Energy-Optimal Control of Underactuated Bipedal Locomotion Systems

The paper deals with modeling and design of energy-optimal motion of mechatronic system having less number of actuators than degrees of freedom. Such mechatronic system is termed underactuated. We consider an underactuated mechatronic system modeled a bipedal locomotion robot with 11 degrees of freedom. The system comprises nine links and is used to represent the bipeds planar dynamics in sagittal plane. The bodies are connected by friction-free hinge joints. Its assumed that the control inputs are torque actuators acting only at hip and knee joints. The ankle and the metatarsal joints of the feet are spanned with springs al-lowing discrete switching of their stiffness parameters in accordance to varying constraints imposed on the systems motion. The algorithm has been developed for synthesizing the energy-optimal anthropomorphic motion of the bipedal locomotion system with passively controlled feet and discrete switching of their joint stiffness parameters. Algorithm uses the smoothing cubic splines for approximation of variable functions, inverse dynamics approach, extern penalty functions method, and minimization of the nonsmooth objective function in orthogonal directions. The efficiency of the developed algorithm has been confirmed by simulation of human gait like motions for considered underactuated system. Applications of the results obtained can be found in robotics, bioengineering (prosthetics, orthotics), others

Energy-Optimal Control of Underactuated Bipedal Locomotion Systems

The paper deals with modeling and design of energy-optimal motion of mechatronic system having less number of actuators than degrees of freedom. Such mechatronic system is termed underactuated. We consider an underactuated mechatronic system modeled a bipedal locomotion robot with 11 degrees of freedom. The system comprises nine links and is used to represent the bipeds planar dynamics in sagittal plane. The bodies are connected by friction-free hinge joints. Its assumed that the control inputs are torque actuators acting only at hip and knee joints. The ankle and the metatarsal joints of the feet are spanned with springs al-lowing discrete switching of their stiffness parameters in accordance to varying constraints imposed on the systems motion. The algorithm has been developed for synthesizing the energy-optimal anthropomorphic motion of the bipedal locomotion system with passively controlled feet and discrete switching of their joint stiffness parameters. Algorithm uses the smoothing cubic splines for approximation of variable functions, inverse dynamics approach, extern penalty functions method, and minimization of the nonsmooth objective function in orthogonal directions. The efficiency of the developed algorithm has been confirmed by simulation of human gait like motions for considered underactuated system. Applications of the results obtained can be found in robotics, bioengineering (prosthetics, orthotics), others

Optimization of control laws of the bipedal locomotion systems

The mathematical statement of the problem of energy-optimal control for a bipedal locomotion system is given. The proposed statement of the problem is characterized by broad utilization of experimental data of normal human locomotion. It is done mainly by means of the mathematical formulation of the constraints imposed both on the phase coordinates and on the controlling stimuli of a system. A numerical method for the solution of the optimal control problems for highly nonlinear and complex bipedal locomotion systems is proposed. The method is based on a special procedure of converting the initial optimal control problem into a standard nonlinear programming problem. This is made by an approximation of the independent variable functions using smoothing cubic splines and by the solution of an inverse dynamics problem. The key features of the method are its high numerical effectiveness and the possibility to satisfy a lot of restrictions imposed on the phase coordinates of the system automatically and accurately. The proposed method is illustrated by computer simulation of the energy-optimal anthropomorphic motion of the bipedal walking robot over a horizontal surface

Energy-optimal control of bipedal locomtion systems

The mathematical statement of the problem of energy-optimal control for a bipedal locomotion system is given. The proposed statement of the problem is characterized by broad utilization of experimental data of normal human locomotion. It is done mainly by means of the mathematical formulation of the constraints imposed both on the phase coordinates and on the controlling stimuli of a system. A numerical method for the solution of optimal control problems for highly nonlinear and complex bipedal locomotion systems is proposed. The method is based on a special procedure of converting the initial optimal control problem into a standard nonlinear programming problem. This is made by an approximation of the independent variable functions using smoothing cubic splines and by the solution of inverse dynamics problem. The key features of the method are its high numerical effectiveness and the possibility to satisfy a lot of restrictions imposed on the phase coordinates of the system automatically and accurately. The proposed method is illustrated by computer simulation of the energy-optimal anthropomorphic motion of the bipedal walking robot over a horizontal surface

Optimization of control laws of the bipedal locomotion systems

The mathematical statement of the problem of energy-optimal control for a bipedal locomotion system is given. The proposed statement of the problem is characterized by broad utilization of experimental data of normal human locomotion. It is done mainly by means of the mathematical formulation of the constraints imposed both on the phase coordinates and on the controlling stimuli of a system. A numerical method for the solution of the optimal control problems for highly nonlinear and complex bipedal locomotion systems is proposed. The method is based on a special procedure of converting the initial optimal control problem into a standard nonlinear programming problem. This is made by an approximation of the independent variable functions using smoothing cubic splines and by the solution of an inverse dynamics problem. The key features of the method are its high numerical effectiveness and the possibility to satisfy a lot of restrictions imposed on the phase coordinates of the system automatically and accurately. The proposed method is illustrated by computer simulation of the energy-optimal anthropomorphic motion of the bipedal walking robot over a horizontal surface

Parametric optimization of motion and stiffness characteristics of passive drives of a bipedal walking robot

The problem of optimization both structural parameters of passive drives and motion of a bipedal anthropomorphic robot is studied. The motion of the robot is modeled by taking into account the kinematic characteristics of human gait. At the feet of the robot there are passive drives that are modeled by springs having piece-wise stiffness parameters. The optimization problem has been converted into a nonlinear programming problem by approximation of the generalized coordinates using smoothing cubic splines and solved numerically. Analysis of the solution has shown that the kinematic characteristics of the motion of the robot with passive drives located at the hinges of the feet are relatively close to the same characteristics of a human gait

Mathematical modeling and optimization of human walking on a below-knee prosthesis

The methodology is proposed for determining kinematic, dynamic and energetic characteristics of human walking on a below-knee prosthesis in the case of experimentally prescribed angles at the leg joints. To human walking the approach is used that is based on the formulation of the optimal control problem for corresponding nonlinear dynamical system with phase restrictions and nonsmooth objective function of is evaluated energy consumption. The algorithm for a numerical solution of the problem is developed via parameterization of systems generalized coordinates by cubic smoothing splines, utilization of an inverse dynamics approach, as well as methods of external penalty functions and minimization of nonsmooth functions in the orthogonal directions. The efficiency of the proposed methodology and created algorithm are illustrated by computer simulation of human walking on a below-knee prosthesis over a horizontal surface