On Centroidal Dynamics and Integrability of Average Angular Velocity

In the literature on robotics and multibody dynamics, the concept of average angular velocity has received considerable attention in recent years. We address the question of whether the average angular velocity defines an orientation framethat depends only on the current robot configuration and provide a simple algebraic condition to check whether this holds. In the language of geometric mechanics, this condition corresponds to requiring the flatness of the mechanical connection associated to the robotic system. Here, however, we provide both a reinterpretation and a proof of this result accessible to readers with a background in rigid body kinematics and multibody dynamics but not necessarily acquainted with differential geometry, still providing precise links to the geometric mechanics literature. This should help spreading the algebraic condition beyond the scope of geometric mechanics,contributing to a proper utilization and understanding of the concept of average angular velocity.Comment: 8 pages, accepted for IEEE Robotics and Automation Letters (RA-L

Sensitivity analysis of hybrid systems with state jumps with application to trajectory tracking

This paper addresses the sensitivity analysis for hybrid systems with discontinuous (jumping) state trajectories. We consider state-triggered jumps in the state evolution, potentially accompanied by mode switching in the control vector field as well. For a given trajectory with state jumps, we show how to construct an approximation of a nearby perturbed trajectory corresponding to a small variation of the initial condition and input. A major complication in the construction of such an approximation is that, in general, the jump times corresponding to a nearby perturbed trajectory are not equal to those of the nominal one. The main contribution of this work is the development of a notion of error to clarify in which sense the approximate trajectory is, at each instant of time, a firstorder approximation of the perturbed trajectory. This notion of error naturally finds application in the (local) tracking problem of a time-varying reference trajectory of a hybrid system. To illustrate the possible use of this new error definition in the context of trajectory tracking, we outline how the standard linear trajectory tracking control for nonlinear systems -based on linear quadratic regulator (LQR) theory to compute the optimal feedback gain- could be generalized for hybrid systems

Predicting the post-impact velocity of a robotic arm

Starting from the recorded dynamic response of a 7DOF torque-controlled robot while intentionally impacting a rigid surface, we investigate the possibility of predicting the post-impact robot velocity from the ante-impact velocity and configuration. The velocity prediction is obtained by means of an impact map, derived using the framework of nonsmooth mechanics, that makes use of the known rigid-body robot model and the assumption of a frictionless inelastic impact. The main contribution is proposing a methodology that allows for a meaningful quantitative comparison between the recorded post-impact data, that exhibits a damped oscillatory response after the impact, and the post-impact velocity prediction derived via the rigid-body robot model, that presents no oscillations. The results of this approach are promising and the recorded impact data (18 experiments) is made publicly available, together with the numerical routines employed to generate the quantitative comparison, to further stimulate research in this field

Predicting the Post-Impact Velocity of a Robotic Arm via Rigid Multibody Models: an Experimental Study

Accurate post-impact velocity predictions are essential in developing impact-aware manipulation strategies for robots, where contacts are intentionally established at non-zero speed mimicking human manipulation abilities in dynamic grasping and pushing of objects. Starting from the recorded dynamic response of a 7DOF torque-controlled robot that intentionally impacts a rigid surface, we investigate the possibility and accuracy of predicting the post-impact robot velocity from the pre-impact velocity and impact configuration. The velocity prediction is obtained by means of an impact map, derived using the framework of nonsmooth mechanics, that makes use of the known rigid-body robot model and the assumption of a frictionless inelastic impact.The main contribution is proposing a methodology that allows for a meaningful quantitative comparison between the recorded post-impact data, that exhibits a damped oscillatory response after the impact, and the post-impact velocity prediction derived via the readily available rigid-body robot model, that presents no oscillations and that is the one typically obtained via mainstream robot simulator software. The results of this new approach are promising in terms of prediction accuracy and thus relevant for the growing field of impact-aware robot control. The recorded impact data (18 experiments) is made publicly available, together with the numerical routines employed to generate the quantitative comparison, to further stimulate interest/research in this field

Efficient Geometric Linearization of Moving-Base Rigid Robot Dynamics

The linearization of the equations of motion of a robotics system about a given state-input trajectory, including a controlled equilibrium state, is a valuable tool for model-based planning, closed-loop control, gain tuning, and state estimation. Contrary to the case of fixed based manipulators with prismatic or rotary joints, the state space of moving-base robotic systems such as humanoids, quadruped robots, or aerial manipulators cannot be globally parametrized by a finite number of independent coordinates. This impossibility is a direct consequence of the fact that the state of these systems includes the system's global orientation, formally described as an element of the special orthogonal group SO(3). As a consequence, obtaining the linearization of the equations of motion for these systems is typically resolved, from a practical perspective, by locally parameterizing the system's attitude by means of, e.g., Euler or Cardan angles. This has the drawback, however, of introducing artificial parameterization singularities and extra derivative computations. In this contribution, we show that it is actually possible to define a notion of linearization that does not require the use of a local parameterization for the system's orientation, obtaining a mathematically elegant, recursive, and singularity-free linearization for moving-based robot systems. Recursiveness, in particular, is obtained by proposing a nontrivial modification of existing recursive algorithms to allow for computations of the geometric derivatives of the inverse dynamics and the inverse of the mass matrix of the robotic system. The correctness of the proposed algorithm is validated by means of a numerical comparison with the result obtained via geometric finite difference

Predicting the Post-Impact Velocity of a Robotic Arm via Rigid Multibody Models: an Experimental Study

International audienceAccurate post-impact velocity predictions are essential in developing impact-aware manipulation strategies for robots, where contacts are intentionally established at non-zero speed mimicking human manipulation abilities in dynamic grasping and pushing of objects. Starting from the recorded dynamic response of a 7DOF torque-controlled robot that intentionally impacts a rigid surface, we investigate the possibility and accuracy of predicting the post-impact robot velocity from the pre-impact velocity and impact configuration. The velocity prediction is obtained by means of an impact map, derived using the framework of nonsmooth mechanics, that makes use of the known rigid-body robot model and the assumption of a frictionless inelastic impact.The main contribution is proposing a methodology that allows for a meaningful quantitative comparison between the recorded post-impact data, that exhibits a damped oscillatory response after the impact, and the post-impact velocity prediction derived via the readily available rigid-body robot model, that presents no oscillations and that is the one typically obtained via mainstream robot simulator software. The results of this new approach are promising in terms of prediction accuracy and thus relevant for the growing field of impact-aware robot control. The recorded impact data (18 experiments) is made publicly available, together with the numerical routines employed to generate the quantitative comparison, to further stimulate interest/research in this field

Dual Arm Impact-Aware Grasping through Time-Invariant Reference Spreading Control

With the goal of increasing the speed and efficiency in robotic dual arm manipulation, a novel control approach is presented that utilizes intentional simultaneous impacts to rapidly grasp objects. This approach uses the time-invariant reference spreading framework, in which partly-overlapping ante- and post-impact reference vector fields are used. These vector fields are coupled via the impact dynamics in proximity of the expected impact area, minimizing the otherwise large velocity errors after the impact and the corresponding large control efforts. A purely spatial task is introduced to strongly encourage the synchronization of impact times of the two arms. An interim-impact control phase provides robustness in the execution against the inevitable lack of exact impact simultaneity and the corresponding unreliable velocity error. In this interim phase, a position feedback signal is derived from the ante-impact velocity reference, which is used to enforce sustained contact in all contact points without using velocity error feedback. With an eye towards real-life implementation, the approach is formulated using a QP control framework, and is validated using numerical simulations on a realistic robot model with flexible joints and low-level torque control.Comment: 8 pages, 4 figures, accepted for publication to IFAC World Congress 202

Dual Arm Impact-Aware Grasping through Time-Invariant Reference Spreading Control

With the goal of increasing the speed and efficiency in robotic dual arm manipulation, a novel control approach is presented that utilizes intentional simultaneous impacts to rapidly grasp objects. This approach uses the time-invariant reference spreading framework, in which partly-overlapping ante- and post-impact reference vector fields are used. These vector fields are coupled via the impact dynamics in proximity of the expected impact area, minimizing the otherwise large velocity errors after the impact and the corresponding large control efforts. A purely spatial task is introduced to strongly encourage the synchronization of impact times of the two arms. An interim-impact control phase provides robustness in the execution against the inevitable lack of exact impact simultaneity and the corresponding unreliable velocity error. In this interim phase, a position feedback signal is derived from the ante-impact velocity reference, which is used to enforce sustained contact in all contact points without using velocity error feedback. With an eye towards real-life implementation, the approach is formulated using a QP control framework, and is validated using numerical simulations on a realistic robot model with flexible joints and low-level torque control