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

A modal approach to hyper-redundant manipulator kinematics

This paper presents novel and efficient kinematic modeling techniques for “hyper-redundant” robots. This approach is based on a “backbone curve” that captures the robot's macroscopic geometric features. The inverse kinematic, or “hyper-redundancy resolution,” problem reduces to determining the time varying backbone curve behavior. To efficiently solve the inverse kinematics problem, the authors introduce a “modal” approach, in which a set of intrinsic backbone curve shape functions are restricted to a modal form. The singularities of the modal approach, modal non-degeneracy conditions, and modal switching are considered. For discretely segmented morphologies, the authors introduce “fitting” algorithms that determine the actuator displacements that cause the discrete manipulator to adhere to the backbone curve. These techniques are demonstrated with planar and spatial mechanism examples. They have also been implemented on a 30 degree-of-freedom robot prototype

Computational neural learning formalisms for manipulator inverse kinematics

An efficient, adaptive neural learning paradigm for addressing the inverse kinematics of redundant manipulators is presented. The proposed methodology exploits the infinite local stability of terminal attractors - a new class of mathematical constructs which provide unique information processing capabilities to artificial neural systems. For robotic applications, synaptic elements of such networks can rapidly acquire the kinematic invariances embedded within the presented samples. Subsequently, joint-space configurations, required to follow arbitrary end-effector trajectories, can readily be computed. In a significant departure from prior neuromorphic learning algorithms, this methodology provides mechanisms for incorporating an in-training skew to handle kinematics and environmental constraints

Push recovery with stepping strategy based on time-projection control

In this paper, we present a simple control framework for on-line push recovery with dynamic stepping properties. Due to relatively heavy legs in our robot, we need to take swing dynamics into account and thus use a linear model called 3LP which is composed of three pendulums to simulate swing and torso dynamics. Based on 3LP equations, we formulate discrete LQR controllers and use a particular time-projection method to adjust the next footstep location on-line during the motion continuously. This adjustment, which is found based on both pelvis and swing foot tracking errors, naturally takes the swing dynamics into account. Suggested adjustments are added to the Cartesian 3LP gaits and converted to joint-space trajectories through inverse kinematics. Fixed and adaptive foot lift strategies also ensure enough ground clearance in perturbed walking conditions. The proposed structure is robust, yet uses very simple state estimation and basic position tracking. We rely on the physical series elastic actuators to absorb impacts while introducing simple laws to compensate their tracking bias. Extensive experiments demonstrate the functionality of different control blocks and prove the effectiveness of time-projection in extreme push recovery scenarios. We also show self-produced and emergent walking gaits when the robot is subject to continuous dragging forces. These gaits feature dynamic walking robustness due to relatively soft springs in the ankles and avoiding any Zero Moment Point (ZMP) control in our proposed architecture.Comment: 20 pages journal pape

Faster Motion on Cartesian Paths Exploiting Robot Redundancy at the Acceleration Level

The problem of minimizing the transfer time along a given Cartesian path for redundant robots can be approached in two steps, by separating the generation of a joint path associated to the Cartesian path from the exact minimization of motion time under kinematic/dynamic bounds along the obtained parameterized joint path. In this framework, multiple suboptimal solutions can be found, depending on how redundancy is locally resolved in the joint space within the first step. We propose a solution method that works at the acceleration level, by using weighted pseudoinversion, optimizing an inertia-related criterion, and including null-space damping. Several numerical results obtained on different robot systems demonstrate consistently good behaviors and definitely faster motion times in comparison with related methods proposed in the literature. The motion time obtained with our method is reasonably close to the global time-optimal solution along same Cartesian path. Experimental results on a KUKA LWR IV are also reported, showing the tracking control performance on the executed motions

An Unsupervised Neural Network for Real-Time Low-Level Control of a Mobile Robot: Noise Resistance, Stability, and Hardware Implementation

We have recently introduced a neural network mobile robot controller (NETMORC). The controller is based on earlier neural network models of biological sensory-motor control. We have shown that NETMORC is able to guide a differential drive mobile robot to an arbitrary stationary or moving target while compensating for noise and other forms of disturbance, such as wheel slippage or changes in the robot's plant. Furthermore, NETMORC is able to adapt in response to long-term changes in the robot's plant, such as a change in the radius of the wheels. In this article we first review the NETMORC architecture, and then we prove that NETMORC is asymptotically stable. After presenting a series of simulations results showing robustness to disturbances, we compare NETMORC performance on a trajectory-following task with the performance of an alternative controller. Finally, we describe preliminary results on the hardware implementation of NETMORC with the mobile robot ROBUTER.Sloan Fellowship (BR-3122), Air Force Office of Scientific Research (F49620-92-J-0499

Production of Radioactive Nuclides in Inverse Reaction Kinematics

Efficient production of short-lived radioactive isotopes in inverse reaction kinematics is an important technique for various applications. It is particularly interesting when the isotope of interest is only a few nucleons away from a stable isotope. In this article production via charge exchange and stripping reactions in combination with a magnetic separator is explored. The relation between the separator transmission efficiency, the production yield, and the choice of beam energy is discussed. The results of some exploratory experiments will be presented.Comment: 10 pages, 4 figures, to be submitted to Nucl. Instr. and Met