskeleton

The gravity balancing exoskeleton, designed at University of Delaware, Newark, consists of rigid links, joints and springs, which are adjustable to the geometry and inertia of the leg of a human subject wearing it. This passive exoskeleton does not use any motors but is designed to unload the human leg joints from the gravity load over its range-of-motion. The underlying principle of gravity balancing is to make the potential energy of the combined leg-machine system invariant with configuration of the leg. Additionally, parameters of the exoskeleton can be changed to achieve a prescribed level of gravity assistance, from 0% to 100%. The goal of the results reported in this paper is to provide preliminary quantitative assessment of the changes in kinematics and kinetics of the walking gait when a human subject wears such an exoskeleton. The data on kinematics and kinetics were collected on four healthy and three stroke patients who wore this exoskeleton. These data were computed from the joint encoders and interface torque sensors mounted on the exoskeleton. This exoskeleton was also recently used for a six-week training of a chronic stroke patient, where the gravity assistance was progressively reduced from 100% to 0%. The results show a significant improvement in gait of the stroke patient in terms of range-of-motion of the hip and knee, weight bearing on the hemiparetic leg, and speed of walking. Currently, training studies are underway to assess the long-term effects of such a device on gait rehabilitation of hemiparetic stroke patients.