On the Generation of Smooth Three-Dimensional Rigid Body Motions

This paper addresses the problem of generating smooth trajectories between an initial and final position and orientation in space. The main idea is to define a functional depending on velocity or its derivatives that measures the smoothness of a trajectory and find trajectories that minimize this functional. In order to ensure that the computed trajectories are independent of the parameterization of positions and orientations, we use the notions of Riemannian metric and covariant derivatives from differential geometry and formulate the problem as a variational problem on the Lie group of spatial rigid body displacements, SE (3). We show that by choosing an appropriate measure of smoothness, the trajectories can be made to satisfy boundary conditions on the velocities or higher order derivatives. Dynamically smooth trajectories can be obtained by incorporating the inertia of the system into the definition of the Riemannian metric. We state the necessary conditions for the shortest distance, minimum acceleration and minimum jerk trajectories. Analytical expressions for the smooth trajectories are derived for some special cases. We also provide several examples of the general case where the trajectories are computed numerically

Hybrid Optimal Theory and Predictive Control for Power Management in Hybrid Electric Vehicle

This paper presents a nonlinear-model based hybrid optimal control technique to compute a suboptimal power-split strategy for power/energy management in a parallel hybrid electric vehicle (PHEV). The power-split strategy is obtained as model predictive control solution to the power management control problem (PMCP) of the PHEV, i.e., to decide upon the power distribution among the internal combustion engine, an electric drive, and other subsystems. A hierarchical control structure of the hybrid vehicle, i.e., supervisory level and local or subsystem level is assumed in this study. The PMCP consists of a dynamical nonlinear model, and a performance index, both of which are formulated for power flows at the supervisory level. The model is described as a bi-modal switched system, consistent with the operating mode of the electric ED. The performance index prescribing the desired behavior penalizes vehicle tracking errors, fuel consumption, and frictional losses, as well as sustaining the battery state of charge (SOC). The power-split strategy is obtained by first creating the embedded optimal control problem (EOCP) from the original bi-modal switched system model with the performance index. Direct collocation is applied to transform the problem into a nonlinear programming problem. A nonlinear predictive control technique (NMPC) in conjunction with a sequential quadratic programming solver is used to compute suboptimal numerical solutions to the PMCP. Methods for approximating the numerical solution to the EOCP with trajectories of the original bi-modal PHEV are also presented in this paper. The usefulness of the approach is illustrated via simulation results on several case studies

Hybrid systems for telepresence: Experimental platform design

This paper describes a proposed collaborative research effort between the University of Illinois at Chicago and Roger Williams University in Bristol, Rhode Island. The goal of this research effort is to develop a conceptual framework and an experimental test bed for analysis and design of systems through which a human can have haptic interaction with geographically remote environment. This paper discusses the initial efforts in the development of an experimental test bed for a Haptic Information Communication System (HICS) at Roger Williams University. We present considerations for designing a system capable of remote haptic interaction and present initial conceptual designs of the experimental platform

A notion of passivity for hybrid systems

We propose a notion of passivity for hybrid systems. Our work is motivated by problems in haptics and teleoperation where several computer controlled mechanical systems are connected through a communication channel. To account for time delays and to better react to user actions it is desirable to design controllers that can switch between different operating modes. Each of the interacting systems can be therefore naturally modeled as a hybrid system. A traditional passivity definition requires that a storage function exists that is common to all operating modes. We show that stability of the system can be guaranteed even if different storage function is found for each of the modes, provided appropriate conditions are satisfied when the system switches