Dejan Milutinović

Modeling and Optimal Centralized Control of a Large-Size Robotic Population

This paper describes an approach to the modeling and control of multiagent populations composed of a large number of agents. The complexity of population modeling is avoided by assuming a stochastic approach, under which the agent distribution over the state space is modeled. The dynamics of the state probability density functions is determined, and a control problem of maximizing the probability of robotic presence in a given region is introduced. The Minimum Principle for the optimal control of partial differential equations is exploited to solve this problem, and it is applied to the mission control of a simulated large robotic population

IL-2 Regulates Expansion of CD4+ T Cell Populations by Affecting Cell Death: Insights from Modeling CFSE Data

It is generally accepted that IL-2 influences the dynamics of populations of T cells in vitro and in vivo. However, which parameters for cell division and/or death are affected by IL-2 is not well understood. To get better insights into the potential ways of how IL-2 may influence the population dynamics of T cells, we analyze data on the dynamics of CFSE-labeled polyclonal CD4+ T lymphocytes in vitro after anti-CD3 stimulation at different concentrations of exogenous IL-2. Inferring cell division and death rates from CFSE-delabeling experiments is not straightforward and requires the use of mathematical models. We find that to adequately describe the dynamics of T cells at low concentrations of exogenous IL-2, the death rate of divided cells has to increase with the number of divisions cells have undergone. IL-2 hardly affects the average interdivision time. At low IL-2 concentrations 1) fewer cells are recruited into the response and successfully complete their first division; 2) the stochasticity of cell division is increased; and 3) the rate, at which the death rate increases with the division number, increases. Summarizing, our mathematical reinterpretation suggests that the main effect of IL-2 on the in vitro dynamics of naive CD4+ T cells occurs by affecting the rate of cell death and not by changing the rate of cell division.

Optimal feedback guidance of a small aerial vehicle in a stochastic wind

The navigation of a small unmanned aerial vehicle is challenging due to a large influence of wind to its kinematics. When the kinematic model is reduced to two dimensions, it has the form of the Dubins kinematic vehicle model. Consequently, this paper addresses the problem of minimizing the expected time required to drive a Dubins vehicle to a prescribed target set in the presence of a stochastically varying wind. First, two analytically-derived control laws are presented. One control law does not consider the presence of the wind, whereas the other assumes that the wind is constant and known a priori. In the latter case it is assumed that the prevailing wind is equal to its mean value; no information about the variations of the wind speed and direction is available. Next, by employing numerical techniques from stochastic optimal control, feedback control strategies are computed. These anticipate the stochastic variation of the wind and drive the vehicle to its target set while minimizing the expected tim...

Modelling cell lifespan and proliferation: is likelihood to die or to divide independent of age?

In cell lifespan studies the exponential nature of cell survival curves is often interpreted as showing the rate of death is independent of the age of the cells within the population. Here we present an alternative model where cells that die are replaced and the age and lifespan of the population pool is monitored until a steady state is reached. In our model newly generated individual cells are given a determined lifespan drawn from a number of known distributions including the lognormal, which is frequently found in nature. For lognormal lifespans the analytic steady-state survival curve obtained can be well-fit by a single or double exponential, depending on the mean and standard deviation. Thus, experimental evidence for exponential lifespans of one and/or two populations cannot be taken as definitive evidence for time and age independence of cell survival. A related model for a dividing population in steady state is also developed. We propose that the common adoption of age-independent, constant rates of change in biological modelling may be responsible for significant errors, both of interpretation and of mathematical deduction. We suggest that additional mathematical and experimental methods must be used to resolve the relationship between time and behavioural changes by cells that are predominantly unsynchronized.

Petri net models of robotic tasks

Introduces a robotic task model (RTM) based on Petri nets, that establishes a framework for task evaluation from qualitative and quantitative viewpoints, as well as a methodology for the implementation of robotic task coordination. A testbed for the evaluation of the RTM and the details of its implementation over a network of distributed task executors is described.

Resolving the redundancy of a seven DOF wearable robotic system based on kinematic and dynamic constraint

According to the seven degrees of freedom (DOFs) human arm model composed of the shoulder, elbow, and wrist joints, positioning of the wrist in space and orientating the palm is a task requiring only six DOFs. Due to this redundancy, a given task can be completed by multiple arm configurations, and there is no unique mathematical solution to the inverse kinematics. The redundancy of a wearable robotic system (exoskeleton) that interacts with the human is expected to be resolved in the same way as that of the human arm. A unique solution to the systems redundancy was introduced by combining both kinematic and dynamic criteria. The redundancy of the arm is expressed mathematically by defining the swivel angle: the rotation angle of the plane including the upper and lower arm around a virtual axis connecting the shoulder and wrist joints which are fixed in space. Two different swivel angles were generated based on kinematic and dynamic constraints. The kinematic criterion is to maximize the projection of the longest principle axis of the manipulability ellipsoid for the human arm on the vector connecting the wrist and the virtual target on the head region. The dynamic criterion is to minimize the mechanical work done in the joint space for each two consecutive points along the task space trajectory. These two criteria were then combined linearly with different weight factors for estimating the swivel angle. Post processing of experimental data collected with a motion capturing system indicated that by using the proposed synthesis of redundancy resolution criteria, the error between the predicted swivel angle and the actual swivel angle adopted by the motor control system was less then five degrees. This result outperformed the prediction based on a single criteria.

A Stochastic Approach to Dubins Vehicle Tracking Problems

An optimal feedback control is developed for fixed-speed, fixed-altitude Unmanned Aerial Vehicle (UAV) to maintain a nominal distance from a ground target in a way that anticipates its unknown future trajectory. Stochasticity is introduced in the problem by assuming that the target motion can be modeled as Brownian motion, which accounts for possible realizations of the unknown target kinematics. Moreover, the possibility for the interruption of observations is included by assuming that the duration of observation times of the target is exponentially distributed, giving rise to two discrete states of operation. A Bellman equation based on an approximating Markov chain that is consistent with the stochastic kinematics is used to compute an optimal control policy that minimizes the expected value of a cost function based on a nominal UAV-target distance. Results indicate how the uncertainty in the target motion, the tracker capabilities, and the time since the last observation can affect the control law, and simulations illustrate that the control can further be applied to other continuous, smooth trajectories with no need for additional computation.

An approach to optimization of airport taxiway scheduling and traversal under uncertainty

Airport runways and taxiways have been identified as a key source of system-wide congestion and delay in the over-strained commercial air traffic system. To combat this growing problem, we present a novel approach for taxiway scheduling and traversal. Aircraft must traverse a taxiway, represented by a graph, from gates to their respective runways and arrive at their scheduled times while adhering to safety separation constraints. We describe a combinatorial mixed-integer linear program to determine the push-back time windows, aircraft speeds, stopping times, and in particular, traversal paths for a given graph and an imposed flight schedule as part of a single optimization problem. Safety and scheduling constraints are made robust to probabilistic deviations from the prescribed schedule and aircraft motion, and multiple objective functions are considered to examine the trade-off between taxi times and the probability of safety separation violation. Several scenarios are presented to demonstrate improvements gained from the method and possible uses for this approach.

Self-triggered sampling for second-moment stability of state-feedback controlled SDE systems

Event-triggered and self-triggered control, whereby the times for controller updates are computed from sampled data, have recently been shown to reduce the computational load or increase task periods for real-time embedded control systems. In this work, we propose a self-triggered scheme for nonlinear controlled stochastic differential equations with additive noise terms. We find that the family of trajectories generated by these processes demands a departure from the standard deterministic approach to event- and self-triggering, and, for that reason, we use the statistics of the sampled-data system to derive a self-triggering update condition that guarantees second-moment stability. We show that the length of the times between controller updates as computed from the proposed scheme is strictly positive and provide related examples.

Maximizing dexterous workspace and optimal port placement of a multi-arm surgical robot

Surgical procedures are traditionally performed by two or more surgeons along with staff nurses. One surgeon serves as the primary surgeon and the other serves as his/her assistant. Surgical robotics have redefined the dynamics in which the two surgeons interact with each other and with the surgical site. Raven IV is a new generation of the surgical robot system having four articulated robotic arms in a spherical configuration, each holding an articulated surgical tool. The system allows two surgeons to teleoperate the Raven IV collaboratively from two remote sites. The current research effort aims to configure the link architecture of each robotic arm, along with the position (port placement) and orientation of the Raven IV with respect to the patient, in order to optimize the common workspace reachable by all four robotic arms. The simulation results indicate that tilting the base of the robotic arms in the range of −20 to 20 deg while moving the ports closer together up to 50 mm apart leads to a preferred circular shape of the common workspace with an isotropy value of 0.5. A carefully configured system with multiple surgical robotic arms will enhance the interactive performance of the two surgeons.