Planar Five-link Biped Robot Movement over a Stepped Surface

Abstract

Modeling the anthropomorphic robot movement is of great interest to researchers all over the world. At the same time, the movement control of a walking mechanism is always a high dimension challenge. The difficulty with the anthropomorphic robot control is also caused by the fact that such a mechanism has always a hybrid dynamics and represents a sequential change of two phases – the single support phase and the double support phase (phase of changing robot’s leg). At the single support phase and at another phase the behavior of the biped robot is described by a system of ordinary differential equations and by a system of linear algebraic equations, respectively.The task of biped robot movement control has been studied in detail for the case when the robot moves over the horizontal surface. Obstacles make the task significantly complicated. The paper considers the movement control of the biped robot over the surface that is a periodic alternation of horizontal sections and obstacles. The obstacles represent steps of the same height known. It is assumed that the lengths of horizontal sections and steps are known as well. The objective is to create a control that provides robot’s periodic movement over the specified surface according to inherent characteristics of a walking human.For the single support phase, the outputs are proposed, the equality of which to zero corresponds to the robot’s movement with a given set of characteristics. The paper presents the feedback controls that stabilize the proposed outputs for a finite amount of time. By choosing the feedback parameters, it is possible to adjust the stabilization time so that the outputs become equal to zero when reached the end of each step.It is shown that for the chosen control law, the problem of constructing the control of robot’s periodic movement is reduced to the solution of a nonlinear equation. In the paper, we discuss the approaches to solving this equation and present the results of numerical simulation.The results obtained can be used to solve the problem of providing control of the biped robot movement over the surfaces with obstacles of a more complicated shape.Modeling the anthropomorphic robot movement is of great interest to researchers all over the world. At the same time, the movement control of a walking mechanism is always a high dimension challenge. The difficulty with the anthropomorphic robot control is also caused by the fact that such a mechanism has always a hybrid dynamics and represents a sequential change of two phases – the single support phase and the double support phase (phase of changing robot’s leg). At the single support phase and at another phase the behavior of the biped robot is described by a system of ordinary differential equations and by a system of linear algebraic equations, respectively.The task of biped robot movement control has been studied in detail for the case when the robot moves over the horizontal surface. Obstacles make the task significantly complicated. The paper considers the movement control of the biped robot over the surface that is a periodic alternation of horizontal sections and obstacles. The obstacles represent steps of the same height known. It is assumed that the lengths of horizontal sections and steps are known as well. The objective is to create a control that provides robot’s periodic movement over the specified surface according to inherent characteristics of a walking human.For the single support phase, the outputs are proposed, the equality of which to zero corresponds to the robot’s movement with a given set of characteristics. The paper presents the feedback controls that stabilize the proposed outputs for a finite amount of time. By choosing the feedback parameters, it is possible to adjust the stabilization time so that the outputs become equal to zero when reached the end of each step.It is shown that for the chosen control law, the problem of constructing the control of robot’s periodic movement is reduced to the solution of a nonlinear equation. In the paper, we discuss the approaches to solving this equation and present the results of numerical simulation.The results obtained can be used to solve the problem of providing control of the biped robot movement over the surfaces with obstacles of a more complicated shape.

Planar Walking of a Five-Link Biped Robot over a Stepped Surface with Obstacles of Different Heights and Lengths

“…L . A solution of this system corresponding to phycally reasonable configurations of the robot before the impact, is given by [15] Let us show that the velocities q− at the end of the seventh step are functions of the only parameter which can be chosen as Ẋ− H (i.e. the horizontal component of the velocity of the hip joint before the seventh impact).…”

“…The problem of constructing a periodic motion can thus be reduced to the problem of finding such a value of Ẋ− H that coincides with the value of ẊH just before the seventh impact calculated by using the hybrid model (16) closed by the stabilizing control (12). To solve this problem, we modify the algorithm proposed in [15] for the case when the robot moves over the surface with obstacles of different heights and lengths. We present this algorithm below.…”

“…3) Set t 0 = 0, i = 1. 4) Using the impact model (15), calculate x + . 5) Solve the initial value problem…”

“…In this regard, the following problems should be mentioned: running a 5-link 2D-robot on a Figure 1. Robot scheme horizontal plane [11], rising a 5-link 2D-robot on the stairs [12], walking a 5-link 3D-robot [13,14], and moving a 5-link 2D-robot on a surface with one periodically repeating obstacle [15]. It is worth noting that a topological approach to generating families of walking gaits for 2D and 3D biped robots has been proposed in [16].…”