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The paper explores the challenging task of performing a non-prehensile manipulation of several balls synchronously rolling on the curved hands of Butterfly robots. Each Butterfly robot represents a standard benchmark hardware setup, comprising a DC motor rotating a butterfly-shaped frame in a vertical plane, with a ball moving freely upon it, equipped with integrated computer vision, communication, programmable control, and computation interfaces. The combined dynamics of the considered system, consisting of N ≥ 2 such robots, is inherently underactuated, characterized by N active and N passive degrees of freedom, as well as N independent unilateral constraints that model the interactions between the frames and the balls, assuming no slipping. We focus on designing a model-based centralized feedback controller to achieve synchronized rotations of the balls. We assume the accuracy of our mathematical model and the feasibility of implementing a discretized version of the proposed continuous-time controller with a sufficiently small sampling time, that, in particular, is necessary for numerical differentiation. Relying on orbital stability of nominal periodic solution of the closed-loop system, we will experimentally check robustness to various inevitable challenges such as noises, disturbances, uncertainties, and communication delays. Hence, our concentration lies in designing an orbitally stabilizing controller for the underactuated models. The primary contribution is proposing one set of transverse coordinates, enabling transverse-linearization-based controller design, accompanied by pertinent closed-loop system analysis tools, thereby enhancing the efficacy of solving the manipulation task. Analytical and model-based arguments are validated through successful simulations and experiments conducted on two Butterfly robots, thereby emphasizing the validity and practicality of the proposed approach.

We consider a model of a 24-degree-of-freedom monkey robot that is supposed to perform a brachiation locomotion, i.e. to swing from one row of a horizontal ladder to the next one using the arms. The robot hand is constructed as a planar hook so that the contact point, about which the robot swings, is a passive hinge. We identify the 10 most relevant degrees of freedom for this underactuated mechanical system and formulate a tractable search procedure consisting on the following steps: (a) to introduce a parametrized family of coordination patterns to be enforced on the dynamics with respect to a path coordinate; (b) to formulate geometric equality constraints that are necessary to achieve a periodic locomotion; (c) to generate trajectories from integrable reduced dynamics associated with the passive hinge; (d) to evaluate the energetic cost of transport. Moreover, we observe that a linear approximation of the reduced dynamics can be used for trajectory generation, which allows us to incorporate computation of an approximate gradient of the cost function into the search algorithm significantly improving the computational efficiency.

This article is concerned with the generic structure of the motion coordination system resulting from the application of the method of virtual holonomic constraints (VHCs) to the problem of the generation and robust execution of a dynamic humanlike motion by a humanoid robot. The motion coordination developed using VHCs is based on a motion generator equation, which is a scalar nonlinear differential equation of second order. It can be considered equivalent in function to a central pattern generator in living organisms. The relative time evolution of the degrees of freedom of a humanoid robot during a typical motion are specified by a set of coordination functions that uniquely define the overall pattern of the motion. This is comparable to a hypothesis on the existence of motion patterns in biomechanics. A robust control is derived based on a transverse linearization along the configuration manifold defined by the coordination functions. It is shown that the derived coordination and control architecture possesses excellent robustness properties. The analysis is performed on an example of a real human motion recorded in test experiments.

We propose a novel method to analyze how human operators use hydraulic manipulators of heavy-duty equipment. The approach is novel in the sense that it applies knowledge of motion planning and optimization techniques used in robotics. As an example, we consider the case of operating a forestry crane. To that end, we use motion data that has been recorded during standard operation with the help of sensors and a data acquisition unit. The data backs up the notion that operators work by performing repeatable patterns observed in the trajectories of the manipulator's joints. We show how this nominal behavior is computed, and consequently this allow us to present the following: 1) an analytical procedure to analyze motions, 2) how to represent the "performance" of the operator in a 2D plot, 3) an example of how to use this information to suggest customized control settings, and 4) some complementary ideas needed for improving efficiency through automation.

We study the problem of motion planning for underactuated mechanical systems. The idea is to reduce complexity by imposing via feedback a sufficient number of invariants and then to compute a projection of the dynamics onto an induced invariant sub-manifold of the closed-loop system. The inspiration comes from two quite distant methods, namely the method of virtual holonomic constraints, originally invented for planning and orbital stabilization of gaits of walking machines, and the method of controlled Lagrangians, primarily invented as a nonlinear technique for stabilization of (relative) equilibria of controlled mechanical systems. Both of these techniques enforce the presence of particular invariants that can be described as level sets of conserved quantities induced in the closed-loop system. We link this structural feature of both methods to a procedure to transform a Lagrangian system with control inputs via a feedback action into a control-free Lagrangian system with a sufficient number of first integrals for the full state space or an invariant sub-manifold. In both cases, this transformation allows efficient (analytical) description of a new class of trajectories of forced mechanical systems appropriate for further orbital stabilization. For illustration purposes, we approach the challenging problem for a controlled mechanical system with two passive degrees of freedom: planning periodic (or bounded) forced upperhemisphere trajectories of the spherical pendulum on a puck. Another example of the technique is separately reported in [21].

Working with forestry machines requires great amount of training to be sufficiently skilledto operate forestry cranes. In view of this, introducing automated motions, as those seenin robotic arms, is ambitioned by this industry for shortening the amount of training timeand make the work of the operator easier. Motivated by this fact, we have developedtwo experimental platforms for testing control systems and motion planning algorithms inreal-time. They correspond to a laboratory setup and a commercial version of a hydraulicmanipulator used in forwarder machines. The aim of this article is to present the results ofthis development by providing an overview of our trajectory planning algorithm and motioncontrol method, with a subsequent view of the experimental results. For motion control,we design feedback controllers that are able to track reference trajectories based on sensormeasurements. Likewise, we provide arguments to design controllers in open-loop for thecase of machines lacking of sensing devices. Relying on the tracking efficiency of thesecontrollers, we design time efficient reference trajectories of motions that correspond tologging tasks. To demonstrate performance, we provide an overview of an extensive testingdone on these machines.

This work presents an extension of a design procedure for dynamic output feedback design for systems with nonlinearities satisfying quadratic constraints. In this work we used an axial gas compressor model described by the 3-state Moore-Greitzer compressor model (MG) that has some challenges for output feedback control design (Planovsky and Nikolaev 1990), (Rubanova 2013). The more general constraints for the investigation of the robustness with respect to parametric uncertainties and measurement noise are shown.

A new approach to trajectory planning for underactuated mechanical systems is presented and discussed based on analysis of feasible behaviors of a standard 2-DOF benchmark example - the cart-pendulum system. Following the Controlled Lagrangians approach of Bloch et al. (2000) [7], we present and re-establish known conditions and forms of feedback control laws for this example, which are leading to an equivalent completely integrable closed-loop Euler-Lagrange system; and then extend them. As shown, full integrability and, in particular, the presence of a linear in velocities first integral of dynamics plays the key role in an elegant new procedure for trajectory planning.

This paper is based on a new procedure for dynamic output feedback design for systems with nonlinearities satisfying quadratic constraints. The new procedure is motivated by the challenges of output feedback control design for the 3-state Moore-Greitzer compressor model. First, we use conditions for stability of a transformed system and the associated matching conditions to find the data of the stabilizing controllers for the surge subsystem. Second, using the set of stabilizing controllers satisfying the given constraints for the closed-loop system with the dynamic output feedback controller we made optimization over the parameter set. We present the data of the stabilizing controllers and the new constraints for the corresponding parameters. The contributions in this paper are simplified conditions for the synthesis and optimization over the control parameter set.

We study the problem of motion planning for underactuated mechanical systems. The idea is to reduce complexity by imposing via feedback a sufficient number of invariants and then compute a projection of the dynamics onto an induced invariant sub-manifold of the closed-loop system. The inspiration comes from two quite distant methods, namely the method of virtual holonomic constraints, originally invented for planning and orbital stabilization of gaits of walking machines, and the method of controlled Lagrangians, primarily invented as a nonlinear technique for stabilization of (relative) equilibria of controlled mechanical systems. Both of these techniques enforce the presence of particular invariants that can be described as level sets of conserved quantities induced in the closed-loop system. We link this structural feature of both methods to a procedure to transform a Lagrangian system via a feedback action into a new dynamical system with a sufficient number of first integrals for the full state space or an invariant sub-manifold. In both cases, this transformation allows efficient (analytical) description of a new class of trajectories of forced mechanical systems appropriate for further orbital stabilization. The contribution is illustrated with a spherical pendulum example that is discussed in detail.