We present a control design for N unmanned aerial vehicles (UAVs) tasked with an inspection of M ground moving vehicles. The location of each ground vehicle is known to each UAV, but the navigation ...and intent of each ground vehicle are unknown, therefore, this uncertainty has to be anticipated in each UAV’s navigation. We use the minimum time stochastic optimal control to navigate each UAV towards the inspection of each ground vehicle. Based on this control, we formulate assignments of ground vehicles to be inspected by UAVs as an optimization problem to inspect all ground vehicles in the minimum expected time. Accounting for ground vehicle uncertain trajectories, we update the optimal assignment by a Markov inequality rule. The rule prevents the possibility of indefinite updating of assignments without finishing the inspection of all vehicles. On the other hand, it updates an assignment if it leads to a statistically significant improvement of the inspection expected time. The presented approach is illustrated with numerical examples.
In this paper, a Markov inequality based switching rule is proposed to switch among numerically computed, time optimal controllers in a multiple vehicle intercept problem. Each controller is optimal ...for the intercept of a single vehicle, i.e., for the segment of the complete time varying multiple vehicle target set. The switching rule guarantees that after every switch the time to the target set is shorter with a certain predefined probability. Furthermore, the rule guarantees that the target set is reached after a finite number of switches and the rule scales well with the number of vehicles, i.e., the segments covering the target set. The problem and results are illustrated by a numerical example.
The Multi-pursuer Single-Evader Game Von Moll, Alexander; Casbeer, David; Garcia, Eloy ...
Journal of intelligent & robotic systems,
11/2019, Letnik:
96, Številka:
2
Journal Article
Recenzirano
We consider a general pursuit-evasion differential game with three or more pursuers and a single evader, all with simple motion (fixed-speed, infinite turn rate). It is shown that traditional means ...of differential game analysis is difficult for this scenario. But simple motion and min-max time to capture plus the two-person extension to Pontryagin’s maximum principle imply straight-line motion at maximum speed which forms the basis of the solution using a geometric approach. Safe evader paths and policies are defined which guarantee the evader can reach its destination without getting captured by any of the pursuers, provided its destination satisfies some constraints. A linear program is used to characterize the solution and subsequently the saddle-point is computed numerically. We replace the numerical procedure with a more analytical geometric approach based on Voronoi diagrams after observing a pattern in the numerical results. The solutions derived are open-loop optimal, meaning the strategies are a saddle-point equilibrium in the open-loop sense.
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.
Reach-to-grasp arm postures differ from those in pure reaching because they are affected by grasp position/orientation, rather than simple transport to a position during a reaching motion. This paper ...investigates this difference via an analysis of experimental data collected on reaching and reach-to-grasp motions. A seven-degree-of-freedom (DOFs) kinematic arm model with the swivel angle is used for the motion analysis. Compared to a widely used anatomical arm model, this model distinguishes clearly the four grasping-relevant DOFs (GR-DOFs) that are affected by positions and orientations of the objects to be grasped. These four GR-DOFs include the swivel angle that measures the elbow rotation about the shoulder–wrist axis, and three wrist joint angles. For each GR-DOF, we quantify position vs orientation task-relevance bias that measures how much the DOF is affected by the grasping position vs orientation. The swivel angle and forearm supination have similar bias, and the analysis of their motion suggests two hypotheses regarding the synergistic coordination of the macro- and micro-structures of the human arm (1) DOFs with similar task-relevance are synergistically coordinated; and (2) such synergy breaks when a task-relevant DOF is close to its joint limit without necessarily reaching the limit. This study provides a motion analysis method to reduce the control complexity for reach-to-grasp tasks, and suggests using dynamic coupling to coordinate the hand and arm of upper-limb exoskeletons.
This paper presents an approach to a kinesthetic sense of touch for a finger-like soft robotic actuator innervated with a soft fluidic resistive sensor which is sensitive to bending. The approach is ...based on the sensor resistance reference tracking feedback controller and uses the reference tracking error as a measure of stress resulting from the contact between the actuator and an object. With the proposed approach, we accomplish tasks of detecting a touch between the actuator and an object, keeping the actuator in the compliant touch with the object and creating a map that visualizes objects in the operating space without any visual information. Our results demonstrate that the tracking error signal contains robust information regarding the contact interaction between the actuator and its environment.
The scope of this article is the well-known wall pursuit game, which has been used in the literature to illustrate the existence of a singular surface (dispersal line) and the associated game ...dilemma. We derive an analytical expression for the value function of the game, which is the viscosity solution of the Hamilton-Jacobi-Isaacs equation. Then, we introduce a hold time analysis and the rate of change for the loss of time to capture along the dispersal line, and show that the rate has a well-defined saddle point along the dispersal line, which can be used to resolve the dilemma. Moreover, we prove that the saddle point of the rate characterizes optimal game actions not only on the dispersal line, but also for all other states of the game. Finally, we analyze the same game in a version with a nonzero hold time and show that in that case, the actions from the dispersal line have to be applied both on the dispersal line and in a narrow band around it. To illustrate that, we use an example to compute the band around the line.
We present a task pose planner for a robustly safe automation of suture looping tasks in robotic assisted minimally invasive surgery (RAMIS). Our approach uses pre-planned spiral looping trajectories ...and computes the task pose using a combination of linear programming for position optimization and a brute force iterative orientation search. The optimization maximizes the minimum distance from constraints to account for any uncertainties. We verify our approach in a simulation to be effective in avoiding instrument-tissue collisions, suture entanglement and effective length constraints, and gripper joint limits. In addition, it allows us to create a map that provides the task pose quality at suture exit point locations. With the map, we are able to identify task poses for multiple suture exit points and suitable port placements.
Magnetic microswimmers are useful for navigating and performing tasks at small scales. To demonstrate effective control over such microswimmers, we implemented feedback control of the three-bead ...achiral microswimmers in both simulation and experiment. The achiral microswimmers with the ability to swim in bulk fluid are controlled wirelessly using magnetic fields generated from electromagnetic coils. The achirality of the microswimmers introduces unknown handedness resulting in uncertainty in swimming direction. We use a combination of rotating and static magnetic fields generated from an approximate Helmholtz coil system to overcome such uncertainty. There are also movement uncertainties due to environmental factors such as unsteady flow conditions. A kinematic model based feedback controller was created based on data fitting of experimental data. However, the controller was unable to yield satisfactory performance due to uncertainties from environmental factors; i.e., the time to reach target pose under adverse flow condition is too long. Following the implementation of an integral controller to control the microswimmers＇ swimming velocity, the mieroswimmers were able to reach the target in roughly half the time. Through simulation and experiments, we show that the feedback control law can move an achiral microswimmer from any initial conditions to a target pose.
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