Passive Dynamic Autonomous Control Research Articles

Unified bipedal gait for autonomous transition between walking and running in pursuit of energy minimization

This paper addresses “unified bipedal gait” control, which autonomously selects the energy-minimized gait from walking and running at any feasible gait speeds. Humans select walking/running at low/high speed in pursuit of energy minimization and transition between them naturally. Despite the quite different behaviors of walking and running, human gaits share an inherent controller. The unified bipedal gait uses the inherent controller, which implements passive dynamic autonomous control (PDAC) based on a damping and spring-loaded inverted pendulum (D-SLIP) model. Although this D-SLIP could cause chaotic motions, compliance in the D-SLIP dynamics switches behaviors between walking and running, that is, low/high compliant legs for walking/running. This property is employed by the virtual holonomic constraint of the PDAC to extract the required characteristics of walking/running from the D-SLIP dynamics while restraining the chaotic motions for asymptotic stability. As a result, the unified bipedal gait bifurcates to walking and running via autonomous transition to minimize energy cost at any feasible gait speeds.

PDAC規範リミットサイクル歩容における移動速度制御を用いた目標地点への自律的３次元移動

This paper achieves a 3-D bipedal gait from start to goal points autonomously. A limit-cycle-based gait possesses the good efficiency by a gait speed control in return for difficult footstep planning, although the major approach for 3-D traveling is footstep planning by a constantly stable gait with an emphasis on its accuracy and secureness. Hence, we employ passive dynamic autonomous control belonging to the limit-cycle based gait to achieve highly energy-efficient traveling on the spaces where there is no need to plan the footsteps. The robot interacts with only a leader point by spring and damper, and updates its reference gait speed according to their force. The leader point interacts with the other environments: the goal point by attractive force and obstacles by repulsive force. As a result, the robot can efficiently travel from the start to goal point autonomously while following the leader point not to collide with walls.

3-D Biped Walking Using Double Support Phase and Swing Leg Retraction Based on the Assumption of Point-Contact

This paper describes 3-D biped walking control based on the assumption of point-contact. We previously realized 3-D biped walking on unknown terrain using the Passive Dynamic Autonomous Control (PDAC) approach, which is based on the assumption of pointcontact of a robot foot and virtual holonomic constraint as to robot joints. However, the stable range of walking is narrow and the robustness of walking is not enough for practical use. In order to increase the robustness of walking, we propose swing leg retraction and double support phase in this paper. Swing leg retraction facilitates the stabilization ability of PDACbased walking; also, by use of the double support phase, robot dynamics converges to stable orbit even if disturbance happens at foot-contact. Finally, the proposed biped walking algorithm is verified by numerical simulation and experiments.

PDAC-Based 3-D Biped Walking Adapted to Rough Terrain Environment

This paper deals with the 3-D biped walking of a humanoid type robot over rough terrain. We previously proposed efficient 3-D biped walking control using Passive Dynamic Autonomous Control (PDAC) based on the assumption of point-contact and virtual holonomic constraint of robot joints. Walking adaptability has not, however, been analyzed. We thus analyze the environmental adaptability of PDAC-based walking method in this paper. The robot is modeled as a variable-length 3-D inverted pendulum whose dynamics is modeled as a 2-D autonomous system by applying PDAC. We analyze the stability of the 2-D autonomous system using a Poincaré map and derive the stable range of uneven height over rough terrain. We then experimentally validate 3-D biped walking on unknown rough terrain using our humanoid type robot, Gorilla Robot III.

2A1-U02 PDACに基づく遊脚伸縮運動及び両脚支持期を用いた2足歩行制御(脚移動ロボット(1))

Previously, we have realized an efficient 3-D biped walking based on the Passive Dynamic Autonomous Control (PDAC) that is one of the point-contact methods. However, the stable range of the point-contact method is small and the robustness of the walking is not large enough for practical use. In order to increase robustness of the point-contact method, this paper proposes a swing leg retraction and a double support phase for the point-contact method. The swing leg retraction enhances the convergence range of the walking system; also, by use of the double support phase, the robot dynamics converges to a stable orbit even if a disturbance happens at a foot-contact. The proposed biped walking algorithm is verified by experiments.

Control of lateral motion in bipedal walking based on PDAC

As one of dynamics-based control of biped walking, some researchers presented the control method to take advantage of robot dynamics directly by use of point-contact state between a robot and the ground. Passive Dynamic Autonomous Control (PDAC) was proposed previously as one of point-contact methods. PDAC is based on the two following concepts: 1) point-contact 2) Virtual constraint. As the first step of realisation of 3D dynamic walking, this paper applies PDAC to the lateral motion in bipedal walking and builds the controller. The validity of the control is confirmed by experiment and desired lateral motion is realised.

1A2-A11 点接触仮定と仮想コンプライアンス制御に基づく3次元2足歩行

This paper deals with a 3-D biped walking over rough terrain. The robot is modeled as the special 3-D inverted pendulum that can be changed the length. The dynamics of the 3-D inverted pendulum is modeled as 2-D autonomous system by applying the concepts of the Passive Dynamic Autonomous Control (PDAC). We analyze the stability of the 2-D autonomous system by use of Poincare map, and derive the stable range over rough terrain. By applying the virtual compliance control to an actual robot "Gorilla Robot III," the angle of the pendulum is modified. Finally, the 3-D biped walking over rough terrain is realized by use of the Gorilla Robot III.

Stabilizing and Direction Control of Efficient 3-D Biped Walking Based on PDAC

This paper proposes a 3-D biped dynamic walking algorithm based on passive dynamic autonomous control (PDAC). The robot dynamics is modeled as an autonomous system of a 3-D inverted pendulum by applying the PDAC concept that is based on the assumption of point contact of the robot foot and the virtual constraint as to robot joints. Due to autonomy, there are two conservative quantities named ldquoPDAC constant,rdquo which determine the velocity and direction of the biped walking. We also propose the convergence algorithm to make PDAC constants converge to arbitrary values, so that walking velocity and direction are controllable. Finally, experimental results validate the performance and the energy efficiency of the proposed algorithm.

2P1-C17 PDACに基づく安定化制御を用いた3次元動歩行

This paper addresses a three-dimensional biped dynamic walking control based on Passive Dynamic Autonomous Control (PDAC). In our previous work, the robot dynamics is modeled as a two-dimensional autonomous system of a three-dimensional inverted pendulum by applying the PDAC concept. In addition, the convergence algorithm based on conservative quantities named "PDAC constant" was proposed, so that walking velocity and direction is controllable. In this paper, we apply our control framework to an experimental robot "Multi-locomotion Robot"; then the performance and the efficiency of the proposed control algorithm are verified by experiments.

Control of Smooth Biped Walking by Means of Heel-Off Motion

We propose the control method of biped walking controlled by heel liftoff that eliminates impact when the foot contacts the walking surface that makes walking unstable. In presenting sagittal motion with heel liftoff, we use an approximate 1-mass model and derive dynamics based on this model. Sagittal motion involves two centers of rotation: the ankle joint (phase 1) and the toe (phase 2). In phase 2, heel leftoff lowers the impact when the foot contacts the walking surface. 1D autonomous dynamics (phase) around the contact point is derived by applying Passive Dynamic Autonomous Control, which we proposed previously [15, 16] to dynamics in both phases. Based on this dynamics, we propose simple stabilizing control by varying the Center of Gravity (COG) trajectory in heel-off phase is proposed, and the motion period of the sagittal motion that is employed in order to synchronize the lateral and sagittal motion is calculated. Numerical simulation confirmed that walking dynamics converges at a certain state, and that heel liftoff reduced impact when the foot contacted the walking surface. We studied the energy efficiency of heel-off walking and proposed the mechanics to improve energy efficiency.

Control of the Lateral Motion in Biped Walking Based on the Assumption of Point-contact

This paper proposes the novel control method named Passive Dynamic Autonomous Control (PDAC) PDAC is based on the following concept which Grizzle et al. employed previously : 1) point-contact 2) Virtual constraint. Point-contact means that the contact state between a robot and the ground is point. This makes it possible to generate the robot motion based on the robot inherent dynamics although it becomes difficult to control. Virtual constraint means that all robot joints are connected and interlocked. We present the new approach by means of these concepts to express the whole robot dynamics an an 1-dimensional autonomous system. Due to autonomy, this approach has two following notable points : 1) period from foot-contact to next foot-contact can be obtained 2) there is a conservative quantity to make it possible to stabilize the motion. As the first step of realization of 3 D dynamic walking, this paper applies PDAC to the lateral motion and builds the controller. In addition, the stabilization and motion period control are reported. The validity of these control is confirmed by experiment and desired lateral motion is realized.

2A1-D34 不等間隔の枝幅においてのブラキエーションコントローラの解析的設計手法

In this paper, we present the control method to achieve the continuous brachiation on the irregular ladder. The uniform ladder problem was solved by means of symmetric property previously. However, as for the irregular ladder problem, it's impossible to build the controller based on symmetric property since the motion cannot be designed symmetrically. Therefore, it is necessary to estimate the energy difference caused by symmetry breaking.We apply Passive Dynamic Autonomous Control (PDAC), which was proposed previously, to the locomotion action and evaluate the energy difference. Swing motion is adjusted so as to satisfy the desired energy calculated from the energy difference. The validity of proposed method is tested by the experiment of Gorilla Robot III and the irregular ladder brachiation is realized.