Pål Johan From

Singularity-free dynamic equations of vehicle-manipulator systems

Abstract In this paper we derive the singularity-free dynamic equations of vehicle–manipulator systems using a minimal representation. These systems are normally modeled using Euler angles, which leads to singularities, or Euler parameters, which is not a minimal representation and thus not suited for Lagrange’s equations. We circumvent these issues by introducing quasi-coordinates which allows us to derive the dynamics using minimal and globally valid non-Euclidean configuration coordinates. This is a great advantage as the configuration space of the vehicle in general is non-Euclidean. We thus obtain a computationally efficient and singularity-free formulation of the dynamic equations with the same complexity as the conventional Lagrangian approach. The closed form formulation makes the proposed approach well suited for system analysis and model-based control. This paper focuses on the dynamic properties of vehicle–manipulator systems and we present the explicit matrices needed for implementation together with several mathematical relations that can be used to speed up the algorithms. We also show how to calculate the inertia and Coriolis matrices and present these for several different vehicle–manipulator systems in such a way that this can be implemented for simulation and control purposes without extensive knowledge of the mathematical background. By presenting the explicit equations needed for implementation, the approach presented becomes more accessible and should reach a wider audience, including engineers and programmers.

Optimal Paint Gun Orientation in Spray Paint Applications—Experimental Results

In this paper, we present the experimental results of a new spray paint algorithm presented in previous publications. Both theory and simulations indicate that the proposed method allows a robotic manipulator to paint a given surface using substantially lower joint torques than with conventional approaches. In this paper, we confirm this by implementing the algorithm on an ABB robot and we find that the joint torques needed to follow the trajectory are substantially lower than for the conventional approach. The approach presented is based on the observation that a small error in the orientation of the end effector does not affect the quality of the paint job. It is far more important to maintain constant velocity for the entire trajectory. We thus propose to allow a small error in the specification of the end-effector orientation, and we show how this allows us to obtain a higher constant speed throughout the trajectory. In addition, to improve the uniformity of the paint coating we are also able perform the paint job in less time.

Modeling and motion planning for mechanisms on a non-inertial base

Robotic manipulators on ships and platforms suffer from large inertial forces due to the non-inertial motion of the ship or platform. When operating in high sea state, operation of such manipulators can be made more efficient and robust if these non-inertial effects are taken into account in the motion planning and control systems. Motivated by this application, we present a rigorous and singularity-free formulation of the dynamics of a robotic manipulator mounted on a non-inertial base. We extend the classical dynamics equations for a serial manipulator to include the 6-DoF motion of the non-inertial base. Then, we show two examples of a 1-DoF and a 4-DoF manipulator to illustrate how these non-inertial effects can be taken into account in the motion planning.

A Real-Time Algorithm for Determining the Optimal Paint Gun Orientation in Spray Paint Applications

In this paper, we present a method for increasing the speed at which a standard industrial manipulator can paint a surface. The approach is based on the observation that a small error in the orientation of the end effector does not affect the quality of the paint job. It is far more important to maintain constant velocity throughout the trajectory. We consider the freedom in the end-effector orientation as functional redundancy and represent the restriction on the orientation error as barrier functions or linear matrix inequalities. In doing this, we cast the problem of finding the optimal orientation at every time step into a convex optimization problem that can be solved very efficiently and in real time. We show that the approach allows the end effector to maintain a higher constant velocity throughout the trajectory guaranteeing uniform paint coating and substantially reducing the time needed to paint the object.

Representing Attitudes as Sets of Frames

A general framework for representing continuous sets of frames with the unit quaternion representation is presented. The determination and control of the attitude of a rigid body is important in a wide range of applications and has been given much attention in the control community. Not always, however, must the desired attitude be restricted to one given orientation, but can be given as a discrete or continuous set of orientations subject to some restriction. An attitude can be represented by the four-parameter unit quaternion without the presence of singularities. It is shown how continuous sets of frames can be described by the unit quaternion representation. It is also shown how this set can be reorientated into an arbitrary coordinate system by the quaternion product. Some work is done on finding the attitude that is closest to the desired orientation when the desired orientation is out of reach due to some restriction on the allowed orientations or rotations.

On the influence of ship motion prediction accuracy on motion planning and control of robotic manipulators on seaborne platforms

Robotic manipulators on non-inertial platforms, such as ships, have to endure large inertial forces due to the non-inertial motion of the platform. When the non-inertial platforms motion is known, motion planning and control algorithms can eliminate these perturbations—in fact, in some situations the motion planning algorithms can even leverage the inertial forces to more cheaply move to a target point. However, for many non-inertial platforms, the motion is unknown. In this paper we investigate how prediction errors and the choice of the prediction horizon affect the motion planning and control of robots mounted on a non-inertial base with a particular focus on seaborne platforms. We study the following three aspects: (i) We study prediction of ship motion and how prediction errors affect the motion planning and control of the manipulator. (ii) We evaluate the relationship between prediction accuracy and control. In particular, we study what prediction horizon length is useful for motion planning and control. We also consider how uncertainties in the ship motion predictions map to uncertainties in the future state of the robot and how to include the variance in the cost function to increase the optimal horizon length. (iii) Finally, we study a receding horizon approach, which re-solves the optimal control problem on-line over a horizon as determined to be meaningful from (ii). Several simulations are presented and, to our knowledge, for the first time experiments of ship-manipulator systems based on real ship motion data are presented.

Analysis of a moving remote center of motion for robotics-assisted minimally invasive surgery

This paper presents a novel control architecture for controlling a moving remote center of motion in addition to the end-effector motion during robotic surgery. In minimally invasive surgery, it is common to require that the point at which the robot enters the body, called the incision point or the trocar, does not allow for any lateral motion. It is generally considered that no motion should be applied to this point in order to avoid inflicting damage to the patients skin. However, in surgery, the patients body may be moving, for example due to breathing or the beating of the heart. In order to compensate for this motion-or if we for some other reason want to leverage the possible motion of the incision point to improve performance in any other way-we derive a new framework which allows us to actively control the motion both at the incision point and the end effector. The novelty of the approach lies in the possibility of controlling both the incision point and the end effector to follow a trajectory, and that we find a Jacobian matrix that satisfies the velocity constraints in both the end-effector and the incision point frames. This allows us to formulate a framework that is not only suited for control, but also for analyzing the condition number of the Jacobian and avoid any singular configurations that may arise either as a result of the constrained motion or the manipulator geometry. The approach is verified experimentally on a redundant industrial manipulator.

Control allocation for mobile manipulators with on-board cameras

This paper presents a new set of approaches for teleoperation of mobile manipulators with on-board cameras. Mobile manipulators consist of a robotic arm which provides for interaction and manipulation, and a mobile base which extends the workspace of the arm. While the position of the onboard camera is determined by the base motion, the principal control objective is the motion of the manipulator arm. This calls for intelligent control allocation between the base and the manipulator arm in order to obtain intuitive control of both the camera and the arm. We implement virtual mass-spring-damper forces between the end-effector and the camera so that the camera follows the end-effector with an overdamped characteristics. The operator therefore only needs to control the end-effector motion, while the vehicle with the camera will follow naturally. The operator is thus able to control the more than six degrees of freedom of the vehicle and manipulator through a standard haptic device. The control allocation problem, i.e., whether the vehicle or manipulator arm actuation is applied, is then performed automatically so that the operator can concentrate on the manipulator motion.

The Thorvald II agricultural robotic system

This paper presents a novel and modular approach to agricultural robots. Food production is highly diverse in several aspects. Even farms that grow the same crops may differ in topology, infrastructure, production method, and so on. Modular robots help us adapt to this diversity, as they can quickly be configured for various farm environments. The robots presented in this paper are hardware modular in the sense that they can be reconfigured to obtain the necessary physical properties to operate in different production systems—such as tunnels, greenhouses and open fields—and their mechanical properties can be adapted to adjust for track width, power requirements, ground clearance, load capacity, and so on. The robot’s software is generalizing to work with the great variation of robot designs that can be realized by assembling hardware modules in different configurations. The paper presents several novel ideas for agricultural robotics, as well as extensive field trials of several different versions of the Thorvald II platform.

On the design of a low-cost, light-weight, and highly versatile agricultural robot

This paper describes the development and the main considerations for designing the Thorvald platform, a versatile robot for operation in agricultural fields. The main objective is to develop a robot that can perform all operations, from seeding, to weeding and harvesting. This requires the robot to be able to carry a wide variety of tools. In addition, we require the robot to be lightweight so that it can operate during wet periods without getting stuck or damaging the soil structure. We focus on keeping the overall costs of the robot at a level which makes it economically viable compared to conventional solutions. We obtain this by constructing the frame so that it flexes, which reduces complexity and makes the frame cheap to build, but at the same time guarantees that all wheels are in contact with the ground. We also describe the development of tools to be attached to the platform, and discuss the implications of the flexible design on the robot and tool control.