The power dissipation method and kinematic reducibility of multiple-model robotic systems

This paper develops a formal connection between the power dissipation method (PDM) and Lagrangian mechanics, with specific application to robotic systems. Such a connection is necessary for understanding how some of the successes in motion planning and stabilization for smooth kinematic robotic systems can be extended to systems with frictional interactions and overconstrained systems. We establish this connection using the idea of a multiple-model system, and then show that multiple-model systems arise naturally in a number of instances, including those arising in cases traditionally addressed using the PDM. We then give necessary and sufficient conditions for a dynamic multiple-model system to be reducible to a kinematic multiple-model system. We use this result to show that solutions to the PDM are actually kinematic reductions of solutions to the Euler-Lagrange equations. We are particularly motivated by mechanical systems undergoing multiple intermittent frictional contacts, such as distributed manipulators, overconstrained wheeled vehicles, and objects that are manipulated by grasping or pushing. Examples illustrate how these results can provide insight into the analysis and control of physical systems

Augmenting Sensorimotor Control Using “Goal-Aware” Vibrotactile Stimulation during Reaching and Manipulation Behaviors

We describe two sets of experiments that examine the ability of vibrotactile encoding of simple position error and combined object states (calculated from an optimal controller) to enhance performance of reaching and manipulation tasks in healthy human adults. The goal of the first experiment (tracking) was to follow a moving target with a cursor on a computer screen. Visual and/or vibrotactile cues were provided in this experiment, and vibrotactile feedback was redundant with visual feedback in that it did not encode any information above and beyond what was already available via vision. After only 10 minutes of practice using vibrotactile feedback to guide performance, subjects tracked the moving target with response latency and movement accuracy values approaching those observed under visually guided reaching. Unlike previous reports on multisensory enhancement, combining vibrotactile and visual feedback of performance errors conferred neither positive nor negative effects on task performance. In the second experiment (balancing), vibrotactile feedback encoded a corrective motor command as a linear combination of object states (derived from a linear-quadratic regulator implementing a trade-off between kinematic and energetic performance) to teach subjects how to balance a simulated inverted pendulum. Here, the tactile feedback signal differed from visual feedback in that it provided information that was not readily available from visual feedback alone. Immediately after applying this novel “goal-aware” vibrotactile feedback, time to failure was improved by a factor of three. Additionally, the effect of vibrotactile training persisted after the feedback was removed. These results suggest that vibrotactile encoding of appropriate combinations of state information may be an effective form of augmented sensory feedback that can be applied, among other purposes, to compensate for lost or compromised proprioception as commonly observed, for example, in stroke survivors

Feedback Synthesis for Controllable Underactuated Systems using Sequential Second Order Actions

This paper derives nonlinear feedback control synthesis for general control affine systems using second-order actions---the needle variations of optimal control---as the basis for choosing each control response to the current state. A second result of the paper is that the method provably exploits the nonlinear controllability of a system by virtue of an explicit dependence of the second-order needle variation on the Lie bracket between vector fields. As a result, each control decision necessarily decreases the objective when the system is nonlinearly controllable using first-order Lie brackets. Simulation results using a differential drive cart, an underactuated kinematic vehicle in three dimensions, and an underactuated dynamic model of an underwater vehicle demonstrate that the method finds control solutions when the first-order analysis is singular. Moreover, the simulated examples demonstrate superior convergence when compared to synthesis based on first-order needle variations. Lastly, the underactuated dynamic underwater vehicle model demonstrates the convergence even in the presence of a velocity field.Comment: 9 page

Model-Based Control Using Koopman Operators

This paper explores the application of Koopman operator theory to the control of robotic systems. The operator is introduced as a method to generate data-driven models that have utility for model-based control methods. We then motivate the use of the Koopman operator towards augmenting model-based control. Specifically, we illustrate how the operator can be used to obtain a linearizable data-driven model for an unknown dynamical process that is useful for model-based control synthesis. Simulated results show that with increasing complexity in the choice of the basis functions, a closed-loop controller is able to invert and stabilize a cart- and VTOL-pendulum systems. Furthermore, the specification of the basis function are shown to be of importance when generating a Koopman operator for specific robotic systems. Experimental results with the Sphero SPRK robot explore the utility of the Koopman operator in a reduced state representation setting where increased complexity in the basis function improve open- and closed-loop controller performance in various terrains, including sand.Comment: 8 page