Abstract
In recent years, soft robotics simulators have
evolved to offer various functionalities, including the simu-
lation of different material types (e.g., elastic, hyper-elastic)
and actuation methods (e.g., pneumatic, cable-driven, servo-
motor). These simulators also provide tools for various tasks,
such as calibration, design, and control. However, efficiently
and accurately computing derivatives within these simulators
remains a challenge, particularly in the presence of physical
contact interactions. Incorporating these derivatives can, for
instance, significantly improve the convergence speed of control
methods like reinforcement learning and trajectory optimiza-
tion, enable gradient-based techniques for design, or facilitate
end-to-end machine-learning approaches for model reduction.
This paper addresses these challenges by introducing a unified
method for computing the derivatives of mechanical equations
within the finite element method framework, including contact
interactions modeled as a nonlinear complementarity problem.
The proposed approach handles both collision and friction
phases, accounts for their nonsmooth dynamics, and leverages
the sparsity introduced by mesh-based models. Its effectiveness
is demonstrated through several examples of controlling and
calibrating soft systems.
Results
Top: Optimization of the Young Modulus of the beam (1 and 2) to achieve a target position for the mesh nodes. Young’s modulus is expressed in MPa, distance in mm. We can see from these figures that the gradient information relating to the mechanical parameters of the materials can be used to identify the model parameters, even if there are contacts between the beam and some obstacles.
Bottom: Evolution of the distance to the target for control tasks using the Trunk robot (3) and the Finger robot (4). For the Trunk robot, the current position is compared to the final position, as the target may lie outside the robot’s workspace. Distances are measured in mm. In the case of the Trunk robot, the formulation with gradients leads to the same formulation as the one proposed in the reference articles on soft robotics control using QP approaches. In the case of the Finger robot, the derivative with respect to the actuation accounts for contact information, requiring the applied force to be greater in order to counterbalance the contact force. The results show that gradient information with respect to position and actuation can be used to control soft robots.
Bottom: Evolution of the distance to the target for control tasks using the Trunk robot (3) and the Finger robot (4). For the Trunk robot, the current position is compared to the final position, as the target may lie outside the robot’s workspace. Distances are measured in mm. In the case of the Trunk robot, the formulation with gradients leads to the same formulation as the one proposed in the reference articles on soft robotics control using QP approaches. In the case of the Finger robot, the derivative with respect to the actuation accounts for contact information, requiring the applied force to be greater in order to counterbalance the contact force. The results show that gradient information with respect to position and actuation can be used to control soft robots.