In this paper, a novel optimal technique for joint angles trajectory tracking control of 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 4 steps: 1) Planning stable cycloid trajectory for initial step and subsequent step for climbing upstairs . 2) Inverse Kinematics using  unsupervised artificial neural network with knot shifting procedure for jerk minimization. 3 ) Modeling Dynamics for Toe foot biped model using Lagrange Dynamics along with contact modeling using spring damper system , and finally 4) Real time joint angle trajectory tracking optimization using Temporal Quantized Lagrange Dynamics which takes inverse kinematics output from neural network as its inputs.  Generated patterns have been simulated in MATLAB .
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 .
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