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2013, Lecture Notes on Software Engineering
Abstract-This paper concentrates on three important points: the selection of the suitable direct method used for suboptimal control of the biped robot, the selection of the appropriate nonlinear programming (NLP) algorithm that searches for the global minimum rather than the local minimum, and the effect of different constraints on the energy of the biped robot. To perform the mentioned points, the advantages and disadvantages of the optimal control methods were illustrated. The inverse-dynamics based optimization is preferred because of the ability to convert the original optimal control into algebraic equations which are easy to deal with. The inverse-dynamics-based optimization was classified as spline and the finite difference based optimization. Due to the easy use of the latter, it was used for investigating seven cases with different constraints for 6-DOF biped robot during the single support phase (SSP). Hybrid genetic-sequential quadratic programming (GA-SQP) was used for simulation of the target robot with MATLAB. It can be concluded that more imposed constraints on the biped robot, more energy is needed. In general, more energy can be required in the case of (1) restriction of the swing foot to be level to the ground and (2) reducing the hip height or constraining the hip to move in constant height.
2008
This paper deals with dynamic optimization of biped locomotion. The main focus of this research is motion optimization of double support phase. The optimization problem is dealt by using Pontryagins Maximum Principal. For motion optimization of double support phase, the closed kinematic chain has been considered to be opened at appropriate joint and the components of ground reaction forces has been applied on the tip of front leg and finally the penalty method has been used to tighten the leg to its prescribed location. The feasible sets of motion are taken into consideration by using inequality constraint to limit the joint motion. Also the components of ground reaction forces on front leg have been introduced as control variables in optimization of double support phase. The proposed technique has the ability to generate optimal free motions without specifying joint trajectories and minimized the performance criterion based on joint actuating torques. The two point boundary value problem has been solved by implementing a shooting method. This technique allows for specifying a few parameters to characterize gait pattern. The optimization process has the ability to generate a motion with a minimum of postural and kinematics data. Unlike previous research which used computational intelligent techniques for biped gait optimization, this study focuses on development of purely dynamic synthesis of biped motion during the double support phase.
2007
Fast, dynamic or energy efficient locomotion of bipeds is still an unsolved problem in robotics. Nature seems to have solved many of the arising difficulties in thousands of years of evolution, optimizing both mechanics and control along the way. This paper proposes to use techniques from numerical optimization and optimal control combined with behavior-based control concepts to address some of the problems when designing and controlling two-legged robots. Results from the optimization process will affect both the mechanical construction and the control strategies.
Proceedings of IEEE International Conference on Evolutionary Computation, 1996
This paper deals with the problem of biped locomotion control in the sagittal plane. A model of the biped with five linked rigid bodies is developed to simulate the system dynamics This model has four joints of revolution, one at each link. A Steudy State Genetic Algorithm is used to find the necessary torques in each joint to obtain a desired trajectory for the biped's trunk center of mass. Each of the individuals in the GA consists ofa set of command sequences given to the biped, the jitness being obtained through simulation of the resulting motion and its comparison to the desired trajectory.
2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422), 2003
Methods for modeling, simulating and optimizing the dynamics, stability and performance of legged robot locomotion are discussed in this paper. It is demonstrated how these tools are used in the design, implementation and operation of a humanoid robot. The selection and integration of fundamental hard-and software needed for autonomous operation and high agility is presented for a recently developed fully-actuated 17 DoF humanoid. The results are additionally reported from simulations and gait optimizations completed during its development using a 3D dynamic biped model coupled with multiple physical and stability constraints.
Sadhana, 2015
This paper deals with multi-objective optimization in gait planning of a 7-dof biped robot during its double support phase, while ascending and descending some staircases. For determining dynamic balance margin of the robot in terms of zero-moment point, its double support phase has been assumed to be consisting of two single support phases on non-coincidental parallel surfaces. Thus, dynamic balance margin of the biped robot during its double support phase is obtained by using a virtual zero-moment point of the system. Moreover, a smooth transition from single to double support phases in a cycle is to be maintained for the walking robots. Two contrasting objectives, namely power consumption and dynamic balance margin have been considered during optimization. Pareto-optimal fronts of solutions are obtained using genetic algorithm and particle swarm optimization algorithm, separately. To the best of the authors' knowledge, it is the first attempt to solve multi-objective optimization problem in double support phase of a biped robot.
International Journal of Computer Applications, 2014
This paper proposes a thorough algorithm that can tune the walking parameters (hip height, distance traveled by the hip, and times of single support phase SSP and double support phase DSP) to satisfy the kinematic and dynamic constraints: singularity condition at the knee joint, zero-moment point (ZMP) constraint, and unilateral contact constraints. Two walking patterns of biped locomotion have been investigated using the proposed algorithm. The distinction of these walking patterns is that the stance foot will stay fixed during the first sub-phase of the DSP for pattern 1, while it will rotate simultaneously at beginning of the DSP for pattern 2. A seven-link biped robot is simulated with the proposed algorithm. The results show that the proposed algorithm can compensate for the deviation of the ZMP trajectory due to approximate model of the pendulum model; thus balanced motion could be generated. In addition, it is shown that keeping the stance foot fixed during the first sub-phase of the DSP is necessary to evade deviation of ZMP from its desired trajectory resulting in unbalanced motion; thus, walking pattern 1 is preferred practically.
Proceedings of the 2005 IEEE International Conference on Robotics and Automation, 2005
The objective of this study is to obtain optimal cyclic gaits for a biped without actuated ankle. For the walking, the gait is composed of successive single support phases and instantaneous double support phases that are modeled by passive impact equations. The legs swap their roles from one single support phase to the next one. During each phase the evolution of the joints variables is assumed to be polynomial functions of a scalar path parameter. The coefficients of the polynomial functions are chosen to optimise a torque criterion and to insure a cyclic motion for the biped. Furthermore, the optimal gait is defined with respect to given performances of actuators. The torques and velocities at the output of the gearbox are bounded. For this study, the physical parameters of a prototype are used. Initial starting motions that are composed of a double support and a transitional single support are also defined.
International Journal of Advanced Robotic Systems, 2020
This article proposes a new stable biped walking pattern generator with preset step-length value, optimized by multi-objective JAYA algorithm. The biped robot is modeled as a kinetic chain of 11 links connected by 10 joints. The inverse kinematics of the biped is applied to derive the specified biped hip and feet positions. The two objectives related to the biped walking stability and the biped to follow the preset step-length magnitude have been fully investigated and Pareto optimal front of solutions has been acquired. To demonstrate the effectiveness and superiority of proposed multiobjective JAYA, the results are compared to those of MO-PSO and MO-NSGA-2 optimization approaches. The simulation and experiment results investigated over the real small-scaled biped HUBOT-4 assert that the multi-objective JAYA technique ensures an outperforming effective and stable gait planning and walking for biped with accurate preset steplength value.
Artificial Life and Robotics, 2011
International Journal of Advanced Computer Science and Applications, 2020
In this study, a closed-loop controller is designed to overcome the dynamical insufficiency of the 3D Linear Inverted Pendulum Model (LIPM) via the Genetic Algorithm (GA). The main idea is to still use the 3D LIPM with a closed-loop controller because of its ease at modeling. While suppressing the dynamical flaws only the legs are used, in other words a robot is used which does not have any upper body elements to have a more modular robot. For this purpose, a biped is modeled with the 3D LIPM which is one of the most famous modeling methods of humanoid robots for the ease of modeling and fast calculations during the trajectory planning. After obtaining the simple model, Model Predictive Control (MPC) is applied to the 3D LIPM to find the reference trajectories for the biped while satisfying the Zero Moment Point (ZMP) criteria. The found reference trajectories applied to the full dynamical model on Matlab Simulink and the real biped in the laboratory at Istanbul Technical University. From the simulation results on the flat and inclined surfaces and real-time experiments on a flat surface some dynamical flaws are observed due to the simple modeling. To overcome these flaws a Proportional-Integral (PI) controller is designed, and the optimal value of the controller gains are found by the GA. The results assert that the designed controller can overcome the observed flaws and makes biped move more stable, smoother, and move without steady-state error.
The development of an algorithm to achieve optimal cyclic gaits in space for a thirteen-link biped and twelve actuated joints is proposed. The cyclic walking gait is composed of successive single support phases and impulsive impacts with full contact between the sole of the feet and the ground. The evolution of the joints are chosen as spline functions. The parameters to define the spline functions are determined using an optimization under constraints on the dynamic balance, on the ground reactions, on the validity of impact, on the torques and on the joints velocities. The criterion considered is represented by the integral of the torque norm. The algorithm is tested for a biped robot whose numerical walking results are presented.
IFAC Proceedings Volumes, 2013
Analytical techniques are presented for the motion planning and control of a 10 degree-of-freedom biped walking robot. From the Denavit-Hartenberg method and Newton-Euler equations, joint torques are obtained in terms of joint trajectories and the inverse dynamics are developed for both the single-support and double-support cases. Physical admissibility of the biped trajectory is characterized in terms of the equivalent force-moment and zero-moment point. This methodology has been used to obtain stability of walking biped robot Archie developed in IHRT. A simulation example illustrates the application of the techniques to plan the forward-walking trajectory of the biped robot.
2017
This paper presents energy and stability functions, integrating the stability parameters of the Zero Moment Point (ZMP) classed bipeds where stability parameters are the positions of Center of Mass (CoM) and ZMP respectively. The Energy function is derived using the concept of Orbital Energy and is optimized using Real Coded Genetic Algorithm to produce an optimum set of walk parameters, which consumes minimum energy, during walking. A Stability function is also proposed, which is obtained by modifying the pre-existing ZMP trajectory. The ZMP trajectory is modified in such a manner, that it remains at the center of the convex hull, not only during the single support phase, but also during the transition of the robot from the Double Support Phase (DSP) to Single Support Phase (SSP) and vice-versa. The analytical results show that, when the energy function is optimized, the stability of the robot decreases. Similarly, if the stability function is optimized, the energy consumed by the ...
IOP Conference Series: Materials Science and Engineering, 2016
This paper proposes a novel approach for gait pattern generation of a small biped robot to enhance its walking behavior. This is to aim to make the robot gait more natural and more stable in the walking process. In this study, we mention the approximated optimization method which applied the Differential Evolution algorithm (DE) to objective function approximated by Artificial Neural Network (ANN). In addition, we also present a new humanlike foot structure with toes for the biped robot in this paper. To evaluate this method achievement, the robot was simulated by multi-body dynamics simulation software, Adams (MSC software, USA). As a result, we confirmed that the biped robot with the proposed foot structure can walk naturally. The approximated optimization method based on DE algorithm and ANN is an effective approach to generate a gait pattern for the locomotion of the biped robot. This method is simpler than the conventional methods using Zero Moment Point (ZMP) criterion.
Robotica, 2009
The inverse kinematics of a 12 degrees-of-freedom (DOFs) biped robot is formulated in terms of certain parameters. The biped walking gaits are developed using the parameters. The walking gaits are optimized using genetic algorithm (GA). The optimization is carried out considering relative importance of stability margin and walking speed. The stability margin depends on the position of zero-momentpoint (ZMP) while walking speed varies with step-size. The ZMP is computed by an approximation-based method which does not require system dynamics. The optimal walking gaits are experimentally realized on a biped robot.
International Journal of Computational Intelligence Systems, 2020
This paper treats the optimization of the biped walking trajectory that can be used as a reference trajectory for control. The biped robot is modeled as a kinetic chain of 11 links connected by 10 joints. The inverse kinematics of the biped is derived for the specified positions of the hips and feet. The objective is to optimize the biped robot able to stably and naturally walking with preset foot-lift magnitude (or preset hip-shift, or preset step-length). The stability of the biped robot is quantified by the distance between the ZMP and the foot center in the step cycle, which represents the first objective function. Additionally, for the biped robot to follow the preset foot-lift value, the difference between the magnitude of foot-lift value and the foot-lift preset value represents the second objective function. Specifically, we minimize the value of the two objective functions by considering the gait parameters of biped robot as variables. The new Jaya optimization algorithm is innovatively applied to optimize the biped gait parameters as to ensure the biped robot walking robustly and steadily. The efficiency of the proposed Jaya-based identification method is compared with the Genetic Algorithm (GA), the Particle Swarm Optimization (PSO), the Central Force Optimization (CFO) and improved Differential Evolution (DE) [Modified Differential Evolution (MDE)] algorithms. The simulation results tested on the real small-sized biped robot system HUBOT-4 demonstrate that the novel proposed algorithm offers an efficient and stable gait for biped robot with precise foot-lift value.
2015 15th International Conference on Control, Automation and Systems (ICCAS), 2015
Abstract: Biped robots have several degrees of freedom (DOF) composed of many articulated links connected together by joint which ends up in a complex structure and difficult to make it mimic human like locomotion gait which is dynamic in nature and at the same time stable in the sense of not falling by. This paper presents dynamic equations of motion and its Matlab simulation of joints position. These dynamic equations are derived by starting with the kinematics which includes forward kinematics (FK) derived by using the Denavit-Hartenberg notation and inverse kinematics (IK) and then solving the dynamics of the biped robot. Two well-known methods for solving the dynamic of the robot are Newton-Euler formulation and Euler-Lagrangian formulation. This work uses the Euler-Lagrange formulation as it is a fancy formulation technique for solving dynamics instead of finding all the forces, velocities using Newton-Euler formulation.
Vietnam Journal of Mechanics
This paper proposes a new way to optimize the biped walking gait design for biped robots that permits stable and robust stepping with pre-set foot lifting magnitude. The new meta-heuristic CFO-Central Force Optimization algorithm is initiatively applied to optimize the biped gait parameters as to ensure to keep biped robot walking robustly and steadily. The efficiency of the proposed method is compared with the GA-Genetic Algorithm, PSO-Particle Swarm Optimization and Modified Differential Evolution algorithm (MDE). The simulated and experimental results carried on the prototype small-sized humanoid robot demonstrate that the novel meta-heuristic CFO algorithm offers an efficient and stable walking gait for biped robots with respect to a pre-set of foot-lift height value.
IFAC-PapersOnLine, 2016
This work deals with the stability analysis of two legged (humanoid) robots during walking. This research area is characterized by the fact that there are a lots of publications, a method for synthesizing the gait of a planar biped walking on level ground is presented. Both the single support phase (SSP) and the double support phase (DSP) are considered. A complete step can be divided into a SSP and a DSP. The SSP is characterized by one limb (the swing limb) moving in the forward direction while another limb (the stance limb) is pivoted on the ground. This phase begins with the swing limb tip leaving the ground and terminates with the swing limb touching the ground. Its time period is denoted as TS. In the DSP, both lower limbs are in contact with the ground while the upper body can move forward slightly. The time period of this phase is denoted as TD. In the following step, the roles of the swing limb and the stance limb are exchanged. It has been noticed that the joint angle profiles can be determined if compatible trajectories for the hip and the tip of the swing limb can be prescribed. Also is presented in practical implementation in a real robot.
Intelligent Engineering Systems through Artificial Neural Networks Volume 18, 2008
In this paper, we show that a biped robot can walk dynamically using a simple control technique inspired from human locomotion. We introduce four critical angles that affect robot speed and step length. Our control approach consists in tuning the PID parameters of each joint in each walking phase for introducing active compliance and then to increase stability of the walk. We validated the control approach to a dynamic simulation of our 14DOF biped called ROBIAN. A comparison with human walking is presented and discussed. We prove that we can maintain robot stability and walk cycle's repetition without referencing a predefined trajectory or detecting the center of pressure. Results show that the walk of the biped is very similar to human one. A power consumption analysis confirms that our approach could be implemented on the real robot ROBIAN.
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