2,254 research outputs found
Automatic Differentiation of Rigid Body Dynamics for Optimal Control and Estimation
Many algorithms for control, optimization and estimation in robotics depend
on derivatives of the underlying system dynamics, e.g. to compute
linearizations, sensitivities or gradient directions. However, we show that
when dealing with Rigid Body Dynamics, these derivatives are difficult to
derive analytically and to implement efficiently. To overcome this issue, we
extend the modelling tool `RobCoGen' to be compatible with Automatic
Differentiation. Additionally, we propose how to automatically obtain the
derivatives and generate highly efficient source code. We highlight the
flexibility and performance of the approach in two application examples. First,
we show a Trajectory Optimization example for the quadrupedal robot HyQ, which
employs auto-differentiation on the dynamics including a contact model. Second,
we present a hardware experiment in which a 6 DoF robotic arm avoids a randomly
moving obstacle in a go-to task by fast, dynamic replanning
Inverse Dynamics vs. Forward Dynamics in Direct Transcription Formulations for Trajectory Optimization
Benchmarks of state-of-the-art rigid-body dynamics libraries report better
performance solving the inverse dynamics problem than the forward alternative.
Those benchmarks encouraged us to question whether that computational advantage
would translate to direct transcription, where calculating rigid-body dynamics
and their derivatives accounts for a significant share of computation time. In
this work, we implement an optimization framework where both approaches for
enforcing the system dynamics are available. We evaluate the performance of
each approach for systems of varying complexity, for domains with rigid
contacts. Our tests reveal that formulations using inverse dynamics converge
faster, require less iterations, and are more robust to coarse problem
discretization. These results indicate that inverse dynamics should be
preferred to enforce the nonlinear system dynamics in simultaneous methods,
such as direct transcription.Comment: Accepted to the 2021 IEEE International Conference on Robotics and
Automation (ICRA), Xi'an, China. Supplementary video available in
https://youtu.be/pV4s7hzUgjc. Related code in
https://github.com/JuliaRobotics/TORA.j
Optimizing Dynamic Trajectories for Robustness to Disturbances Using Polytopic Projections
This paper focuses on robustness to disturbance forces and uncertain
payloads. We present a novel formulation to optimize the robustness of dynamic
trajectories. A straightforward transcription of this formulation into a
nonlinear programming problem is not tractable for state-of-the-art solvers,
but it is possible to overcome this complication by exploiting the structure
induced by the kinematics of the robot. The non-trivial transcription proposed
allows trajectory optimization frameworks to converge to highly robust dynamic
solutions. We demonstrate the results of our approach using a quadruped robot
equipped with a manipulator.Comment: Final accepted version to the IEEE/RSJ International Conference on
Intelligent Robots and Systems (IROS) 2020. Supplementary video:
https://youtu.be/vDesP7IpTh
A Family of Iterative Gauss-Newton Shooting Methods for Nonlinear Optimal Control
This paper introduces a family of iterative algorithms for unconstrained
nonlinear optimal control. We generalize the well-known iLQR algorithm to
different multiple-shooting variants, combining advantages like
straight-forward initialization and a closed-loop forward integration. All
algorithms have similar computational complexity, i.e. linear complexity in the
time horizon, and can be derived in the same computational framework. We
compare the full-step variants of our algorithms and present several simulation
examples, including a high-dimensional underactuated robot subject to contact
switches. Simulation results show that our multiple-shooting algorithms can
achieve faster convergence, better local contraction rates and much shorter
runtimes than classical iLQR, which makes them a superior choice for nonlinear
model predictive control applications.Comment: 8 page
Whole Body Model Predictive Control with a Memory of Motion: Experiments on a Torque-Controlled Talos
This paper presents the first successful experiment implementing whole-body model predictive control with state feedback on a torque-control humanoid robot. We demonstrate that our control scheme is able to do whole-body target tracking, control the balance in front of strong external perturbations and avoid collision with an external object. The key elements for this success are threefold. First, optimal control over a receding horizon is implemented with Crocoddyl, an optimal control library based on differential dynamics programming, providing state-feedback control in less than 10 msecs. Second, a warm start strategy based on memory of motion has been implemented to overcome the sensitivity of the optimal control solver to initial conditions. Finally, the optimal trajectories are executed by a low-level torque controller, feedbacking on direct torque measurement at high frequency. This paper provides the details of the method, along with analytical benchmarks with the real humanoid robot Talos
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