Collision-free inverse kinematics of the redundant seven-link manipulator used in a cucumber picking robot

The paper presents results of research on an inverse kinematics algorithm that has been used in a functional model of a cucumber-harvesting robot consisting of a redundant P6R manipulator. Within a first generic approach, the inverse kinematics problem was reformulated as a non-linear programming problem and solved with a Genetic Algorithm (GA). Although solutions were easily obtained, the considerable calculation time needed to solve the problem prevented on-line implementation. To circumvent this problem, a second, less generic, approach was developed which consisted of a mixed numerical-analytic solution of the inverse kinematics problem exploiting the particular structure of the P6R manipulator. Using the latter approach, calculation time was considerably reduced. During the early stages of the cucumber-harvesting project, this inverse kinematics algorithm was used off-line to evaluate the ability of the robot to harvest cucumbers using 3D-information obtained from a cucumber crop in a real greenhouse. Thereafter, the algorithm was employed successfully in a functional model of the cucumber harvester to determine if cucumbers were hanging within the reachable workspace of the robot and to determine a collision-free harvest posture to be used for motion control of the manipulator during harvesting. The inverse kinematics algorithm is presented and demonstrated with some illustrative examples of cucumber harvesting, both off-line during the design phase as well as on-line during a field test

Collision-free inverse kinematics of a 7 link cucumber picking robot

The paper presents results of research on inverse kinematics algorithms to be used in a functional model of a cucumber harvesting robot consisting of a redundant manipulator with one prismatic and six rotational joints (P6R). Within a first generic approach, the inverse kinematics problem was reformulated as a non-linear programming problem and solved with a generic algorithm. Solutions were easily obtained, but the considerable calculation time needed to solve the problem prevented on line implementation. To circumvent this problem, a second, less generic approach was developed consisting of a mixed numerical-analytic solution of the inverse kinematics problem exploiting the particular structure of the P6R manipulator. This approach facilitated rapid and robust calculation of the inverse kinematics of the cucumber harvester. During the early stages of the cucumber harvesting project, this inverse kinematics algorithm was used to off-line evaluate the ability of the robot to harvest cucumbers using 3D-information of a cucumber crop obtained in a real greenhouse. Thereafter, the algorithm was employed successfully in a functional model of the cucumber harvester to determine if cucumbers were hanging within the reachable workspace of the robot and to determine a collision-free harvest posture to be used for motion control of the manipulator during harvesting

A fast branch-and-prune algorithm for the position analysis of spherical mechanisms

The final publication is available at link.springer.comDifferent branch-and-prune schemes can be found in the literature for numerically solving the position analysis of spherical mechanisms. For the prune operation, they all rely on the propagation of motion intervals. They differ in the way the problem is algebraically formulated. This paper exploits the fact that spherical kinematic loop equations can be formulated as sets of 3 multi-affine polynomials. Multi-affinity has an important impact on how the propagation of motion intervals can be performed because a multi-affine polynomial is uniquely determined by its values at the vertices of a closed hyperbox defined in its domain.Peer ReviewedPostprint (author's final draft

Automatic Differentiation of Rigid Body Dynamics for Optimal Control and Estimation

Many algorithms for control, optimization and estimation in robotics depend on derivatives of the underlying system dynamics, e.g. to compute linearizations, sensitivities or gradient directions. However, we show that when dealing with Rigid Body Dynamics, these derivatives are difficult to derive analytically and to implement efficiently. To overcome this issue, we extend the modelling tool `RobCoGen' to be compatible with Automatic Differentiation. Additionally, we propose how to automatically obtain the derivatives and generate highly efficient source code. We highlight the flexibility and performance of the approach in two application examples. First, we show a Trajectory Optimization example for the quadrupedal robot HyQ, which employs auto-differentiation on the dynamics including a contact model. Second, we present a hardware experiment in which a 6 DoF robotic arm avoids a randomly moving obstacle in a go-to task by fast, dynamic replanning

Kinematically optimal hyper-redundant manipulator configurations

“Hyper-redundant” robots have a very large or infinite degree of kinematic redundancy. This paper develops new methods for determining “optimal” hyper-redundant manipulator configurations based on a continuum formulation of kinematics. This formulation uses a backbone curve model to capture the robot's essential macroscopic geometric features. The calculus of variations is used to develop differential equations, whose solution is the optimal backbone curve shape. We show that this approach is computationally efficient on a single processor, and generates solutions in O(1) time for an N degree-of-freedom manipulator when implemented in parallel on O(N) processors. For this reason, it is better suited to hyper-redundant robots than other redundancy resolution methods. Furthermore, this approach is useful for many hyper-redundant mechanical morphologies which are not handled by known methods

An algebraic method to check the singularity-free paths for parallel robots

Trajectory planning is a critical step while programming the parallel manipulators in a robotic cell. The main problem arises when there exists a singular configuration between the two poses of the end-effectors while discretizing the path with a classical approach. This paper presents an algebraic method to check the feasibility of any given trajectories in the workspace. The solutions of the polynomial equations associated with the tra-jectories are projected in the joint space using Gr{\"o}bner based elimination methods and the remaining equations are expressed in a parametric form where the articular variables are functions of time t unlike any numerical or discretization method. These formal computations allow to write the Jacobian of the manip-ulator as a function of time and to check if its determinant can vanish between two poses. Another benefit of this approach is to use a largest workspace with a more complex shape than a cube, cylinder or sphere. For the Orthoglide, a three degrees of freedom parallel robot, three different trajectories are used to illustrate this method.Comment: Appears in International Design Engineering Technical Conferences & Computers and Information in Engineering Conference , Aug 2015, Boston, United States. 201

Local sensory control of a dexterous end effector

A numerical scheme was developed to solve the inverse kinematics for a user-defined manipulator. The scheme was based on a nonlinear least-squares technique which determines the joint variables by minimizing the difference between the target end effector pose and the actual end effector pose. The scheme was adapted to a dexterous hand in which the joints are either prismatic or revolute and the fingers are considered open kinematic chains. Feasible solutions were obtained using a three-fingered dexterous hand. An algorithm to estimate the position and orientation of a pre-grasped object was also developed. The algorithm was based on triangulation using an ideal sensor and a spherical object model. By choosing the object to be a sphere, only the position of the object frame was important. Based on these simplifications, a minimum of three sensors are needed to find the position of a sphere. A two dimensional example to determine the position of a circle coordinate frame using a two-fingered dexterous hand was presented