Dynamics and control of a class of underactuated mechanical systems

This paper presents a theoretical framework for the dynamics and control of underactuated mechanical systems, defined as systems with fewer inputs than degrees of freedom. Control system formulation of underactuated mechanical systems is addressed and a class of underactuated systems characterized by nonintegrable dynamics relations is identified. Controllability and stabilizability results are derived for this class of underactuated systems. Examples are included to illustrate the results; these examples are of underactuated mechanical systems that are not linearly controllable or smoothly stabilizable

Second order sliding mode control of underactuated Mechanical systems I: Local stabilization with application to an inverted pendulum

International audienceSecond order sliding mode control synthesis is developed for underactuated mechanical systems, operating under uncertainty conditions. In order to locally stabilize an underactuated system around an unstable equilibrium, an output is specified in such a way that the corresponding zero dynamics is locally asymptotically stable. Then, the desired stability property of the closed-loop system is provided by applying a quasihomogeneous second order sliding mode controller, driving the system to the zero dynamics manifold in finite time. Although the present synthesis exhibits an infinite number of switches on a finite time interval, it does not rely on the generation of first order sliding modes, while providing robustness features similar to those possessed by their standard sliding mode counterparts. A second order sliding mode appears on the zero dynamics manifold which is of co-dimension greater than the control space dimension. Performance issues of the proposed synthesis are illustrated in numerical and experimental studies of a cart-Pendulum system

A Bio-Inspired Manipulator with Claw Prototype for Winged Aerial Robots: Benchmark for Design and Control

Nature exhibits many examples of birds, insects and flying mammals with flapping wings and limbs offering some functionalities. Although in robotics, there are some examples of flying robots with wings, it has not been yet a goal to add to them some manipulation-like capabilities, similar to ones that are exhibited on birds. The flying robot (ornithopter) that we propose improves the existent aerial manipulators based on multirotor platforms in terms of longer flight duration of missions and safety in proximity to humans. Moreover, the manipulation capabilities allows them to perch in inaccessible places and perform some tasks with the body perched. This work presents a first prototype of lightweight manipulator to be mounted to an ornithopter and a new control methodology to balance them while they are perched and following a desired path with the end effector imitating their beaks. This allows for several possible applications, such as contact inspection following a path with an ultrasonic sensor mounted in the end effector. The manipulator prototype imitates birds with two-link legs and a body link with an actuated limb, where the links are all active except for the first passive one with a grabbing mechanism in its base, imitating a claw. Unlike standard manipulators, the lightweight requirement limits the frame size and makes it necessary to use micro motors. Successful experimental results with this prototype are reported.European Research Council 78824

Optimal Control for Articulated Soft Robots

Soft robots can execute tasks with safer interactions. However, control techniques that can effectively exploit the systems' capabilities are still missing. Differential dynamic programming (DDP) has emerged as a promising tool for achieving highly dynamic tasks. But most of the literature deals with applying DDP to articulated soft robots by using numerical differentiation, in addition to using pure feed-forward control to perform explosive tasks. Further, underactuated compliant robots are known to be difficult to control and the use of DDP-based algorithms to control them is not yet addressed. We propose an efficient DDP-based algorithm for trajectory optimization of articulated soft robots that can optimize the state trajectory, input torques, and stiffness profile. We provide an efficient method to compute the forward dynamics and the analytical derivatives of series elastic actuators (SEA)/variable stiffness actuators (VSA) and underactuated compliant robots. We present a state-feedback controller that uses locally optimal feedback policies obtained from DDP. We show through simulations and experiments that the use of feedback is crucial in improving the performance and stabilization properties of various tasks. We also show that the proposed method can be used to plan and control underactuated compliant robots, with varying degrees of underactuation effectively.Comment: 14 pages, 15 figures, IEEE Transaction on Robotics (TRO

Model learning for trajectory tracking of robot manipulators

Abstract Model based controllers have drastically improved robot performance, increasing task accuracy while reducing control effort. Nevertheless, all this was realized with a very strong assumption: the exact knowledge of the physical properties of both the robot and the environment that surrounds it. This assertion is often misleading: in fact modern robots are modeled in a very approximate way and, more important, the environment is almost never static and completely known. Also for systems very simple, such as robot manipulators, these assumptions are still too strong and must be relaxed. Many methods were developed which, exploiting previous experiences, are able to refine the nominal model: from classic identification techniques to more modern machine learning based approaches. Indeed, the topic of this thesis is the investigation of these data driven techniques in the context of robot control for trajectory tracking. In the first two chapters, preliminary knowledge is provided on both model based controllers, used in robotics to assure precise trajectory tracking, and model learning techniques. In the following three chapters, are presented the novelties introduced by the author in this context with respect to the state of the art: three works with the same premise (an inaccurate system modeling), an identical goal (accurate trajectory tracking control) but with small differences according to the specific platform of application (fully actuated, underactuated, redundant robots). In all the considered architectures, an online learning scheme has been introduced to correct the nominal feedback linearization control law. Indeed, the method has been primarily introduced in the literature to cope with fully actuated systems, showing its efficacy in the accurate tracking of joint space trajectories also with an inaccurate dynamic model. The main novelty of the technique was the use of only kinematics information, instead of torque measurements (in general very noisy), to online retrieve and compensate the dynamic mismatches. After that the method has been extended to underactuated robots. This new architecture was composed by an online learning correction of the controller, acting on the actuated part of the system (the nominal partial feedback linearization), and an offline planning phase, required to realize a dynamically feasible trajectory also for the zero dynamics of the system. The scheme was iterative: after each trial, according to the collected information, both the phases were improved and then repeated until the task achievement. Also in this case the method showed its capability, both in numerical simulations and on real experiments on a robotics platform. Eventually the method has been applied to redundant systems: differently from before, in this context the task consisted in the accurate tracking of a Cartesian end effector trajectory. In principle very similar to the fully actuated case, the presence of redundancy slowed down drastically the learning machinery convergence, worsening the performance. In order to cope with this, a redundancy resolution was proposed that, exploiting an approximation of the learning algorithm (Gaussian process regression), allowed to locally maximize the information and so select the most convenient self motion for the system; moreover, all of this was realized with just the resolution of a quadratic programming problem. Also in this case the method showed its performance, realizing an accurate online tracking while reducing both the control effort and the joints velocity, obtaining so a natural behaviour. The thesis concludes with summary considerations on the proposed approach and with possible future directions of research

Control of an Underactuated Three-Link Passive-Active- Active Manipulator Based on Three Stages and Stability Analysis

This paper presents a novel three-stage control strategy for the motion control of an underactuated three-link passive-active-active (PAA) manipulator. First, a nonlinear control law is designed to make the angle and angular velocity of the third link convergent to zero. Then, a swing-up control law is designed to increase the system energy and control the posture of the second link. Finally, an integrated method with linear control and nonlinear control is introduced to stabilize the manipulator at the straight-up position. The stability of the control system is guaranteed by Lyapunov theory and LaSalle's invariance principle. Compared to other approaches, the proposed strategy innovatively introduces a preparatory stage to drive the third link to stretch-out toward the second link in a natural way, which makes the swing-up control easy and quick. Besides, the intergraded method ensures the manipulator moving into the balancing stage smoothly and easily. The effectiveness and efficiency of the control strategy are demonstrated by numerical simulations

Stabilization Control for the Giant Swing Motion of the Horizontal Bar Gymnastic Robot Using Delayed Feedback Control

Open-loop dynamic characteristics of an underactuated system with nonholonomic constraints, such as a horizontal bar gymnastic robot, show the chaotic nature due to its nonlinearity. This chapter deals with the stabilization problems of periodic motions for the giant swing motion of gymnastic robot using chaos control methods. In order to make an extension of the chaos control method and apply it to a new practical use, some stabilization control strategies were proposed, which were, based on the idea of delayed feedback control (DFC), devised to stabilize the periodic motions embedded in the movements of the gymnastic robot. Moreover, its validity has been investigated by numerical simulations. First, a method named as prediction-based DFC was proposed for a two-link gymnastic robot using a Poincar section. Meanwhile, a way to calculate analytically the error transfer matrix and the input matrix that are necessary for discretization was investigated. Second, an improved DFC method, multiprediction delayed feedback control, using a periodic gain, was extended to a four-link gymnastic robot. A set of plural Poincare maps were defined with regard to the original continuous-time system as a T-periodic discrete-time system. Finally, some simulation results showed the effectiveness of the proposed methods