Trajectory optimization of Biped Robots with Maximum Load Carrying Capacities: Iterative Linear Programming Approach

A computational approach is presented to obtain the optimal path of the end-effector for the 10 DOF bipedal robot to increase its load carrying capacity for a given task from point to point. The synthesizing optimal trajectories problem of a robot is formulated as a problem of trajectory optimization. An Iterative Linear Programming method (ILP) is developed for finding a numerical solution for this nonlinear trajectory. This method is used for determining the maximum dynamic load carrying capacity of bipedal robot walking subjected to torque actuators, stability and jerk limits constraints. First, the Lagrangian dynamic equation should be written to be suitable for the load dynamics which together with kinematic equations are substantial for determining the optimal trajectory. After that, a representation of the state space of the dynamic equations is introduced also the linearized dynamic equations are needed to obtain the numerical solution of the trajectory optimization followed by formulation for the optimal trajectory problem with a maximum load. Finally, the method of ILP and the computational aspect is applied to solve the problem of trajectory synthesis and determine the dynamic load carrying capacity (DLCC) to the bipedal robot for each of the linear and circular path. By implementing on an experimental biped robot, the simulation results were validated.