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.

Our work addresses the problem of planning an optimal pitching trajectory for compliant serial manipulators. We propose a generic framework for finding the longest possible pitch given angle, velocity, and torque constraints. Within this framework we can decompose an original infinite-dimensional task to finite number of similar steps. As a result, the implemented procedure gives an optimal release configuration, temporal control torque profiles satisfying dynamic constraints, and optimal stiffness coefficients for compliant joints. Computational complexity of the nonlinear optimization task was reduced applying a novel motion parametrization method. The proposed method was illustrated for a particular example and experimentally verified with the KUKA LWR4+ arm.

We approach a problem of motion planning and stabilization for a benchmark example, known as the “Butterfly” robot. It was proposed as a benchmark challenge for developing systematic techniques for nonprehensile rolling manipulation. A dynamical model of the underactuated system with a non-unilateral contact is derived. The recently proposed methodologies, known as virtual-holonomic-constraints-based motion planning and transverse-linearization-based orbital stabilization, are appropriately extended to suit the task. Finally, the feasibility is demonstrated through a hardware implementation and an experimental validation of the concept.

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 allows us to present the following: 1) an analytical procedure to analyze motions, 2) how to represent the “performance” of the operator in a 2-D 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 consider planning and implementation of fast motions for industrial manipulators constrained to a given geometric path. With such a problem formulation, which is quite reasonable for many standard operation scenarios, it is intuitively clear that a feedback controller should be designed to achieve orbital stabilization of a time-optimal trajectory instead asymptotic. We propose an algorithm to convert an asymptotically stabilizing controller into an orbitally stabilizing one and check achievable performance in simulations and, more importantly, in experiments performed on a standard industrial robot ABB IRB 140 with the IRC5-system extended with an open control interface. It is verified that the proposed re-design allows significantly reduced deviations of the actual trajectories from the desired one at high speeds not only for a chosen base feedback design but also outperforming the state-of-the-art commercial implementation offered by ABB Robotics.

Virtual environment-assisted teleoperation has great potential as a human-robot interaction paradigm for field robotic systems, in particular when combined with elements of automation. Unstructured outdoor environments present a complex problem with many challenging elements. For the specific application of forestry machines, we investigate which steps are required in order to implement such a system, what potential benefits there are, and how individual components can be adapted to efficiently assist forestry machine operators in their daily work in the near future. An experimental prototype of a teleoperation system with virtual environment-based feedback is constructed using a scenario-based design process. The feasibility of the implementation is partly verified through experimental studies.

We consider a benchmark example of a three-link planar biped walker with torso, which is actuated in between the legs. The torso is thought to be kept upright by two identical torsional springs. The mathematical model reflects a three-degree-of-freedom mechanical system with impulse effects, which describe the impacts of the swing leg with the ground, and the aim is to induce stable limit-cycle walking on level ground. The main contribution is a novel systematic trajectory planning procedure for solving the problem of gait synthesis. The key idea is to find a system of ordinary differential equations for the functions describing a synchronization pattern for the time evolution of the generalized coordinates along a periodic motion. These functions, which are known as virtual holonomic constraints, are also used to compute an impulsive linear system that approximates the time evolution of the subset of coordinates that are transverse to the orbit of the continuous part of the periodic solution. This auxiliary system, which is known as transverse linearization, is used to design a nonlinear exponentially orbitally stabilizing feedback controller. The performance of the closed-loop system and its robustness with respect to various perturbations and uncertainties are illustrated via numerical simulations.

A short term goal in the forest industry is semi-automation of existing machines for the tasks of logging and harvesting. One way to assist drivers is to provide a set of predefined trajectories that can be used repeatedly in the process. In recent years much effort has been directed to the design of control strategies and task planning as part of this solution. However, commercialization of such automatic schemes requires the installation of various sensing devices, computers and most of all a redesign of the machine itself, which is currently undesired by manufacturers. Here we present an approach of implementing predefined trajectories in an open-loop fashion, which avoids the complexity of sensor and computer integration. The experimental results are carried out on a commercial hydraulic crane to demonstrate that this solution is feasible in practice.

Successful recognition and pose estimation of logs and trees as well as workspace modeling in the forest environment is essential for extensive automation of the harvesting and logging tasks of forestry machines. However, the free form features of logs, few reliable textural features, large edge extraction errors, and segmentation faults caused by the barks on the surface of the logs present clear challenges for recognition and classification. To solve these problems, robust algorithms able to recognize and estimate poses of a variety of objects even under poor and partial inputs need to be developed. In this paper we focus on the most relevant task of recognizing and estimating postures of a bunch of logs located on the ground with varying orientation and distance. Experiments carried out with the help of a structured light camera demonstrate the feasibility of the proposed algorithm.

We consider a 24-degrees-of-freedom monkey robot that is supposed to perform brachiation locomotion, i.e. swinging 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: (a) introduce a family of coordination patterns to be enforced on the dynamics with respect to a path coordinate; (b) formulate geometric equality constraints that are necessary for periodic locomotion; (c) generate trajectories from integrable reduced dynamics associated with the passive hinge; (d) 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 the gradient of the cost function into the search algorithm.

We consider a 3-link planar walker with two legs and an upper body. An actuator is introduced between the legs, and the torso is kept upright by torsional springs. The model is a 3-DOF impulsive mechanical system, and the aim is to induce stable limit-cycle walking in level ground. To solve the problem, the ideas of the virtual holonomic constraints approach are explored, used and extended. The contribution is a novel systematic motion planning procedure for solving the problem of gait synthesis, which is challenging for non-feedback linearizable mechanical systems with two or more passive degrees of freedom. For a preplanned gait we compute an impulsive linear system that approximates dynamics transversal to the periodic solution. This linear system is used for the design of a stabilizing feedback controller. Results of numerical simulations are presented to illustrate the performance of the closed loop system.

Ball dribbling is a central element of basketball. One main challenge for realizing basketball robots is to stabilize periodic motions of the ball. This task is nontrivial due to the discrete-continuous nature of the corresponding dynamics. The ball can be only controlled during ball-manipulator contact and moves freely otherwise. We propose a manipulator equipped with a spring that gets compressed when the ball bounces against it. Hence, we can have continuous-time control over this underactuated Ball-Spring-Manipulator system until the spring releases its accumulated energy back to the ball. This paper illustrates a systematic way of planning such a modified dribbling motion, computing an analytical transverse linearization and achieving orbital stabilization.

A new approach for solving an optimal control problem of ball pitching with an underactuated human-like robot arm is proposed. The system dynamics is simplified to a planar two-link robot with actuation only at the shoulder joint and a passive spring at the elbow joint representing the stiffness of the arm. The objective is to accelerate the ball from an initial configuration at rest in such a way that the projection of its velocity along a certain elevation angle is maximal at a predefined release line. The suggested procedure makes use of a parameterization of the robot motion in terms of geometric relations among the generalized coordinates. We systematically formulate a necessary condition for an optimal motion resulting in a nonlinear differential equation that describes a synchronization of the joint angles. A suitable solution is found by numerically searching over a finite number of free initial conditions.

Ball dribbling is a central element of basketball. One main challenge for realizing basketball robots is to stabilize periodic motion of the ball. The task is nontrivial due to the discrete-continuous nature of the corresponding dynamics. This paper proposes to add an elastic element to the manipulator so the ball can be controlled in a continuous-time phase instead of an intermittent contact. Optimal catching and pushing trajectories are planned for the underactuated system based on the virtual holonomic constraints approach. First experimental studies are presented to evaluate the approach.

In the forest industry, trees are logged and harvested by human-operated hydraulic manipulators. Eventually, these tasks are expected to be automated with optimal performance. However, with todays technology the main problem is implementation. While prototypes may have rich sensing information, real cranes lack certain sensing devices, such as encoders for position sensing. Automating these machines requires unconventional solutions. In this paper, we consider the motion planning problem, which involves a redesign of optimal trajectories, so that open loop control strategies can be applied using feed-forward control signals whenever sensing information is not available.

We consider trajectory planning for an underactuated 3DOF helicopter, using the virtual holonomic constraint approach. First we choose constraint functions that describe the configuration variables along a desired motion in terms of some independent parametrization variable. This lets us describe the closed-loop system by some reduced order dynamics, the solution of which gives a feasible trajectory for the desired motion. By using the method of transverse linearization for controller design, we achieve exponential orbital stability to a desired trajectory. Numerical simulations confirm this property and show good convergence to a desired periodic motion when initialized from a resting state.

The steps for modeling and control of a hydraulic rotary actuator are discussed. Our aim is to present experimental results working with a particular sensing device for angular position as a complement to pressure sensing devices. We provide the steps in experimental system identification used for modeling the system dynamics. The cascade controller designed contains an inner loop for an accurate tracking of torque while stabilizing position reference trajectories. The performance of this design is experimentally verified.

The problem of swinging up inverted pendulums has often been solved by stabilization of a particular class of homoclinic structures present in the dynamics of the standard pendulum. In this article new arguments are suggested to show how different homoclinic curves can be preplanned for dynamics of the passive-link of the robot. This is done by reparameterizing the motion according to geometrical relations among the generalized coordinates. It is also shown that under certain conditions there exist periodic solutions surrounding such homoclinic orbits. These trajectories admit designing feedback controllers to ensure exponential orbital stabilization. The method is illustrated by simulations and supported by experimental studies.

We consider trajectory planning for kinematically redundant manipulators used on forestry machines. The analysis of recorded data from human operation reveals that the driver does not use the full potential of the machine due to the complexity of the manipulation task. We suggest an optimization procedure that takes advantage of the kinematic redundancy so that time-efficient joint and velocity profiles along the path can be obtained. Differential constraints imposed by the manipulator dynamics are accounted for by employing a phase-plane technique for admissible path timings. Velocity constraints of the individual joints are particularly restrictive in hydraulic manipulators. Our study aims for semi-autonomous schemes that can provide assistance to the operator for executing global motions.

A planar compass-like biped on a shallow slope is one of the simplest models of a passive walker. It is a 2-degree-of-freedom (DOF) impulsive mechanical system that is known to possess periodic solutions reminiscent of human walking. Finding such solutions is a challenging computational task that has attracted many researchers who are motivated by various aspects of passive and active dynamic walking. We propose a new approach to find stable as well as unstable hybrid limit cycles without integrating the full set of differential equations and, at the same time, without approximating the dynamics. The procedure exploits a time-independent representation of a possible periodic solution via a virtual holonomic constraint. The description of the limit cycle obtained in this way is useful for the analysis and characterization of passive gaits as well as for design of regulators to achieve gaits with the smallest required control efforts. Some insights into the notion of hybrid zero dynamics, which are related to such a description, are presented as well.

Control of robotic systems subject to friction phenomena is an important issue since growing demands on accuracy require elimination of friction disturbances. If several models-e.g., friction model, rigid-body dynamics-are required to describe the behavior with high precision, each model requires the knowledge of numerous parameters (perhaps time-varying) as well as an increased number of signals and sensors. In order to tackle this double limitation, an observer is proposed, addressing both the problem of velocity reconstruction and friction estimation in the joint of an inverted pendulum. Firstly, an adaptive two-level velocity observer is defined to reconstruct relevant unmeasured velocities, using estimation of the friction model error. Secondly, the observer is exploited for model-based friction compensation. Capabilities of the algorithm proposed are demonstrated by means of experiments on the Furuta pendulum.

A teleoperation system has been developed for a hydraulic crane, of the type used on a forwarder vehicle, which travels off-road and collects logs cut by a harvester. The system developed consists of a 3D virtual environment, which allows the user to input a desired position for the crane tip using either the mouse or a joystick. The desired position is then transmitted (via UDP/IP) to a local control system. The crane is a redundant manipulator, so movements of the individual links are calculated using a pseudoinverse method, and controlled using PIDs with friction compensation. Encoder data from the crane links are continuously sent back to the user side, and the crane’s movement is visualized in the virtual environment. The system has been tested on a real forwarder crane, experimental results and a video of the system’s performance are provided.

Recently, a new technique for generating periodic motions in mechanical systems which have less actuators than degrees of freedom has been proposed. A motivating example for studying such motions is a dynamically stabilized walking robot, where the target trajectory is periodic, and one of the joints - the ankle joint - is unactuated, or weakly actuated. In this paper, the technique is implemented on the Furuta pendulum, an experimental testbed that is simpler than a walking robot but retains many of the key challenges - it is underactuated, open-loop unstable, and practical problems such as friction and velocity estimation must be overcome. We present a detailed description of the practical implementation of the controller. The experiments show that the technique is sufficiently robust to be useful in practice.

The Furuta pendulum consists of an arm rotating in the horizontal plane and a pendulum attached to its end. Rotation of the arm is controlled by a DC motor, while the pendulum is moving freely in the plane, orthogonal to the arm. Motivated, in particular, by possible applications for walking/running/balancing robots, we consider the Furuta pendulum as a system for which synchronized periodic motions of all the generalized coordinates are to be created and stabilized. The goal is to achieve, via appropriate feedback control action, orbitally exponentially stable oscillations of the pendulum of various shapes around its upright and downward positions, accompanied with oscillations of the arm. Our approach is based on the idea of stabilization of a particular virtual holonomic constraint imposed on the configuration coordinates, which has been theoretically developed recently. Here, we elaborate on the complete design procedure. The results are illustrated not only through numerical simulations but also through successful experimental tests.