Near-time optimal path planning using potential functions

Sundar, Satish; Shiller, Zvi

doi:10.1109/iros.1991.174675

Cited by 5 publications

(4 citation statements)

References 15 publications

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“…g k 5 g ref,k 2 g k , and P, Q, and R are constant positivedefinite weighting matrices. Equation (15) and the first term of equation (16) penalize the deviation from the reference along the horizon. The second term of equation (16) penalizes the control input in terms of energy consumption.…”

Section: Basic Mpc Algorithmmentioning

confidence: 99%

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Obstacle avoidance of autonomous vehicles based on model predictive control

Park

Kim

Yoon³

et al. 2009

Proceedings of the Institution of Mechanical Engineers, Part D:

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This paper presents an obstacle avoidance scheme for autonomous vehicles as an active safety procedure in unknown environments. Safe trajectories are generated using the non-linear model predictive framework, in which the simplified dynamics of the vehicle are used to predict the state of the vehicle over the look-ahead horizon. To compensate for the slight dissimilarity between the simplified model and the actual vehicle, a separate controller is designed to track the generated trajectory. The longitudinal dynamics of the vehicle are controlled using the inverse dynamics of the vehicle powertrain model, and the lateral dynamics are controlled using a linear quadratic regulator. In the non-linear model predictive framework, to obtain safe trajectories, local obstacle information is incorporated into the performance index using a parallax-based method. Simulation results on a full non-linear vehicle model show that the proposed combination of model-predictive-control-based trajectory generation and tracking controller gives satisfactory online obstacle avoidance performance.

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Section: Basic Mpc Algorithmmentioning

confidence: 99%

“…In order to avoid local minima problems, modified versions of the potential field method have been proposed. Examples are using harmonic potential fields [13,14], or navigation functions [15]. Also, the wavefront propagation method generates artificial potential fields without local minima [16].…”

Section: Introductionmentioning

confidence: 99%

Obstacle avoidance of autonomous vehicles based on model predictive control

Park

Kim

Yoon³

et al. 2009

Proceedings of the Institution of Mechanical Engineers, Part D:

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“…The first two terms of the above expression are guaranteed to be greater than or equal to zero by enforcing conditions (31), (34), and (42). This reduces the avoidance conditions in the joint q0 _ q space to guaranteeing that Z t t0 2 1 (q; _ q)e t n ( _ q)D 01 (q)e n (q) 3 dt + 2 2 (q; _ q)e t n (q)D 01 (q)e n ( _ q) 3 0: (54) Before tackling the above expression, the relation between a unit vector in the position space and the corresponding one in the velocity space needs to be examined.…”

Section: _ Dmentioning

confidence: 99%

“…No method for computing this limit was provided. Sundar and Shiller combined the idea of acceleration lines with that of potential fields to achieve a near time-optimal trajectory to the target [34]. Their strategy is to augment the above technique with an acceleration potential and a deceleration potential at the terminal points of motion.…”

Section: Introductionmentioning

confidence: 99%

Constrained motion control using vector potential fields

Masoud

2000

IEEE Trans. Syst., Man, Cybern. A

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This paper discusses the generation of a control signal that would instruct the actuators of a robotics manipulator to drive motion along a safe and well-behaved path to a desired target. The proposed concept of navigation control along with the tools necessary for its construction achieve this goal. The most significant tool is the artificial vector potential field which shows a better ability to steer motion than does a scalar potential field. The synthesis procedure emphasizes flexibility so that the effort needed to modify the control is commensurate with the change in the geometry of the workspace. Theoretical development along with simulation results are provided. Index Terms-Motion planning, nonlinear control, robotics manipulators, vector potential fields. NOMENCLATURE NC Navigation control. PF Potential field. VPF Vector potential field. SPF Scalar potential field. BVP Boundary value problem. VBVP Vector boundary value problem. SBVP Scalar boundary value problem. BEM Boundary element method. LAC Local alignment control. PPC Penetration prevention control. BLAC Boundary local alignment control. BPPC Boundary penetration prevention control.

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On time-optimal feedback control

Sundar¹,

Shiller²

Proceedings of 1994 American Control Conference - ACC '94

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A b s t r a c t Time-optimal feedback control can be computed by solving tlie I-Iamilton-Jacobi-Belliiiaii (IIJB) equation. To date, this problem has not, been solved for nonlinear systems, such as articulat,ed robot,ic nianipulators, partly due to the difficulty in efficientsly finding a solution to tlie II.JI3 equation.In this paper, a new sufficient optiniality condition for time-optimal feedback control is present,ed. It generalizes tlie previous sufficiency condit~ions, the H J B equation and a Lyapunov-based condition derived in [ll]. The new condition is satisfied by a class of piecewise C3 continuous functions, t8ermed geiiemlized value functioas, as is demonstrat,ed in an example for a simple nonlinear system.[ 181 C. R. W ylie, A dvorzced Engin eevi ng Afu th e rn ci tic.s,

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Near-time optimal path planning using potential functions

Cited by 5 publications

References 15 publications

Obstacle avoidance of autonomous vehicles based on model predictive control

Obstacle avoidance of autonomous vehicles based on model predictive control

Constrained motion control using vector potential fields

On time-optimal feedback control

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