  In this paper, a novel optimal technique for joint angles trajectory tracking
control with energy optimization for a biped robot with toe foot is proposed.
For the task of climbing stairs by a 9-link biped model, a cycloid trajectory
for swing phase is proposed in such a way that the cycloid variables depend on
the staircase dimensions. Zero Moment Point(ZMP) criteria is taken for
satisfying stability constraint. This paper mainly can be divided into 3 steps:
1) Planning stable cycloid trajectory for initial step and subsequent step for
climbing upstairs and Inverse Kinematics using an unsupervised artificial
neural network with knot shifting procedure for jerk minimization. 2) Modeling
Dynamics for Toe foot biped model using Lagrange Dynamics along with contact
modeling using spring-damper system followed by developing Neural Network
Temporal Quantized Lagrange Dynamics which takes inverse kinematics output from
neural network as its inputs. 3) Using Ant Colony Optimization to tune PD
(Proportional Derivative) controller parameters and torso angle with the
objective to minimize joint space trajectory errors and total energy consumed.
Three cases with variable staircase dimensions have been taken and a brief
comparison is done to verify the effectiveness of our proposed work Generated
patterns have been simulated in MATLAB .

Robotics;Neural and Evolutionary Computing;Systems and Control;Systems and Control