RAPTOR

RAPid and robust Trajectory Optimization for Robots

Performing trajectory design for humanoid robots with high degrees of freedom is computationally challenging. The trajectory design process also often involves carefully selecting various hyperparameters and requires a good initial guess which can further complicate the development process. This work introduces a generalized gait optimization framework that directly generates smooth and physically feasible trajectories. The proposed method demonstrates faster and more robust convergence than existing techniques and explicitly incorporates closed-loop kinematic constraints that appear in many modern humanoids.

• RAPTOR is smooth.

RAPTOR directly parameterizes the trajectory in a smooth representation, for example, polynomials, and optimizes on this smooth representation.

• RAPTOR is robust.

Don't know how to initialize the optimization problem? It's okay! RAPTOR can handle it. For humanoid gait optimization problems, we simply assign random initial guesses and RAPTOR can still converge to feasible solutions!

• RAPTOR is fast.

RAPTOR is fully implemented in C++. It is able to solve the humanoid gait optimization problems in seconds!

Trajectory Optimization Demos

Digit walking

Digit walking forward with 0.0 m/s and 0.10 m step height (periodic)

Digit walking forward with 0.5 m/s and 0.15 m step height (periodic)

Digit walking forward with 1.0 m/s and 0.20 m step height (periodic)

Digit turning (periodic)

Digit stepping upward (periodic)

Digit walking forward with different step lengths and step heights (periodic)

Talos walking

Talos walking forward with 0.0 m/s and 0.10 m step height (periodic)

Talos walking forward with 0.5 m/s and 0.15 m step height (periodic)

Talos walking forward with 1.0 m/s and 0.20 m step height (periodic)

Kinova-gen3

Obstacle Avoidance Example:
The robot starts from blue configuration and targets at the green configuration. The obstacles are shown in red. The waypoints generated by RRT are shown in black. We solve an optimization problem at each iteration to generate a smooth trajectory that avoids the obstacles while getting to the next waypoint.
The formulation of the optimization problem is a discrete version of our previous work ARMOUR, where constraints are only considered on discrete time samples, rather than continuous time intervals to guarantee safety.

Inverse Kinematics Example:
Solving a series of inverse kinematics in seconds!

Links

Paper

Codebase

Authors

Bohao Zhang¹

Ram Vasudevan²

¹ Robotics Institute, University of Michigan, Ann Arbor ² Mechanical Engineering, University of Michigan, Ann Arbor

This work is developed under RoahmLab.

BibTeX

@misc{zhang2024rapidrobusttrajectoryoptimization,
	title={Rapid and Robust Trajectory Optimization for Humanoids}, 
	author={Bohao Zhang and Ram Vasudevan},
	year={2024},
	eprint={2409.00303},
	archivePrefix={arXiv},
	primaryClass={cs.RO},
	url={https://arxiv.org/abs/2409.00303}}
					    

Contact

We are actively developing the codebase and appreciate any feedback!
If you have any questions about the paper, please feel free to contact Bohao Zhang.
If you have any questions about the code and would like to report any bugs or problems, please raise a new issue in the Issues page in the RAPTOR repo. We will try to respond to it as soon as possible.
If you would like to request any related new features and have suggestions on how to improve the performance of RAPTOR, please raise a new discussion in the Discussions page in the RAPTOR repo.

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