Angela Schöllig

The Flying Machine Arena as of 2010

The Flying Machine Arena (FMA) is an indoor research space built specifically for the study of autonomous systems and aerial robotics. In this video, we give an overview of this testbed and some of its capabilities. We show the FMA infrastructure and hardware, which includes a fleet of quadrocopters and a motion capture system for vehicle localization. The physical components of the FMA are complemented by specialized software tools and components that facilitate the use of the space and provide a unified framework for communication and control. The flexibility and modularity of the experimental platform is highlighted by various research projects and demonstrations.

Synchronizing the motion of a quadrocopter to music

This paper presents a quadrocopter flying in rhythm to music. The quadrocopter performs a periodic side-to-side motion in time to a musical beat. Underlying controllers are designed that stabilize the vehicle and produce a swinging motion. Synchronization is then achieved by using concepts from phase-locked loops. A phase comparator combined with a correction algorithm eliminate the phase error between the music reference and the actual quadrocopter motion. Experimental results show fast and effective synchronization that is robust to sudden changes in the reference amplitude and frequency. Changes in frequency and amplitude are tracked precisely when adding an additional feedforward component, based on an experimentally determined look-up table.

Feasiblity of motion primitives for choreographed quadrocopter flight

This paper describes a method for checking the feasibility of quadrocopter motions. The approach, meant as a validation tool for preprogrammed quadrocopter performances, is based on first principles models and ensures that a desired trajectory respects both vehicle dynamics and motor thrust limits. We apply this method towards the eventual goal of using parameterized motion primitives for expressive quadrocopter choreographies. First, we show how a large class of motion primitives can be formulated as truncated Fourier series. We then show how the feasibility check can be applied to such motions by deriving explicit parameter constraints for two particular parameterized primitives. The predicted feasibility constraints are compared against experimental results from quadrocopters in the ETH Flying Machine Arena.

A hybrid Bellman equation for bimodal systems

In this paper we present a dynamic programming formulation of a hybrid optimal control problem for bimodal systems with regional dynamics. In particular, based on optimality-zone computations, a framework is presented in which the resulting hybrid Bellman equation guides the design of optimal control programs with, at most, N discrete transitions.

A Hybrid Bellman Equation for systems with regional dynamics

In this paper, we study hybrid systems with regional dynamics, i.e., systems where transitions between different dynamical regimes occur as the continuous state of the system reaches given switching surfaces. In particular, we focus our attention on the optimal control problem associated with such systems, and we present a Hybrid Bellman Equation for such systems that provide a characterization of global optimality, given an upper bound on the number of switches. Not surprisingly, the solution will be hybrid in nature in that it will depend on not only the continuous control signals, but also on discrete decisions as to what domains the system should go through in the first place. A number of examples are presented to highlight the operation of the proposed approach.

Independent vs. joint estimation in multi-agent iterative learning control

This paper studies iterative learning control (ILC) in a multi-agent framework, wherein a group of agents simultaneously and repeatedly perform the same task. The agents improve their performance by using the knowledge gained from previous executions. Assuming similarity between the agents, we investigate whether exchanging information between the agents improves an individuals learning performance. That is, does an individual agent benefit from the experience of the other agents? We consider the multi-agent iterative learning problem as a two-step process of: first, estimating the repetitive disturbance of each agent; and second, correcting for it. We present a comparison of an agents disturbance estimate in the case of (I) independent estimation, where each agent has access only to its own measurement, and (II) joint estimation, where information of all agents is globally accessible. We analytically derive an upper bound of the performance improvement due to joint estimation. Results are obtained for two limiting cases: (i) pure process noise, and (ii) pure measurement noise. The benefits of information sharing are negligible in (i). For (ii), a performance improvement is observed when a high similarity between the agents is guaranteed.

Sensitivity of Joint Estimation in Multi-Agent Iterative Learning Control

Abstract We consider a group of agents that simultaneously learn the same task, and revisit a previously developed algorithm, where agents share their information and learn jointly. We have already shown that, as compared to an independent learning model that disregards the information of the other agents, and when assuming similarity between the agents, a joint algorithm improves the learning performance of an individual agent. We now revisit the joint learning algorithm to determine its sensitivity to the underlying assumption of similarity between agents. We note that an incorrect assumption about the agents’ degree of similarity degrades the performance of the joint learning scheme. The degradation is particularly acute if we assume that the agents are more similar than they are in reality; in this case, a joint learning scheme can result in a poorer performance than the independent learning algorithm. In the worst case (when we assume that the agents are identical, but they are, in reality, not) the joint learning does not even converge to the correct value. We conclude that, when applying the joint algorithm, it is crucial not to overestimate the similarity of the agents; otherwise, a learning scheme that is independent of the similarity assumption is preferable.