Real-Time Motion Planning of Legged Robots: A Model Predictive Control Approach

We introduce a real-time, constrained, nonlinear Model Predictive Control for the motion planning of legged robots. The proposed approach uses a constrained optimal control algorithm known as SLQ. We improve the efficiency of this algorithm by introducing a multi-processing scheme for estimating value function in its backward pass. This pass has been often calculated as a single process. This parallel SLQ algorithm can optimize longer time horizons without proportional increase in its computation time. Thus, our MPC algorithm can generate optimized trajectories for the next few phases of the motion within only a few milliseconds. This outperforms the state of the art by at least one order of magnitude. The performance of the approach is validated on a quadruped robot for generating dynamic gaits such as trotting.Comment: 8 page

Switching Quantum Dynamics for Fast Stabilization

Control strategies for dissipative preparation of target quantum states, both pure and mixed, and subspaces are obtained by switching between a set of available semigroup generators. We show that the class of problems of interest can be recast, from a control--theoretic perspective, into a switched-stabilization problem for linear dynamics. This is attained by a suitable affine transformation of the coherence-vector representation. In particular, we propose and compare stabilizing time-based and state-based switching rules for entangled state preparation, showing that the latter not only ensure faster convergence with respect to non-switching methods, but can designed so that they retain robustness with respect to initialization, as long as the target is a pure state or a subspace.Comment: 15 pages, 4 figure

Second order sliding mode control of underactuacted mechanical systems II: Orbital stabilization of an inverted pendulum with application to swing up / balancing control

International audienceOrbital stabilization of an underactuated cart-pendulum system is under study. The quasihomogeneous control synthesis is utilized to design a second order sliding mode controller that drives the actuated cart to a periodic reference orbit in finite time, while the non-actuated pendulum produces bounded oscillations. A modified Van der Pol oscillator is introduced into the synthesis as an asymptotic generator of the periodic motion. The resulting closed-loop system is capable of moving from one orbit to another by simply changing the parameters of the Van der Pol modification. Performance issues of the proposed synthesis are illustrated in numerical and experimental studies of the swing up/balancing control problem of moving a pendulum, located on an actuated cart, from its stable downward position to the unstable inverted position and stabilizing it about the vertical

Analysis and Design of Hybrid Control Systems

Different aspects of hybrid control systems are treated: analysis, simulation, design and implementation. A systematic methodology using extended Lyapunov theory for design of hybrid systems is developed. The methodology is based on conventional control designs in separate regions together with a switching strategy. Dynamics are not well defined if the control design methods lead to fast mode switching. The dynamics depend on the salient features of the implementation of the mode switches. A theorem for the stability of second order switching together with the resulting dynamics is derived. The dynamics on an intersection of two sliding sets are defined for two relays working on different time scales. The current simulation packages have problems modeling and simulating hybrid systems. It is shown how fast mode switches can be found before or during simulation. The necessary analysis work is a very small overhead for a modern simulation tool. To get some experience from practical problems with hybrid control the switching strategy is implemented in two different software environments. In one of them a time-optimal controller is added to an existing PID controller on a commercial control system. Successful experiments with this hybrid controller shows the practical use of the method

Space programs summary no. 37-63, volume 1 for the period 1 March - 30 April 1970. Flight projects

Mariner Mars 1971, Mariner Venus-Mercury 1973 and Viking Orbiter 1975 status report

Adaptive, fast walking in a biped robot under neuronal control and learning

Human walking is a dynamic, partly self-stabilizing process relying on the interaction of the biomechanical design with its neuronal control. The coordination of this process is a very difficult problem, and it has been suggested that it involves a hierarchy of levels, where the lower ones, e.g., interactions between muscles and the spinal cord, are largely autonomous, and where higher level control (e.g., cortical) arises only pointwise, as needed. This requires an architecture of several nested, sensori–motor loops where the walking process provides feedback signals to the walker's sensory systems, which can be used to coordinate its movements. To complicate the situation, at a maximal walking speed of more than four leg-lengths per second, the cycle period available to coordinate all these loops is rather short. In this study we present a planar biped robot, which uses the design principle of nested loops to combine the self-stabilizing properties of its biomechanical design with several levels of neuronal control. Specifically, we show how to adapt control by including online learning mechanisms based on simulated synaptic plasticity. This robot can walk with a high speed (> 3.0 leg length/s), self-adapting to minor disturbances, and reacting in a robust way to abruptly induced gait changes. At the same time, it can learn walking on different terrains, requiring only few learning experiences. This study shows that the tight coupling of physical with neuronal control, guided by sensory feedback from the walking pattern itself, combined with synaptic learning may be a way forward to better understand and solve coordination problems in other complex motor tasks

H2 optimal control algorithms for vehicle control

Vzestup autonomních vozidel a e-mobility umožňuje nasazení pokročilých řídicích systémů. Řízení na úrovni dynamiky vozidla poskytuje vyšší bezpečnost a lepší odezvu speciálně při velmi rychlých manévrech. Tato práce bere v potaz fyzikální limity dané cestou, pneumatikami a dynamikou vozidla a navrhuje řešení pro řízení podélné dynamiky. Cílem je maximalizovat podélné zrychlení vozidla. V této práci je použit jako nelineární verifikační a validační model jednostopý model vozidla, který zahrnuje Pacejkovu magickou rovnici pro modelování pneumatik. Jsou zde navrženy 2 možné přístupy k řešení. V první části je prezentováno řízení podélného skluzu lambda. Stavový model pro návrh řídicího systému je odvozen z nelineárního modelu v pracovním bodě s konstantním zrychlením. Protože rychlost je stav systému nelze zde použít běžné linearizační metody - nejedná se o linearizaci v ekvilibriu. Místo toho je použita linearizace podél trajektorie. Toto výustí v použití LPV technik. Dále je navržen řídicí algoritmus založený na použití LQ metodologie, který řídí podélný skluz. V druhé části je představen řídicí systém založený na sledování úhlové rychlosti kol. Jádro tohoto systému tvoří zpětnovazební LQ řídicí smyčka pro řízení úhlové rychlosti omega kola. Referenční signál úhlové rychlosti kol je vypočítáván na základě požadavku na lambdu. Jako nejvyšší v hierarchii je zpětnovazební smyčka řízení zrychlení. Nakonec jsou provedeny virtuální jízdní testy, které porovnávají řídicí sytém založený na sledování úhlové rychlosti kol a systém bez regulace na klouzavém povrchu.Trend of autonomous vehicles and e-mobility is in favor of an advanced control system development and deployment. Vehicle dynamics level control systems providing safety limits and high performance response, especially during high dynamics maneuvers, are necessary. This work provides solution for vehicle longitudinal dynamics (vehicle acceleration) considering physical limits given by road, tire and vehicle dynamics respectively. The goal is to maximize vehicle longitudinal acceleration. Considered mathematical model is nonlinear single-track model incorporating nonlinear Pacejka magic formula as a tire model. This work proposes two possible control approaches. In first part the direct longitudinal slip ratio lambda control is presented. Design model for control system is derived as a linearized state-space model at constant acceleration operation point. Therefore, the common linearization approach, at system equilibrium, is not possible and the linearization along system trajectory is used. Such solution results in involvement of LPV techniques, as vehicle velocity is state variable. Next, the LQ optimal control framework is employed to deliver control algorithms providing constant longitudinal slip ratio trajectory tracing. Augmented direct slip ratio lambda control based on wheel angular velocity tracking is proposed in second part. The core of suggested hierarchical control system is the LQ-based closed loop for single wheel angular velocity omega tracking. The omega set-point signal is computed based on lambda demand. Finally, the vehicle longitudinal acceleration controller is designed. Virtual riding tests comparing the omega tracking based control system and open loop behavior on slippery surface are provided at the end of thesis