https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1065&context=usafresearch

A review of space robotics technologies for on-orbit servicing

1. Control Methodology 2. Dynamical Systems 3. Applications to Social and Environmental Problems

Dynamics and Control

In this paper, automatic motion control is investigated for one of wheeled inverted pendulum (WIP) models, which have been widely applied for modeling of a large range of two wheeled modern vehicles. First, the underactuated WIP model is decomposed into a fully actuated second order subsystem Σa consisting of planar movement of vehicle forward and yaw angular motions, and a nonactuated first order subsystem Σb of pendulum motion. Due to the unknown dynamics of subsystem Σa and the universal approximation ability of neural network (NN), an adaptive NN scheme has been employed for motion control of subsystem Σa . The model reference approach has been used whereas the reference model is optimized by the finite time linear quadratic regulation technique. The pendulum motion in the passive subsystem Σb is indirectly controlled using the dynamic coupling with planar forward motion of subsystem Σa , such that satisfactory tracking of a set pendulum tilt angle can be guaranteed. Rigours theoretic analysis has been established, and simulation studies have been performed to demonstrate the developed method.

Neural network-based motion control of an underactuated wheeled inverted pendulum model.

This paper presents a novel implementation of an integral sliding-mode controller (ISMC) on a two-wheeled mobile robot (2 WMR). The 2 WMR consists of two wheels in parallel and an inverse pendulum, which is inherently unstable. It is the first time that the sliding-mode control method is employed for real-time control of a 2 WMR platform and several critical issues are addressed. First, the 2 WMR is underactuated, which uses only one actuator to achieve position control of the wheels while balancing the pendulum around the upright position. ISMC is suitable for control of the underactuated 2 WMR, because ISMC has an extra degree of freedom in control when sliding mode is achieved. In this paper, we utilize this extra degree of freedom to implement a linear nominal controller, which is found adequate in stabilizing the sliding manifold in a range around the equilibrium. Second, the 2 WMR system is in presence of both matched and unmatched uncertainties. The implemented ISMC, with an integral sliding surface and a switching term, is able to completely nullify the influence from the matched uncertainties. The implemented linear nominal controller stabilizes the sliding manifold that is subject to unmatched uncertainties. Third, references design are addressed when implementing ISMC on the 2 WMR. The effectiveness of ISMC is verified through intensive simulation and experiment results.

Design and Implementation of Integral Sliding-Mode Control on an Underactuated Two-Wheeled Mobile Robot

An underactuated mechanical system (UMS) is a system which has fewer independent control actuators than degrees of freedom to be controlled. Control of UMS is considered as one of the most active fields of research because of its diverse engineering applications. This survey reviews UMS from its history to the state-of-the-art research on modelling, classification, control, and to some extent, provides some unique insights for bottleneck issues and future research directions.

/pdf/a-survey-of-underactuated-mechanical-systems-4tw16vhjoz.pdf

A Survey of Underactuated Mechanical Systems

In this paper, the dynamic model of a wheeled inverted pendulum (eg, 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 vehicle's 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

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 (2003), Quasimoro (Salerno and Angeles, 2003), Joe (Grasser et al., 2002)) 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 a two-level controller for tracking vehicle orientation and heading speed set-points, while controlling the vehicle pitch within a specified range. Simulation results are provided to show the efficacy of the controller.

Velocity control of a wheeled inverted pendulum by partial feedback linearization

The motion of a free-floating space robot is characterized by the principle of conservation of angular momentum. It is well known that these angular momentum equations are nonholonomic, i.e., are nonintegrable rate equations. If the base of the free-floating robot is partially actuated, it is difficult to determine joint trajectories that will result in point-to-point motion of the entire robot system in its configuration space. However, if the drift-less system associated with the angular momentum conservation equations is differentially flat, point-to-point maneuvers of the free-floating robot in its configuration space can be constructed by properly choosing trajectories in the differentially flat space. The primary advantages of this approach is that it avoids the use of nonlinear programming (NLP) to solve the nonintegrable rate equations, which at best can provide only approximate solutions. A currently open research problem is how to design a differentially flat space robot with under-actuated base. The contributions of this technical note are as follows: i) study systematically the structure of the nonholonomic rate constraint equations of a free-floating open-chain space robot with two momentum wheels at the base and arbitrarily oriented joint axes; ii) identify a set of sufficient conditions on the inertia distribution under which the system exhibits differential flatness; iii) exploit these design conditions for point-to-point trajectory planning and control of the space robot.

A Differentially Flat Open-Chain Space Robot with Arbitrarily Oriented Joint Axes and Two Momentum Wheels at the Base

This paper presents a methodology for trajectory planning and tracking control of a tractor with a steerable trailer based on the system's dynamic model. The theory of differential flatness is used as the basic approach in these developments. Flat outputs are found that linearize the system's dynamic model using dynamic feedback linearization, a subclass of differential flatness. It is demonstrated that this property considerably simplifies motion planning and the development of controller. Simulation results are presented in the paper, which show that the developed controller has the desirable performance with exponential stability.

Motion Planning and Control of a Tractor With a Steerable Trailer Using Differential Flatness

The motion of free-floating space robots is characterized by nonholonomic, i.e., non-integrable rate constraint equations. These constraints originate from principles of conservation of linear and angular momentum. It is well known that these rate constraints can also be written as input-affine drift-less control systems. Trajectory planning of these systems is extremely challenging and computation intensive since the motion must satisfy differential constraints. However, under certain conditions, these drift-less control systems can be shown to be differentially flat. The property of flatness allows a computationally in-expensive way to plan trajectories for the dynamic system between two configurations as well as develop feedback controllers. Nonholonomic rate constraints for free-floating planar open-chain robots are systematically studied to determine the design conditions under which the system exhibits differential flatness. Under these design conditions, the property of flatness is used for trajectory planning and feedback control under perturbations in the initial state.

Jaume Franch

Papers

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

Velocity control of a wheeled inverted pendulum by partial feedback linearization

A Differentially Flat Open-Chain Space Robot with Arbitrarily Oriented Joint Axes and Two Momentum Wheels at the Base

Motion Planning and Control of a Tractor With a Steerable Trailer Using Differential Flatness

Design of differentially flat planar space robots: a step forward in their planning and control