Algorithms for time–optimal control of CNC machines along curved tool paths

Timar, Sebastian; Farouki, Rida T.; Smith, Tait S.; Boyadjieff, Casey L.

doi:10.1016/j.rcim.2004.05.004

Cited by 95 publications

(29 citation statements)

References 23 publications

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“…The time-optimal setting of the cornering feedrate function parameters, combined with the three-phase feedrate profiles along linear segments, offers a simple kinematic basis for efficient execution of piecewise-linear paths with rounded corners, that avoids the complicated mathematical formulations and algorithmic implementations incurred by the formal "bang-bang" solutions [1,6,17,19] to time-optimal motion problems under prescribed acceleration bounds. The proposed strategy yields significant time savings, while globally satisfying the specified acceleration bounds over the entire path.…”

Section: Corner Rounding and Feedrate Algorithmsmentioning

confidence: 99%

Efficient high-speed cornering motions based on continuously-variable feedrates. II. Implementation and performance analysis

Nittler

Farouki

2016

Int J Adv Manuf Technol

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A novel high-speed cornering strategy for piecewise-linear motions is proposed, based on the G 2 continuous Pythagorean-hodograph (PH) rounding segments and continuously-variable feedrates described in Part I of this two-part paper. This strategy employs an accelerationlimited approach to feedrate scheduling, including smooth deceleration and acceleration profiles along linear segments entering and leaving the rounded segments. A G-code part program parsing software package has been developed, that automatically identifies toolpath corners and inserts appropriately-sized PH quintic corner rounding segments, with associated feedrate suppression ratios. The method has been tested on a three-axis CNC mill with an openarchitecture controller incorporating real-time interpolators that realize smoothly varying feedrates along the PH corner curves. Tests on a representative selection of toolpaths yield substantial savings (up to 40 %) in execution times, compared to the traditional "full stop" strategy for unmodified sharp corners.

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Section: Corner Rounding and Feedrate Algorithmsmentioning

confidence: 99%

Efficient high-speed cornering motions based on continuously-variable feedrates. II. Implementation and performance analysis

Nittler

Farouki

2016

Int J Adv Manuf Technol

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“…Let z * denote an optimal point of (8), and λ * , ν * the corresponding optimal Lagrange multipliers of the equality and inequality constraints in (8). Then, the derivative dr * dts (T s ) of the maximum travel range r * = c T z * to the sampling time t s , evaluated at the actual sampling time T s is given by [17]:…”

Section: Problemsmentioning

confidence: 99%

“…The goal is to find the system input that steers the system output from a given initial condition to the desired end condition in minimal time while respecting the system constraints. The literature on timeoptimal motion control is vast and contains both online [1] and offline [2], [3], [4], [5], [6] optimization methods, and focusses mainly on robotic manipulators [7], [8], [9], [10] and linear time-invariant (LTI) systems [1], [2], [3], [4], [5]. Depending on the linearity of the system and the parametrization of the motion trajectory, these algorithms yield an approximate [6], [4], [5] or an exact solution of the time-optimal PTP motion control problem [1], [2], [3].…”

Section: Introductionmentioning

confidence: 99%

Efficient Computation of Time-Optimal Point-to-Point Motion Trajectories

Janssens

Loock

Pipeleers

et al. 2015

IEEE Trans. Contr. Syst. Technol.

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Abstract-This paper presents an efficient algorithm to solve time-optimal point-to-point motion control problems for discretetime linear time-invariant systems with linear system constraints. Instead of using a bisection algorithm and solving a linear feasibility problem in each iteration, this paper proposes an iterative algorithm that is based on the Newton-Raphson method. In each iteration a maximum range problem is solved, maximizing the travel range of a system for a given motion time and system constraints. Although each iteration of the proposed algorithm is computationally more expensive than an iteration of the bisection algorithm, numerical examples demonstrate that the presented approach is generally more efficient thanks to a great reduction in the number of optimization problems to be solved.

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“…There are a number of trajectory planning algorithms which generate trajectory to drive a manipulator or motion stage with constraints on joint torques or actuator forces along a given geometric path in minimum or near-minimum time [1][2][3][4][5][6][7][8]. In most of these pieces of earlier work, either the system dynamics is simplified (for example, Coriolis and centrifugal terms are omitted in industrial robot dynamics) or hardware capability constraints are developed without higher order states (e.g., jerk constraint [5]).…”

Section: Introductionmentioning

confidence: 99%

Feedrate optimization for smooth minimum-time trajectory generation with higher order constraints

Bharathi

Dong

2015

Int J Adv Manuf Technol

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The generation of a time-optimal feedrate trajectory under various machine and process-related constraints has received significant attention in CNC machining and robotics applications. While most of the existing feedrate planning algorithms take velocity and acceleration into the consideration as capability constraints, the introduction of higher order dynamic states, such as jerk and/or jounce, makes the feedrate planning and optimization extremely challenging, as the dimension of the planning problem is increased accordingly. This paper proposes a heuristic trajectory planning algorithm that can provide a near-optimal minimum time trajectory for problems with higher order dynamic states. The algorithm starts with a non-timeoptimal but feasible velocity trajectory, which is interpolated from a number of knot points by piecewise spline interpolation with high-order continuity. Then, the trajectory is improved by scanning and increasing the velocity at each knot points while maintaining the feasibility of the resulting trajectory. A near-optimal trajectory is achieved when the improvement in travel time from the last scan iteration is smaller than a given value. The algorithm supports the incorporation of higher order dynamic states (up to the fifth derivative of displacement) in constraints for optimization without sacrificing the computational efficiency. Examples including linear and curved toolpath are presented to illustrate the effectiveness of this algorithm for high-speed contouring.

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Algorithms for time–optimal control of CNC machines along curved tool paths

Cited by 95 publications

References 23 publications

Efficient high-speed cornering motions based on continuously-variable feedrates. II. Implementation and performance analysis

Efficient high-speed cornering motions based on continuously-variable feedrates. II. Implementation and performance analysis

Efficient Computation of Time-Optimal Point-to-Point Motion Trajectories

Feedrate optimization for smooth minimum-time trajectory generation with higher order constraints

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