Uwe Mettin

Stable dynamic walking over uneven terrain

We propose a constructive control design for stabilization of non-periodic trajectories of underactuated robots. An important example of such a system is an underactuated “dynamic walking” biped robot traversing rough or uneven terrain. The stabilization problem is inherently challenging due to the nonlinearity, open-loop instability, hybrid (impact) dynamics, and target motions which are not known in advance. The proposed technique is to compute a transverse linearization about the desired motion: a linear impulsive system which locally represents “transversal” dynamics about a target trajectory. This system is then exponentially stabilized using a modified receding-horizon control design, providing exponential orbital stability of the target trajectory of the original nonlinear system. The proposed method is experimentally verified using a compass-gait walker: a two-degree-of-freedom biped with hip actuation but pointed stilt-like feet. The technique is, however, very general and can be applied to a wide variety of hybrid nonlinear systems.

A Passive 2-DOF Walker: Hunting for Gaits Using Virtual Holonomic Constraints

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.

Parallel Elastic Actuators as a Control Tool for Preplanned Trajectories of Underactuated Mechanical Systems

A lack of sufficient actuation power as well as the presence of passive degrees of freedom are often serious constraints for feasible motions of a robot. Installing passive elastic mechanisms in parallel with the original actuators is one of a few alternatives that allows for large modifications of the range of external forces or torques that can be applied to the mechanical system. If some motions are planned that require a nominal control input above the actuator limitations, then we can search for auxiliary spring-like mechanisms complementing the control scheme in order to overcome the constraints. The intuitive idea of parallel elastic actuation is that spring-like elements generate most of the nominal torque required along a desired trajectory, so the control efforts of the original actuators can be mainly spent in stabilizing the motion. Such attractive arguments are, however, challenging for robots with non-feedback linearizable non-minimum phase dynamics that have one or several passive degrees of freedom. We suggest an approach to resolve the apparent difficulties and illustrate the method with an example of an underactuated planar double pendulum. The results are tested both in simulations and through experimental studies.

Increasing the Level of Automation in the Forestry Logging Process with Crane Trajectory Planning and Control

Working with forestry machines requires a great deal of training to be sufficiently skilled to operate forestry cranes. In view of this, it would be desirable within the forestry industry to introduce automated motions, such as those seen in robotic arms, to shorten the training time and make the work of the operator easier. Motivated by this fact, we have developed two experimental platforms for testing control systems and motion-planning algorithms in real time. They correspond to a laboratory setup and a commercial version of a hydraulic manipulator used in forwarder machines. The aim of this article is to present the results of this development by providing an overview of our trajectory-planning algorithm and motion-control 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 sensor measurements. Likewise, we provide arguments to design controllers in an open-loop for machines that lack sensing devices. Relying on the tracking efficiency of these controllers, we design time-efficient reference trajectories of motions that correspond to logging tasks. To demonstrate performance, we provide an overview of extensive testing done on these machines.

Modeling and control of hydraulic rotary actuators used in forestry cranes

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.

Virtual environment teleoperation of a hydraulic forestry crane

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 cranes movement is visualized in the virtual environment. The system has been tested on a real forwarder crane, experimental results and a video of the systems performance are provided.

Stable Walking Gaits for a Three-Link Planar Biped Robot With One Actuator

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.

Identification and Control of a Hydraulic Forestry Crane

This article presents the identification and control of an electro-hydraulic crane. The crane is of the type used on forestry vehicles known as forwarders, which travel off-road collecting logs cut by the harvesters. The dynamics identified include significant frictional forces, dead zones, and structural and hydraulic vibrations. The control algorithm proposed, comprised of a linear controller and a compensator for nonlinearities, is able to accurately track a reference trajectory for the end effector, despite uncertainties in the arm mechanics and hydraulic system dynamics. A further control design is presented which uses an inner loop to compensate for vibrations in the hydraulic system, and its performance is experimentally verified.

Analysis of human-operated motions and trajectory replanning for kinematically redundant manipulators

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.

Optimal ball pitching with an underactuated model of a human arm

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.