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bezier_COM_Traj

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Copyright 2018-2020 LAAS-CNRS

Authors: Pierre Fernbach and Steve Tonneau

Description

bezier_COM_Traj implements tools to compute Bezier trajectories given various sets of constraints: initial and terminal conditions (position, velocities, acceleration), additional linear constraints on the complete trajectory, and, most interestingly, constraints related to the center of mass dynamics.

The trajectories are genererated through the resolution of convex optimization (Quadratic Programms), and thus allow to specify a cost functional to minimize.

The library is implemented in C++, but also provides Python bindings.

Two types of applications can be used so far:

  • First, zero step capturability: Given the centroidal state of a robot, determines whether it is possible for the robot to come to a stop without violating frictional constraints. In this formulation, the problem can be solved continuously, and angular momentum constraints can be used.

  • Second, the general case (which encompasses zero step capturability): Given a sequence of discrete contact configurations, and given the current state of the robot, and a desired target state, compute a kinematically and dynamically accurate trajectory for the center of mass of the robot. In this general case, the trajectory is checked at discrete intervals (the verification is not continuous). Furthermore, at this point angular momentum is not handled (this is a TODO and not a limitation of the approach).