Identification of Fully Physical Consistent Inertial Parameters using Optimization on Manifolds

This paper presents a new condition, the fully physical consistency for a set of inertial parameters to determine if they can be generated by a physical rigid body. The proposed condition ensure both the positive definiteness and the triangular inequality of 3D inertia matrices as opposed to existing techniques in which the triangular inequality constraint is ignored. This paper presents also a new parametrization that naturally ensures that the inertial parameters are fully physical consistency. The proposed parametrization is exploited to reformulate the inertial identification problem as a manifold optimization problem, that ensures that the identified parameters can always be generated by a physical body. The proposed optimization problem has been validated with a set of experiments on the iCub humanoid robot.Comment: 6 pages, published in Intelligent Robots and Systems (IROS), 2016 IEEE/RSJ International Conference o

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

Numerical Methods to Compute the Coriolis Matrix and Christoffel Symbols for Rigid-Body Systems

The growth of model-based control strategies for robotics platforms has led to the need for additional rigid-body-dynamics algorithms to support their operation. Toward addressing this need, this article summarizes efficient numerical methods to compute the Coriolis matrix and underlying Christoffel Symbols (of the first kind) for tree-structure rigid-body systems. The resulting algorithms can be executed purely numerically, without requiring any partial derivatives that would be required in symbolic techniques that do not scale. Properties of the presented algorithms share recursive structure in common with classical methods such as the Composite-Rigid-Body Algorithm. The algorithms presented are of the lowest possible order: $O(Nd)$ for the Coriolis Matrix and $O(Nd^2)$ for the Christoffel symbols, where $N$ is the number of bodies and $d$ is the depth of the kinematic tree. A method of order $O(Nd)$ is also provided to compute the time derivative of the mass matrix. A numerical implementation of these algorithms in C/C++ is benchmarked showing computation times on the order of 10-20 $\mu$s for the computation of the Coriolis matrix and $40-120$ $\mu$s for the computation of the Christoffel symbols for systems with $20$ degrees of freedom. These results demonstrate feasibility for the adoption of these numerical methods within control loops that need to operate at $1$kHz rates or higher, as is commonly required for model-based control applications

Elastic Structure Preserving Impedance Control for Nonlinearly Coupled Tendon-Driven Systems

Traditionally, most of the nonlinear control techniques for elastic robotic systems focused on achieving a desired closed-loop behavior by modifying heavily the intrinsic properties of the plant. This is also the case of elastic tendon-driven systems, where the highly nonlinear couplings lead to several control challenges. Following the current philosophy of exploiting the mechanical compliance rather than fighting it, this letter proposes an Elastic Structure Preserving impedance (ESPi) control for systems with coupled elastic tendinous transmissions. Our strategy achieves a globally asymptotically stable closed-loop system that minimally shapes the intrinsic inertial and elastic structure. %to add desired stiffness and damping on the link side. It further allows to impose a desired link-side impedance behavior. Simulations performed on the tendon-driven index finger of the DLR robot David show satisfactory results of link-side interaction behavior and set-point regulation

On the closed form computation of the dynamic matrices and their differentiations

In this paper we review and extend some classic results on rigid body dynamics, in order to give a symbolic expression of the different derivatives of the matrices of the dynamic model of a general tree-structured robot. In what follows the matrices are differentiated with respect to time, state and dynamic parameters. Obviously from the derivatives of the single matrices it is possible to recover the derivatives of the direct and inverse dynamic functions and classic results like the regressor matrix. Moreover an iterative algorithm is sketched which allows to compute all these derivatives as well as the kinematics and dynamics of the robot