Swing up control of inverted pendulum

Furuta, K.; Yamakita, Masaki; Kobayashi, Shinichi

doi:10.1109/iecon.1991.239008

Cited by 140 publications

(64 citation statements)

References 4 publications

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“…|u| = u max , that bound the reachable set for its parent node. This control policy agrees with the bang-bang control strategies that have been proposed elsewhere for the inverted pendulum [12].…”

Section: A Swing Up Control For An Underactuated Pendulumsupporting

confidence: 86%

Reachability-guided sampling for planning under differential constraints

Shkolnik

Walter

Tedrake

2009

2009 IEEE International Conference on Robotics and Automation

119

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Abstract-Rapidly-exploring Random Trees (RRTs) are widely used to solve large planning problems where the scope prohibits the feasibility of deterministic solvers, but the efficiency of these algorithms can be severely compromised in the presence of certain kinodynamics constraints. Obstacle fields with tunnels, or tubes are notoriously difficult, as are systems with differential constraints, because the tree grows inefficiently at the boundaries. Here we present a new sampling strategy for the RRT algorithm, based on an estimated feasibility set, which affords a dramatic improvement in performance in these severely constrained systems. We demonstrate the algorithm with a detailed look at the expansion of an RRT in a swingup task, and on path planning for a nonholonomic car. I. INTRODUCTIONThe problem of robotic motion planning, whether for a wheeled robot, an aerial vehicle, or a quadruped, has motivated the development of powerful tools for planning in high dimensional spaces. Of these techniques, randomized sample-based planning strategies have proven particularly effective in quickly solving for a series of actions that drive the system to a desired state. Perhaps the most widely used single-query sample-based planners are those based upon Rapidly-exploring Randomized Trees (RRTs). RRTs have been used to solve a broad range of planning problems that include motion for manipulators and kinematic chains [1], [2].It is well-known that these algorithms can quickly become inefficient when planning on systems with complicated kinodynamic constraints [3], and there has been considerable work in attempting to modify the basic RRT algorithm for these situations [3], [4]. The essential symptom of this inefficiency is that nodes at the boundaries of these constraints tend to be sampled and expanded repeatedly, with little progress towards the ultimate goal.In this paper, we present a modified adaptive sampling strategy for the RRT algorithm which takes into account local reachability, as defined by differential constraints, while building the tree. The algorithm is based on the observation that sampling points at random and checking collisions is relatively cheap, but adding extra nodes to the tree (through the Extend algorithm) is relatively more expensive -both in its instantaneous cost and in the added cost of having a larger tree. Therefore, we attempt to build sparse trees through kinodynamic obstacles, with a simple heuristic that quickly throws away random samples that otherwise would not have the effect of extending the tree into previously unexplored regions of state space. This effectively changes the sampling distribution, so that points are selected uniformly from a

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Section: A Swing Up Control For An Underactuated Pendulumsupporting

confidence: 86%

Reachability-guided sampling for planning under differential constraints

Shkolnik

Walter

Tedrake

2009

2009 IEEE International Conference on Robotics and Automation

119

View full text Add to dashboard Cite

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“…Aquí se presentan limitaciones en el movimiento del carro y por lo tanto hay restricciones; este problema fue sorteado en el año 1991 con el reemplazo del carro sobre riel por un motor eléctrico que maneja directamente un brazo horizontal [2], como se muestra en la figura 2. Este dispositivo es conocido como el péndulo invertido rotacional simple o de Furuta y su conformación se da por dos elementos, el primero de ellos se mueve únicamente en un plano horizontal y es controlado por un motor eléctrico de corriente continua CC (sistema actuado), el segundo elemento corresponde al péndulo o brazo colgante que es libre de moverse en un plano vertical (sistema sub-actuado).…”

Section: Iunclassified

Control De Un Péndulo De Furuta. Una Revisión Del Estado Del Arte.

García¹,

Buitrago²,

Ramírez³

2015

Sci. tech

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“…It should be noticed that Eq (4) can be numerically solved from a specified control torque u(t), and the forces F x0 and F y0 can be obtained from Eqs (5)- (7). Next, it is assumed that the control torque is a PID controller, i.e.…”

Section: Mathematical Model and Statement Of The Problemmentioning

confidence: 99%

“…On the other hand, the problem of swinging up and controlling a pendulum has been considered in the classical Refs [7][8]. Other more complex control strategies reveal the great interest of the inverted pendulum in the field of control, as it is the case of control strategies based on space-state methods [9][10][11], control stabilization around homoclinic orbits [12], energy methods [13], passivity control [14] and bounded control [15] among others.…”

Section: Introductionmentioning

confidence: 99%

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Stability and chaotic behavior of a PID controlled inverted pendulum subjected to harmonic base excitations by using the normal form theory

Pérez-Polo

Molina

Chica

et al. 2014

Applied Mathematics and Computation

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In this paper we investigate the stability and the onset of chaotic oscillations around the pointing-up position for a simple inverted pendulum that is driven by a control torque and is harmonically excited in the vertical and horizontal directions. The driven control torque is defined as a proportional plus integral plus derivative (PID) control of the deviation angle with respect to the pointing-down equilibrium position.The parameters of the PID controller are tuned by using the Routh criterion to obtain a stable weak focus around the pointing-up position, whose stability is investigated by using the normal form theory. The normal form theory is also used to deduce a simplified mathematical model that can be resolved analytically and compared with the numerical simulation of the complete mathematical model. From the harmonic prescribed motions for the pendulum base, necessary conditions for chaotic motion are deduced by means of the Melnikov function. When the pendulum is close to the unstable pointing-up position, the PID parameters are changed and the chaotic motion is destroyed, which is achieved by employing very small control signals even in the presence of random noise. The results of the analytical calculations are verified by full numerical simulations.

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Swing up control of inverted pendulum

Cited by 140 publications

References 4 publications

Reachability-guided sampling for planning under differential constraints

Reachability-guided sampling for planning under differential constraints

Control De Un Péndulo De Furuta. Una Revisión Del Estado Del Arte.

Stability and chaotic behavior of a PID controlled inverted pendulum subjected to harmonic base excitations by using the normal form theory

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