This paper addresses the problem of exponentially stabilizing periodic orbits in a special class hybrid models-systems with impulse effects-through control Lyapunov functions. The orbit is assumed to lie C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> submanifold Z that contained zero set an output function and invariant under both continuous discrete dynamics; associated restriction dynamics are termed dynamics. furthermore be stable...

This paper presents a novel method to address the actuator saturation for nonlinear hybrid systems by directly incorporating user-defined input bounds in controller design. In particular, we consider application of bipedal walking and show that our [based on quadratic programming (QP) implementation control Lyapunov function (CLF)-based controller] enables gradual performance degradation while still continuing walk under increasingly stringent bounds. We draw previous work, which has...

Hybrid zero dynamics extends the Byrnes-Isidori notion of to a class hybrid models called systems with impulse effects. Specifically, given smooth submanifold that is contained in set an output function and invariant under both continuous flow system effects as well its reset map, restriction dynamics. Prior results on stabilization periodic orbits have relied input-output linearization transverse variables. The principal result this paper shows how control Lyapunov functions can be used...

This paper reports on an underactuated 3D bipedal robot with passive feet that can start from a quiet standing position, initiate walking gait, and traverse the length of laboratory (approximately 10 m) at speed roughly 1 m/s. The controller was developed using method virtual constraints, control design first used planar point-feet robots Rabbit MABEL. For preliminary experiments reported here, constraints were experimentally tuned to achieve robust then walking. A key feature leading...

We specify and analyse models that capture the geometry of purposeful motion a collective mobile agents, with focus on planar motion, dyadic strategies attention graphs which are static, directed cyclic. Strategies formulated as constraints joint shape space implemented through feedback laws for actions individual here modelled self-steering particles. By reduction to labelled (using redundant parametrization account cycle closure constraints) further time rescaling, we characterize various...

Pursuit strategies (formulated using constant-speed particle models) provide a means for achieving cohesive behavior in systems of multiple mobile agents. In the present paper, we explore an n-agent cyclic pursuit scheme (i.e. agent i pursues i+1, modulo n) which each employs constant bearing strategy. We demonstrate existence invariant submanifold, and state necessary sufficient conditions rectilinear circling relative equilibria on that submanifold. full analysis steady-state solutions...

Pursuit strategies for interacting particles and feedback laws to execute them are formulated in three dimensions, focusing on constant bearing (CB) pursuit - a case of interest biology. In the analysis such setting n engaged cyclic pursuit, we reveal interesting invariant manifold dynamics associated explicit integrability properties, as well conditions special solutions relative equilibria.

The study of cyclic pursuit as a means to collective behavior in nature and artificial multi-agent systems is current interest. Here we examine the nonlinear closed loop dynamics planar based on constant bearing (CB) strategy. We show that there exists family rectilinear relative equilibria admit nearby periodic orbits an appropriate low dimensional space found by methods symmetry, reduction constraint. also demonstrate existence other families exhibit attractivity or instability.

This paper presents a novel method for directly incorporating user-defined control input saturations into the calculation of Lyapunov function (CLF)-based walking controller biped robot. Previous work by authors has demonstrated effectiveness CLF controllers stabilizing periodic gaits walkers, and current expands on those results providing more effective means handling saturations. The new approach, based convex optimization routine running at 1 kHz update rate, is useful not only torque but...

This paper investigates a modification of cyclic constant bearing (CB) pursuit in multi-agent system which each agent pays attention to neighbor and beacon. The problem admits shape equilibria with collective circling about the beacon, radius angular separation agents determined by choice parameters feedback law. Stability is shown for 2-agent system, results are demonstrated on mobile robots tracked motion capture system.

Recent work has formulated 2- and 3-dimensional models steering control laws for motion camouflage, a stealthy pursuit strategy observed in nature. Here we extend the model to encompass use of high-gain law presence sensor noise as well case when evader's is driven by stochastic process, demonstrating (in planar setting) that camouflage still accessible mean) finite time. We also discuss family admissible evader controls, laying out groundwork future game-theoretic study optimal evasion strategies.

We investigate low-dimensional examples of cyclic pursuit in a collective, wherein each agent employs constant bearing (CB) steering law relative to exactly one other agent. For the case three agents plane, we characterize equilibria and pure shape associated closed-loop dynamics. Re-scaling time yields reduction phase space two dimensions effective tools for stability analysis. Study bifurcation family collinear dependent on single CB control parameter reveals presence rich collection...

Cyclic pursuit systems provide a means to generate useful global behaviors in collective of autonomous agents based on dyadic interactions between neighboring cycle graph. Here we consider modified version the cyclic framework which stationary beacon provides an additional reference for system. Building proposed our previous work, derive necessary conditions stability circling equilibria n-agent Furthermore, employ change variables reveal existence family invariant manifolds related spiral...

Cooperative motion control of teams agile unmanned vehicles presents modeling challenges at several levels. The "microscopic equations" describing individual vehicle dynamics and their interaction with the environment may be known fairly precisely, but are generally too complicated to yield qualitative insights level multi-vehicle trajectory coordination. Interacting particle models suitable for coordinating trajectories, require care ensure that not driven in a "costly" manner. From point...

This paper addresses estimation of states and control parameters in cyclic pursuit systems. Classical observability tests are employed to derive conditions under which system (i.e. agent positions) observable several types schemes, including constant bearing beacon-referenced Under straightforward on the parameters, it is demonstrated that relative positions other agents (as well as beacon, when applicable) can be accurately estimated by an observer based only direct sensing one neighbor....

Abstract We describe a method for encoding binary messages in traffic infrastructure using specially designed rotating targets with barcode-like retroreflective characteristics which encode the data reflected Lidar intensity patterns. These Lidar-readable Rotational Barcodes can be installed as elements of Infrastructure to Vehicle (ITV) signaling, and they also on vehicles provide identification (e.g. an emergency vehicle) or function (VTV) signaling. Since many self-driving already use...

Motivated by real-world applications of unmanned aerial vehicles, this paper introduces a steering control law for pair agents maneuvering in the vicinity fixed beacon 3-dimensional setting. This is modification previously studied constant bearing (CB) pursuit law, sense that it incorporates an additional term to allocate attention beacon. We investigate behavior closed-loop dynamics two-agent mutual system wherein each agent employs beacon-referenced CB with regards other and stationary...