| 1. |
- Ardeshiri, Tohid, 1980-, et al.
(författare)
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Convex Optimization Approach for Time-Optimal Path Tracking of Robots with Speed Dependent Constraints
- 2010
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The task of generating time optimal trajectories for a six degrees of freedom industrial robot is discussed and an existing convex optimization formulation of the problem is extended to include new types of constraints. The new constraints are speed dependent and can be motivated from physical modeling of the motors and the drive system. It is shown how the speed dependent constraints should be added in order to keep the convexity of the overall problem. A method to, conservatively, approximate the linear speed dependent constraints by a convex constraint is also proposed. A numerical example proves versatility of the extension proposed in this paper.
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| 2. |
- Ardeshiri, Tohid, 1980-, et al.
(författare)
-
Convex Optimization Approach for Time-Optimal Path Tracking of Robots with Speed Dependent Constraints
- 2011
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Ingår i: Proceedings of the 18th IFAC World Congress. - : IFAC. - 9783902661937 ; , s. 14648-14653
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Konferensbidrag (refereegranskat)abstract
- The task of generating time optimal trajectories for a six degrees of freedom industrial robot is discussed and an existing convex optimization formulation of the problem is extended to include new types of constraints. The new constraints are speed dependent and can be motivated from physical modeling of the motors and the drive system. It is shown how the speed dependent constraints should be added in order to keep the convexity of the overall problem. A method to, conservatively, approximate the linear speed dependent constraints by a convex constraint is also proposed. A numerical example proves versatility of the extension proposed in this paper.
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| 3. |
- Bakarac, Peter, et al.
(författare)
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Explicit MPC Based on Approximate Dynamic Programming
- 2018
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Ingår i: 2018 EUROPEAN CONTROL CONFERENCE (ECC). - 9783952426982 - 9781538653036
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Konferensbidrag (refereegranskat)abstract
- In this paper we show how to synthesize simple explicit MPC controllers based on approximate dynamic programming. Here, a given MPC optimization problem over a finite horizon is solved iteratively as a series of problems of size one. The optimal cost function of each subproblem is approximated by a quadratic function that serves as a cost-to-go function for the subsequent iteration. The approximation is designed in such a way that closed-loop stability and recursive feasibility is maintained. Specifically, we show how to employ sum-of-squares relaxations to enforce that the approximate cost-to-go function is bounded from below and from above for all points of its domain. By resorting to quadratic approximations, the complexity of the resulting explicit MPC controller is considerably reduced both in terms of memory as well as the on-line computations. The procedure is applied to control an inverted pendulum and experimental data are presented to demonstrate viability of such an approach.
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| 4. |
- Barbosa, Filipe Marques, et al.
(författare)
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Fast or Cheap: Time and Energy Optimal Control of Ship-to-Shore Cranes
- 2023
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Ingår i: Special issue: 22nd IFAC World Congress. - : ELSEVIER. ; , s. 3126-3131
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Konferensbidrag (refereegranskat)abstract
- This paper addresses the trade-off between time and energy-efficiency for the problem of loading and unloading a ship. Container height constraints and energy consumption and regeneration are dealt with. We build upon a previous work that introduced a coordinate system suitable to deal with container avoidance constraints and incorporate the energy related modeling. In addition to changing the coordinate system, standard epigraph reformulations result in an optimal control problem with improved numerical properties. The trade-of is dealt with through the use of weighting of the total time and energy consumption in the cost function. An illustrative example is provided, demonstrating that the energy consumption can be substantially reduced while retaining approximately the same loading time.
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| 5. |
- Barbosa, Filipe Marques, et al.
(författare)
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Time-optimal control of cranes subject to container height constraints
- 2022
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Ingår i: Proceedings of 2022 American Control Conference (ACC). - : Institute of Electrical and Electronics Engineers (IEEE). - 9781665451963 - 9781665451970 - 9781665494809 ; , s. 3558-3563
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- The productivity and efficiency of port operations strongly depend on how fast a ship can be unloaded and loaded again. With this in mind, ship-to-shore cranes perform the critical task of transporting containers into and onto a ship and must do so as fast as possible. Though the problem of minimizing the time spent in moving the payload has been addressed in previous studies, the different heights of the container stacks have not been the focus. In this paper, we perform a change of variable and reformulate the optimization problem to deal with the constraints on the stack heights. As consequence, these constraints become trivial and easy to represent since they turn into bound constraints when the problem is discretized for the numerical solver. To validate the idea, we simulate a small-scale scenario where different stack heights are used. The results confirm our idea and the representation of the stack constraints become indeed trivial. This approach is promising to be applied in real crane operations and has the potential to enhance their automation.
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| 6. |
- Besselmann, Thomas, et al.
(författare)
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Explicit MPC for LPV Systems: Stability and Optimality
- 2012
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Ingår i: IEEE Transactions on Automatic Control. - 0018-9286 .- 1558-2523. ; 57:9, s. 2322-2332
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Tidskriftsartikel (refereegranskat)abstract
- This paper considers high-speed control of constrained linear parameter-varying systems using model predictive control. Existing model predictive control schemes for control of constrained linear parameter-varying systems typically require the solution of a semi-definite program at each sampling instance. Recently, variants of explicit model predictive control were proposed for linear parameter-varying systems with polytopic representation, decreasing the online computational effort by orders of magnitude. Depending on the mathematical structure of the underlying system, the constrained finite-time optimal control problem can be solved optimally, or close-to-optimal solutions can be computed. Constraint satisfaction, recursive feasibility and asymptotic stability can be guaranteed a priori by an appropriate selection of the terminal state constraints and terminal cost. The paper at hand gathers previous developments and provides new material such as a proof for the optimality of the solution, or, in the case of close-to-optimal solutions, a procedure to determine a bound on the suboptimality of the solution.
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| 7. |
- Dhar, Abhishek, et al.
(författare)
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Disturbance-Parametrized Robust Lattice-based Motion Planning
- 2023
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Ingår i: IEEE Transactions on Intelligent Vehicles. - 2379-8858 .- 2379-8904.
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Tidskriftsartikel (refereegranskat)abstract
- This paper introduces a disturbance-parametrized (DP) robust lattice-based motion-planning framework for nonlinear systems affected by bounded disturbances. A key idea in this work is to rigorously exploit the available knowledge about the disturbance, starting already offline at the time when a library of DP motion primitives is computed and ending not before the motion has been executed online. Given an up-to-date-estimate of the disturbance, the lattice-based motion planner performs a graph search online, to non-conservatively compute a disturbance aware optimal motion plan with formally motivated margins to obstacles. This is done utilizing the DP motion primitives, around which tubes are generated utilizing a suitably designed robust controller. The sizes of the tubes are dependent on the upper bounds of the disturbance appearing in the error between the actual system trajectory and the DP nominal trajectory, which in turn along with the overall optimality of the plan is dependant on the user-selected resolution of the available disturbance estimates. Increasing the resolution of the disturbance parameter results in smaller sizes of tubes around the motion primitives and can significantly reduce the conservativeness compared to traditional approaches, thus increasing the performance of the computed motion plans. The proposed strategy is implemented on an Euler-Lagrange-based ship model which is affected by a significant wind disturbance and the efficiency of the strategy is validated through a suitable simulation example.
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| 8. |
- Falkeborn, Rikard, et al.
(författare)
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Low-Rank Exploitation in Semidefinite Programming for Control
- 2010
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Ingår i: Proceedings of the 2010 IEEE International Symposium on Computer-Aided Control System Design. - Linköping : Linköping University Electronic Press. - 9781424453542 - 9781424453559 ; , s. 24-28
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Konferensbidrag (refereegranskat)abstract
- Many control related problems can be cast as semidefinite programs but, even though there exist polynomial time algorithms and good publicly available solvers, the time it takes to solve these problems can be long. Something many of these problems have in common, is that some of the variables enter as matrix valued variables. This leads to a low-rank structure in the basis matrices which can be exploited when forming the Newton equations. In this paper, we describe how this can be done, and show how our code can be used when using SDPT3. The idea behind this is old and is implemented in LMI Lab, but we show that when using a modern algorithm, the computational time can be reduced. Finally, we describe how the modeling language YALMIP is changed in such a way that our code can be interfaced using standard YALMIP commands, which greatly simplifies for the user.
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| 9. |
- Falkeborn, Rikard, et al.
(författare)
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Low-Rank Exploitation in Semidefinite Programming for Control
- 2011
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Ingår i: International Journal of Control. - : Taylor & Francis. - 0020-7179 .- 1366-5820. ; 84:12, s. 1975-1982
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Tidskriftsartikel (refereegranskat)abstract
- Many control-related problems can be cast as semidefinite programs. Even though there exist polynomial time algorithms and excellent publicly available solvers, the time it takes to solve these problems can be excessive. What many of these problems have in common, in particular in control, is that some of the variables enter as matrix-valued variables. This leads to a low-rank structure in the basis matrices which can be exploited when forming the Newton equations. In this article, we describe how this can be done, and show how our code, called STRUL, can be used in conjunction with the semidefinite programming solver SDPT3. The idea behind the structure exploitation is classical and is implemented in LMI Lab, but we show that when using a modern semidefinite programming framework such as SDPT3, the computational time can be significantly reduced. Finally, we describe how the modelling language YALMIP has been changed in such a way that our code, which can be freely downloaded, can be interfaced using standard YALMIP commands. This greatly simplifies modelling and usage.
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| 10. |
- Forsling, Robin, 1988-, et al.
(författare)
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Conservative Linear Unbiased Estimation Under Partially Known Covariances
- 2022
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Ingår i: IEEE Transactions on Signal Processing. - : IEEE. - 1053-587X .- 1941-0476. ; 70, s. 3123-3135
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Tidskriftsartikel (refereegranskat)abstract
- Mean square error optimal estimation requires the full correlation structure to be available. Unfortunately, it is not always possible to maintain full knowledge about the correlations. One example is decentralized data fusion where the cross-correlations between estimates are unknown, partly due to information sharing. To avoid underestimating the covariance of an estimate in such situations, conservative estimation is one option. In this paper the conservative linear unbiased estimator is formalized including optimality criteria. Fundamental bounds of the optimal conservative linear unbiased estimator are derived. A main contribution is a general approach for computing the proposed estimator based on robust optimization. Furthermore, it is shown that several existing estimation algorithms are special cases of the optimal conservative linear unbiased estimator. An evaluation verifies the theoretical considerations and shows that the optimization based approach performs better than existing conservative estimation methods in certain cases.
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