Biped robots have gained much attention for decades. A variety of researches has been conducted to make them able to assist or even substitute for humans in performing special tasks. In addition, studying biped robots is important in order to understand the human locomotion and to develop and improve control strategies for prosthetic and orthotic limbs. Some challenges encountered in the design of biped robots are: (1) biped robots have unstable structures due to the passive joint located at the unilateral foot-ground contact. (2) They have different configuration when switching from walking phase to another. During the single support phase, the robot is under-actuated, while turning into an over-actuated system during the double-support phase. (3) Biped robots have many degrees of freedom, and (4) interact with different unknown environments. Therefore, this work is focused on offline computational optimal control strategies for zero-moment point-based biped robots. Computational optimal control has been performed to investigate the effects of some imposed constraints on biped locomotion, such as enforcing swing foot to move level to the ground, hip motion with constant height etc. finite difference approach has been used to transcribe infinite dimensional optimal control problem into finite dimensional suboptimal control problem. Then parameter optimization has been used to get suboptimal trajectory of the biped with the imposing different constraints. In general, any artificially imposed constraint to biped locomotion can lead to increase in value of input control torques. On the other hand, suboptimal trajectory of biped robot during complete gait cycle had been accomplished with different cases such that continuous dynamic response occurs. Enforcing the biped locomotion to move with linear transition of zero-moment point during the DSP can lead to more energy consumption.
Table of Contents
1 Computational Optimal Control: Theory and Simulation
1.1 Forward dynamics-based optimization
1.2 Inverse dynamics-based optimization
1.2.1 Discretization
1.2.2 Parameter optimization
1.2.3 Motivating example
1.3 The effect of miscellaneous imposed constraints on performance index of biped locomotion during the SSP
1.3.1 Dynamic modeling
1.3.2 Discretization and parameter optimization
1.4 Suboptimal trajectory planning of biped robot during complete gait cycle
1.4.1 Dynamic modeling
1.4.2 Discretization and parameter optimization
1.5 Simulation Results
1.5.1 The effect of constraints on the performance index of biped locomotion during the SSP
1.5.2 Suboptimal trajectory planning of biped locomotion during complete gait cycle
Objectives and Research Focus
This work aims to develop and investigate computational optimal control strategies for zero-moment point (ZMP)-based biped robots, specifically focusing on the generation of feasible walking patterns while managing the energy consumption and constraints of the robotic mechanism.
- Analysis of direct optimal control methods for bipedal locomotion.
- Investigation of the impact of various constraints (such as foot motion and hip height) on actuating torques.
- Development of suboptimal trajectory planning to ensure continuity of actuating forces during gait transitions.
- Evaluation of discretization techniques and nonlinear programming algorithms for trajectory optimization.
Excerpt from the Book
1.2.1.1 Spline-based discretization
Spline-based optimization has been used extensively in literature. The first reference [Seg05] used a piecewise fourth-order spline function to discretize the problem; the cubic spline functions may result in discontinuities in the third derivative of the approximated joint displacements. However, literature has approved the efficiency of the cubic–spline functions in implementation. In the following, we consider two efficient tools for the solution of inverse-dynamics approach: the piecewise cubic spline functions and the finite difference equations. A detailed study on the spline based optimization of the biped robot can be found in [Seg05]. To motivate our analysis, let us consider the following simple optimal problem cited from [Pan92].
Summary of Chapters
1 Computational Optimal Control: Theory and Simulation: This chapter introduces the theoretical foundations of optimal control for biped robots and reviews direct versus indirect methods.
1.1 Forward dynamics-based optimization: Describes the mathematical formulation of forward dynamics problems and the use of discretization to convert them into nonlinear programming.
1.2 Inverse dynamics-based optimization: Explores the inverse dynamics approach, comparing its efficiency against forward dynamics and detailing discretization techniques.
1.3 The effect of miscellaneous imposed constraints on performance index of biped locomotion during the SSP: Investigates seven specific simulated cases to study how constraints affect the performance of biped locomotion during the single support phase.
1.4 Suboptimal trajectory planning of biped robot during complete gait cycle: Proposes solutions for the discontinuity of actuating torques at transition points during different gait phases.
1.5 Simulation Results: Presents the findings regarding the effect of various constraints on the performance index and evaluates the generated walking patterns.
Keywords
Biped robot, optimal control, ZMP, trajectory planning, gait cycle, discretization, nonlinear programming, SQP, GA, dynamic modeling, single support phase, performance index, actuating torques, constraint optimization, locomotion
Frequently Asked Questions
What is the primary focus of this research?
The research focuses on the offline computational optimal control of biped robots, specifically aimed at generating feasible, stable walking patterns while minimizing energy consumption.
What are the main thematic areas covered?
The study covers direct optimal control theory, the comparison of forward and inverse dynamics, discretization methods, and trajectory planning across different walking phases.
What is the main objective of the work?
The primary objective is to develop a robust approach for suboptimal trajectory planning that ensures smooth transitions of actuating torques and ground reaction forces during biped gait.
Which scientific methods are employed?
The work employs computational optimal control, finite difference approaches, spline-based discretization, and nonlinear programming algorithms such as SQP and genetic algorithms.
What is discussed in the main body of the report?
The main body discusses the mathematical formulation of optimal control problems, the impact of physical constraints on energy requirements, and simulation studies of various gait cases.
Which keywords characterize this work?
The work is characterized by terms such as biped robot, optimal control, ZMP, trajectory planning, discretization, and energy consumption.
How does the research address the discontinuity issue in biped locomotion?
It addresses discontinuity at gait transition instances by proposing a suboptimal trajectory planning strategy using linear transition functions for ground reaction forces.
Why are constrained motion and energy consumption important in this study?
Constrained motion directly affects the required actuating torques; the study demonstrates that additional constraints generally increase the energy consumption required for locomotion.
What role do MATLAB routines play in this optimization?
MATLAB routines such as fmincon and genetic algorithms are used to solve the nonlinear programming problems resulting from the discretization process.
- Quote paper
- Dr. Hayder Al-Shuka (Author), 2018, Design of walking patterns for zero-momentum point (ZMP)-based biped robots. A computational optimal control approach, Munich, GRIN Verlag, https://www.grin.com/document/434367
