Using Genetic Algorithms to Optimize Control Lyapunov Functions

The problem of simultaneously tuning the control law and the control Lyapunov function (CLF) for nonlinear systems is considered, and a genetic algorithm optimization method is proposed as a general solution. It is shown that direct sampling of the nonlinear effects on the CLF offers an advantage over robust linear control methods that assume a linearized system with the nonlinearities treated as uncertainties. While the genetic algorithm approach is not guaranteed to find a solution, experimentation suggests that it does possess a high likelihood of finding "good" solutions to some nontrivial problems. The control law and the local CLF are tuned simultaneously to maximize the rate of convergence and minimize the control effort of nonlinear systems. Two control laws are tested: 1. an LQR full-state feedback controller, and 2. a Sontag-like nonlinear full-state feedback controller. It is assumed that a quadratic Lyapunov function is a local CLF for the nonlinear systems considered. The proposed optimization method does not offer a strict guarantee on controller performance. However, it is suggested that with enough randomized performance sampling, the controller will achieve the estimated performance level with sufficiently high confidence, making the proposed method a practical solution for real-world controller design.Mechanical & Aerospace Engineerin

Fast Grasp Contact Computation for a Serial Robot

A system includes a controller and a serial robot having links that are interconnected by a joint, wherein the robot can grasp a three-dimensional (3D) object in response to a commanded grasp pose. The controller receives input information, including the commanded grasp pose, a first set of information describing the kinematics of the robot, and a second set of information describing the position of the object to be grasped. The controller also calculates, in a two-dimensional (2D) plane, a set of contact points between the serial robot and a surface of the 3D object needed for the serial robot to achieve the commanded grasp pose. A required joint angle is then calculated in the 2D plane between the pair of links using the set of contact points. A control action is then executed with respect to the motion of the serial robot using the required joint angle

Applying Workspace Limitations in a Velocity-Controlled Robotic Mechanism

A robotic system includes a robotic mechanism responsive to velocity control signals, and a permissible workspace defined by a convex-polygon boundary. A host machine determines a position of a reference point on the mechanism with respect to the boundary, and includes an algorithm for enforcing the boundary by automatically shaping the velocity control signals as a function of the position, thereby providing smooth and unperturbed operation of the mechanism along the edges and corners of the boundary. The algorithm is suited for application with higher speeds and/or external forces. A host machine includes an algorithm for enforcing the boundary by shaping the velocity control signals as a function of the reference point position, and a hardware module for executing the algorithm. A method for enforcing the convex-polygon boundary is also provided that shapes a velocity control signal via a host machine as a function of the reference point position

Applied Joint-Space Torque and Stiffness Control of Tendon-Driven Fingers

Existing tendon-driven fingers have applied force control through independent tension controllers on each tendon, i.e. in the tendon-space. The coupled kinematics of the tendons, however, cause such controllers to exhibit a transient coupling in their response. This problem can be resolved by alternatively framing the controllers in the joint-space of the manipulator. This work presents a joint-space torque control law that demonstrates both a decoupled and significantly faster response than an equivalent tendon-space formulation. The law also demonstrates greater speed and robustness than comparable PI controllers. In addition, a tension distribution algorithm is presented here to allocate forces from the joints to the tendons. It allocates the tensions so that they satisfy both an upper and lower bound, and it does so without requiring linear programming or open-ended iterations. The control law and tension distribution algorithm are implemented on the robotic hand of Robonaut-2

Robotic Finger Assembly

A robotic hand includes a finger with first, second, and third phalanges. A first joint rotatably connects the first phalange to a base structure. A second joint rotatably connects the first phalange to the second phalange. A third joint rotatably connects the third phalange to the second phalange. The second joint and the third joint are kinematically linked such that the position of the third phalange with respect to the second phalange is determined by the position of the second phalange with respect to the first phalange

Robust Operation of Tendon-Driven Robot Fingers Using Force and Position-Based Control Laws

A robotic system includes a tendon-driven finger and a control system. The system controls the finger via a force-based control law when a tension sensor is available, and via a position-based control law when a sensor is not available. Multiple tendons may each have a corresponding sensor. The system selectively injects a compliance value into the position-based control law when only some sensors are available. A control system includes a host machine and a non-transitory computer-readable medium having a control process, which is executed by the host machine to control the finger via the force- or position-based control law. A method for controlling the finger includes determining the availability of a tension sensor(s), and selectively controlling the finger, using the control system, via the force or position-based control law. The position control law allows the control system to resist disturbances while nominally maintaining the initial state of internal tendon tensions

Robotic Finger Assembly

A robotic hand includes a finger with first, second, and third phalanges. A first joint rotatably connects the first phalange to a base structure. A second joint rotatably connects the first phalange to the second phalange. A third joint rotatably connects the third phalange to the second phalange. The second joint and the third joint are kinematically linked such that the position of the third phalange with respect to the second phalange is determined by the position of the second phalange with respect to the first phalange

Tendon Driven Finger Actuation System

A humanoid robot includes a robotic hand having at least one finger. An actuation system for the robotic finger includes an actuator assembly which is supported by the robot and is spaced apart from the finger. A tendon extends from the actuator assembly to the at least one finger and ends in a tendon terminator. The actuator assembly is operable to actuate the tendon to move the tendon terminator and, thus, the finger

Diffuse Hard X-ray Emission in Starburst Galaxies as Synchrotron from Very High Energy Electrons

[Abdriged] The origin of the diffuse hard X-ray (2 - 10 keV) emission from starburst galaxies is a long-standing problem. We suggest that synchrotron emission of 10 - 100 TeV electrons and positrons (e+/-) can contribute to this emission, because starbursts have strong magnetic fields. We consider three sources of e+/- at these energies: (1) primary electrons directly accelerated by supernova remnants; (2) pionic secondary e+/- created by inelastic collisions between CR protons and gas nuclei in the dense ISMs of starbursts; (3) pair e+/- produced between the interactions between 10 - 100 TeV gamma-rays and the intense far-infrared (FIR) radiation fields of starbursts. We create one-zone steady-state models of the CR population in the Galactic Center (R <= 112 pc), NGC 253, M82, and Arp 220's nuclei, assuming a power law injection spectrum for electrons and protons. We compare these models to extant radio and GeV and TeV gamma-ray data for these starbursts, and calculate the diffuse synchrotron X-ray and Inverse Compton (IC) luminosities of these starbursts. If the primary electron spectrum extends to ~PeV energies and has a proton/electron injection ratio similar to the Galactic value, we find that synchrotron contributes 2 - 20% of their unresolved, diffuse hard X-ray emission. Inverse Compton emission is likewise a minority of the unresolved X-ray emission in these starbursts, from 0.1% in the Galactic Center to 10% in Arp 220's nuclei. We also model generic starbursts, including submillimeter galaxies, in the context of the FIR--X-ray relation, finding that up to 2% in the densest starbursts with our fiducial assumptions. Neutrino and TeV gamma-ray data can further constrain the synchrotron X-ray emission of starbursts. Our models do not constrain hard synchrotron X-ray emission from any additional hard components of primary e+/- from sources like pulsars in starbursts.Comment: Accepted by ApJ; 31 pages, emulateapj forma