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. 2023 Feb 10;14(2):417.
doi: 10.3390/mi14020417.

Symmetrical Efficient Gait Planning Based on Constrained Direct Collocation

Boyang Chen  1 , Xizhe Zang  1 , Yue Zhang  1 , Liang Gao  1 , Yanhe Zhu  1 , Jie Zhao  1
Affiliations

Symmetrical Efficient Gait Planning Based on Constrained Direct Collocation

Boyang Chen et al. Micromachines (Basel). .

Abstract

Biped locomotion provides more mobility and effectiveness compared with other methods. Animals have evolved efficient walking patterns that are pursued by biped robot researchers. Current researchers have observed that symmetry is a critical criterion to achieve efficient natural walking and usually realize symmetrical gait patterns through morphological characteristics using simplified dynamic models or artificial priors of the center of mass (CoM). However, few considerations of symmetry and energy consumption are introduced at the joint level, resulting in inefficient leg motion. In this paper, we propose a full-order biped gait planner in which the symmetry requirement, energy efficiency, and trajectory smoothness can all be involved at the joint level, and CoM motion is automatically determined without any morphological prior. In order to achieve a symmetrical and efficient walking pattern, we first investigated the characteristic of a completely symmetrical gait, and a group of nearly linear slacked constraints was designed for three phases of planning. Then a Constrained Direct Collocation (DIRCON)-based full-order biped gait planner with a weighted cost function for energy consumption and trajectory smoothness is proposed. A dynamic simulation with our newly designed robot model was performed in CoppliaSim to test the planner. Physical comparison experiments on a real robot device finally validated the symmetry characteristic and energy efficiency of the generated gait. In addition, a detailed presentation of the real biped robot is also provided.

Keywords: energy efficiency; robotics; symmetrical biped gait planning; trajectory optimization.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1
Decision variables of three footholds in one single gait planning.
Figure 2
Figure 2
Composition and size of the robot. The left diagram shows joint distribution that fixed joints marked in red and actuated joints numbered in green. The middle diagram shows that the width of the robot is 275 mm. Two types of feet are shown in the right diagram and the length of the feet used in this paper is 190 mm and the width is 75 mm.
Figure 3
Figure 3
The layout of on-board equipment. The main equipment is numbered according to Table 3. (a) Base link appearance. (b) Inside oblique drawing (left). (c) Inside oblique drawing (right). (d) Inside oblique drawing.
Figure 3
Figure 3
The layout of on-board equipment. The main equipment is numbered according to Table 3. (a) Base link appearance. (b) Inside oblique drawing (left). (c) Inside oblique drawing (right). (d) Inside oblique drawing.
Figure 4
Figure 4
Planned symmetrical joint-level trajectories. In the left diagram, significant symmetry can be found and all the trajectories are within the kinematic limits. Reference joint inputs are shown in the right which the max torque is 9.8 Nm.
Figure 5
Figure 5
Five key frames of dynamic simulation. (a) The right supporting foot is taking off from the ground. (b) Right foot is swinging forward. (c) Right swing foot is touching down (d) Left foot is taking off from the ground. (e) The left foot is swinging forward.
Figure 6
Figure 6
Generated position trajectories and tracking performance in CoppeliaSim. (a) Left Hip Pitch position. (b) Left Hip Pitch position. (c) Left Knee position. (d) Right Knee position. (e) Left Ankle position. (f) Right Ankle position.
Figure 7
Figure 7
Feedback input trajectories of each active joint. (a) Roll and Yaw input of symmetric gait. (b) Roll and Yaw input of non-symmetric gait. (c) Pitch and Knee input of symmetric gait. (d) Pitch and Knee input of non-symmetric gait. (e) Ankle input of symmetric gait. (f) Ankle input of non-symmetric gait.
Figure 7
Figure 7
Feedback input trajectories of each active joint. (a) Roll and Yaw input of symmetric gait. (b) Roll and Yaw input of non-symmetric gait. (c) Pitch and Knee input of symmetric gait. (d) Pitch and Knee input of non-symmetric gait. (e) Ankle input of symmetric gait. (f) Ankle input of non-symmetric gait.
Figure 8
Figure 8
The positions and tracking performance of each active joint for two steps. (a) Left Hip Roll tracking performance. (b) Right Hip Roll tracking performance. (c) Left Hip Roll tracking performance. (d) Right Hip Roll tracking performance. (e) Left Hip Pitch tracking performance. (f) Right Hip Pitch tracking performance. (g) Left Knee tracking performance. (h) Left Knee tracking performance.(i) Left Ankle tracking performance. (j) Right Ankle tracking performance.
Figure 8
Figure 8
The positions and tracking performance of each active joint for two steps. (a) Left Hip Roll tracking performance. (b) Right Hip Roll tracking performance. (c) Left Hip Roll tracking performance. (d) Right Hip Roll tracking performance. (e) Left Hip Pitch tracking performance. (f) Right Hip Pitch tracking performance. (g) Left Knee tracking performance. (h) Left Knee tracking performance.(i) Left Ankle tracking performance. (j) Right Ankle tracking performance.
Figure 9
Figure 9
Five key frames of non-symmetrical walking experiment.
Figure 10
Figure 10
Five key frames of symmetrical walking experiment.
See this image and copyright information in PMC

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