Use case
Optimizing dynamic trajectories for robustness to disturbances using polytopic projections
Discover how Artelys Knitro has facilitated the dynamic trajectory of objects in complex environments by innovatively addressing challenges related to the violation of motion constraints and nonlinearities with its advanced algorithms in the article from “2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)”.

When an external force is applied to a legged robot that has manipulation capabilities, it may cause the robot to slip, lose contact between a foot and the environment, or to fail to track the desired path. In each of these cases, the robot motion fails because the external force causes a violation of the so-called motion constraints.

To avoid such situations, it is essential to robustly optimize dynamic trajectories allowing the system to deal with disturbance forces and uncertain payloads. The problem can be modeled using advanced mathematical programs involving many nonlinearities

Thanks to its efficient interior-point method, Artelys Knitro allows researchers to determine highly robust dynamic trajectories. The benefits of robust optimization have been demonstrated using a quadruped robot equipped with a manipulator able to execute a pick-and-place of a bottle on a table, even on a skateboard.

Start with a tutorial!


You’re not familiar with nonlinear optimization? This tutorial will present some examples of nonlinear problems for various applications. You will discover nonlinear programming methods using the Artelys Knitro solver in a Python notebook, through different examples.

Free trial


Get your trial license to test Artelys Knitro’s performances on your own mathematical optimization problem. The trial package includes free support and maintenance. You can have access to Artelys Knitro for free with a 1-month unlimited version or a 6-month limited version.

Artelys Knitro has unmatched performance

Best Nonlinear



Artelys Knitro has been ranked every year by public benchmarks consistently showing Artelys Knitro finds both feasible and proven optimal solutions faster than competing solvers.




The Artelys technical support team comprises Artelys’consultants (PhD-level) who are used to solving the most difficult problems and deploying enterprise-wide optimization solutions. They can advise on algorithmic or software features that may result in enhanced performance in your usage of Artelys Knitro.

Updates and

new features


The development team works continuously to provide two releases of Artelys Knitro every year. Based on feedback, we always improve our solver to meet users’ requirements and need to solve larger models faster.

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