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

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

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

Extended Seismic Source Characterisation using Linear Programming Inversion in a Dual Formulation

A linear programming (LP) inversion method in a dual formulation was applied to reconstruct the kinematics of finite seismic ruptures. In a general setting, this approach can yield results from several data sets: strong ground motion, teleseismic waveforms or/and geodesic data (static deformation). The dual formulation involves the transformation of a normal solution space into an equivalent but reduced space: the dual space. The practical result of this transformation is a simpler inversion problem that is therefore faster to resolve, more stable and more robust. The developed algorithm includes a forward problem that calculates Green’s functions using a finite differences method with a 3D structure model. To evaluate the performance of this algorithm, we applied it to the reconstitution of a realistic slip distribution model from a data set synthesised using this model, i.e., the solution of the forward problem. Several other standard inversion approaches were applied to the same synthetic data for comparison

Automated sequence and motion planning for robotic spatial extrusion of 3D trusses

While robotic spatial extrusion has demonstrated a new and efficient means to fabricate 3D truss structures in architectural scale, a major challenge remains in automatically planning extrusion sequence and robotic motion for trusses with unconstrained topologies. This paper presents the first attempt in the field to rigorously formulate the extrusion sequence and motion planning (SAMP) problem, using a CSP encoding. Furthermore, this research proposes a new hierarchical planning framework to solve the extrusion SAMP problems that usually have a long planning horizon and 3D configuration complexity. By decoupling sequence and motion planning, the planning framework is able to efficiently solve the extrusion sequence, end-effector poses, joint configurations, and transition trajectories for spatial trusses with nonstandard topologies. This paper also presents the first detailed computation data to reveal the runtime bottleneck on solving SAMP problems, which provides insight and comparing baseline for future algorithmic development. Together with the algorithmic results, this paper also presents an open-source and modularized software implementation called Choreo that is machine-agnostic. To demonstrate the power of this algorithmic framework, three case studies, including real fabrication and simulation results, are presented.Comment: 24 pages, 16 figure

Multibody Dynamics Model of a Human Hand for Haptics Interaction

In this paper we propose a strategy for modelling a human hand for Haptics interaction. The strategy consists in a parallel computing architecture that calculates the dynamics of a hand; this is accomplished by computing the dynamics of each finger in a parallel manner. In this approach multiple threads (e.g. haptics thread, graphics thread, collision detection thread, etc.) run concurrently and therefore we developed a synchronization mechanism for data exchange. We describe in detail the elements of the developed software