William B. Dunbar

Distributed receding horizon control for multi-vehicle formation stabilization

We consider the control of interacting subsystems whose dynamics and constraints are decoupled, but whose state vectors are coupled non-separably in a single cost function of a finite horizon optimal control problem. For a given cost structure, we generate distributed optimal control problems for each subsystem and establish that a distributed receding horizon control implementation is stabilizing to a neighborhood of the objective state. The implementation requires synchronous updates and the exchange of the most recent optimal control trajectory between coupled subsystems prior to each update. The key requirements for stability are that each subsystem not deviate too far from the previous open-loop state trajectory, and that the receding horizon updates happen sufficiently fast. The venue of multi-vehicle formation stabilization is used to demonstrate the distributed implementation.

Distributed Receding Horizon Control of Dynamically Coupled Nonlinear Systems

This paper considers the problem of distributed control of dynamically coupled nonlinear systems that are subject to decoupled constraints. Examples of such systems include certain large scale process control systems, chains of coupled oscillators and supply chain management systems. Receding horizon control (RHC) is a method of choice in these venues as constraints can be explicitly accommodated. In addition, a distributed control approach is sought to enable the autonomy of the individual subsystems and reduce the computational burden of centralized implementations. In this paper, a distributed RHC algorithm is presented for dynamically coupled nonlinear systems that are subject to decoupled input constraints. By this algorithm, each subsystem computes its own control locally. Provided an initially feasible solution can be found, subsequent feasibility of the algorithm is guaranteed at every update, and asymptotic stabilization is established. The theoretical conditions for feasibility and stability are shown to be satisfied for a set of coupled Van der Pol oscillators that model a walking robot experiment. In simulations, distributed and centralized receding horizon controllers are employed for stabilization of the oscillators. The numerical experiments show that the controllers perform comparably, while the computational savings of the distributed implementation over the centralized implementation is clearly demonstrated.

Model predictive control of coordinated multi-vehicle formations

A generalized model predictive control (MPC) formulation is derived that extends the existing theory to a multi-vehicle formation stabilization problem. The vehicles are individually governed by nonlinear and constrained dynamics. The extension considers formation stabilization to a set of permissible equilibria, rather than a unique equilibrium. Simulations for three vehicle formations with input constrained dynamics on configuration space SE(2) are performed using a nonlinear trajectory generation (NTG) software package developed at Caltech. Preliminary results and an outline of future work for scaling/decentralizing the MPC approach and applying it to an emerging experimental testbed are given.

Sequence-specific detection of individual DNA polymerase complexes in real time using a nanopore

Nanoscale pores have potential to be used as biosensors and are an established tool for analysing the structure and composition of single DNA or RNA molecules. Recently, nanopores have been used to measure the binding of enzymes to their DNA substrates. In this technique, a polynucleotide bound to an enzyme is drawn into the nanopore by an applied voltage. The force exerted on the charged backbone of the polynucleotide by the electric field is used to examine the enzyme-polynucleotide interactions. Here we show that a nanopore sensor can accurately identify DNA templates bound in the catalytic site of individual DNA polymerase molecules. Discrimination among unbound DNA, binary DNA/polymerase complexes, and ternary DNA/polymerase/deoxynucleotide triphosphate complexes was achieved in real time using finite state machine logic. This technique is applicable to numerous enzymes that bind or modify DNA or RNA including exonucleases, kinases and other polymerases.

Cooperative control of multi-vehicle systems using cost graphs and optimization

We introduce a class of triangulated graphs for algebraic representation of formations that allows one to specify a mission cost for a group of vehicles. This representation plus the navigational information allows one to formally specify and solve tracking problems for groups of vehicles in formations using an optimization-based approach. The approach is illustrated using a collection of six underactuated vehicles that track a desired trajectory in formation.

Distributed Receding Horizon Control of Vehicle Platoons: Stability and String Stability

This paper considers the problem of distributed control of a platoon of vehicles with nonlinear dynamics. We present distributed receding horizon control algorithms and derive sufficient conditions that guarantee asymptotic stability, leader-follower string stability, and predecessor-follower string stability, following a step speed change in the platoon. Vehicles compute their own control in parallel, and receive communicated position and velocity error trajectories from their immediate predecessor. Leader-follower string stability requires additional communication from the lead car at each update, in the form of a position error trajectory. Predecessor-follower string stability, as we define it, implies leader-follower string stability. Predecessor-follower string stability requires stricter constraints in the local optimal control problems than the leader-follower formulation, but communication from the lead car is required only once at initialization. Provided an initially feasible solution can be found, subsequent feasibility of the algorithms are guaranteed at every update. The theory is generalized for nonlinear decoupled dynamics, and is thus applicable to fleets of planes, robots, or boats, in addition to cars. A simple seven-car simulation examines parametric tradeoffs that affect stability and string stability. Analysis on platoon formation, heterogeneity and size (length) is also considered, resulting in intuitive tradeoffs between lead car and following car control flexibility.

Recent advances in nanopore sequencing.

The prospect of nanopores as a next‐generation sequencing platform has been a topic of growing interest and considerable government‐sponsored research for more than a decade. Oxford Nanopore Technologies recently announced the first commercial nanopore sequencing devices, to be made available by the end of 2012, while other companies (Life, Roche, and IBM) are also pursuing nanopore sequencing approaches. In this paper, the state of the art in nanopore sequencing is reviewed, focusing on the most recent contributions that have or promise to have next‐generation sequencing commercial potential. We consider also the scalability of the circuitry to support multichannel arrays of nanopores in future sequencing devices, which is critical to commercial viability.

The Caltech Multi-Vehicle Wireless Testbed

We introduce the Caltech Multi-Vehicle Wireless Testbed (MVWT), a platform for testing decentralized control methodologies for multiple vehicle coordination and formation stabilization. The testbed consists of eight mobile vehicles, an overhead vision system that provides GPS-like state information and wireless Ethernet for communications. Each vehicle rests on omni-directional casters and is powered by two high-performance ducted fans. Thus, a unique feature of our testbed is that the vehicles have second order dynamics, requiring real-time feedback algorithms to stabilize the system while performing cooperative tasks. The testbed will be used by various research groups at Caltech and elsewhere to validate theoretical advances in multi-vehicle coordination and control, networked control systems, real-time networking and high confidence distributed computation.

Receding horizon control of multi-vehicle formations: a distributed implementation

We consider the control of interacting subsystems whose dynamics and constraints are decoupled, but whose state vectors are coupled non-separably in a single cost function of a finite horizon optimal control problem. For a given cost structure, we generate distributed optimal control problems for each subsystem and establish that a distributed receding horizon control implementation is stabilizing. The implementation requires synchronous updates and the exchange of the most recent optimal control trajectory between coupled subsystems prior to each update. Key requirements for stability are that each subsystem not deviates too far from the previous open-loop state trajectory, and that the receding horizon updates happen sufficiently fast. The venue of multi-vehicle formation stabilization is used to demonstrate the distributed implementation and simulations are provided.

Electronic control of DNA polymerase binding and unbinding to single DNA molecules.

DNA polymerases catalyze template-dependent genome replication. The assembly of a high affinity ternary complex between these enzymes, the double strand-single strand junction of their DNA substrate, and the deoxynucleoside triphosphate (dNTP) complementary to the first template base in the polymerase active site is essential to this process. We present a single molecule method for iterative measurements of DNA-polymerase complex assembly with high temporal resolution, using active voltage control of individual DNA substrate molecules tethered noncovalently in an alpha-hemolysin nanopore. DNA binding states of the Klenow fragment of Escherichia coli DNA polymerase I (KF) were diagnosed based upon their ionic current signature, and reacted to with submillisecond precision to execute voltage changes that controlled exposure of the DNA substrate to KF and dNTP. Precise control of exposure times allowed measurements of DNA-KF complex assembly on a time scale that superimposed with the rate of KF binding. Hundreds of measurements were made with a single tethered DNA molecule within seconds, and dozens of molecules can be tethered within a single experiment. This approach allows statistically robust analysis of the assembly of complexes between DNA and RNA processing enzymes and their substrates at the single molecule level.