Keyframe-based multi-contact motion synthesis

Abstract

Most of the human daily activities include acyclic multi-contact motions. Yet, generating such motions is challenging because of its high-dimensional and nonlinear solution space made by combinations of individual movements of body parts. In this paper, we present a novel keyframe-based framework to automatically generate multi-contact character motions. Our system consists of two components: key-pose planning and interpolation. Given initial and goal poses in which each contact can be repositioned at most one time during the transition, our key-pose planning step generates intermediate key-poses that represent contact changes, taking into account a set of principles for goal-directed movements. Next, the key-poses of each joint are independently interpolated to generate an acyclic multi-contact motion. We demonstrate that our framework can synthesize plausible interaction motions with a number of man-made objects, such as chairs and bicycles, without using any motion data. In addition, we show the scalability of our method by creating a long-term motion of climbing a ladder.

Appendices

Appendix A: Height of the pelvis

Let $\bar{y}$ denote the highest value between the height of the previous key-pose and the height of the goal pose for the goal-directed movement and mobility. Then, the pelvis height is determined as $\min (\bar{y}, y^{LF}, y^{RF})$. Here, $y^{*F}$ is the maximum height of the pelvis from the given foot position and has two options: from the heel position or the toe position. The height from the toe position is determined by the tip-toe pose. Therefore, each height is simply computed because the position of the heel or toe is given by the contact position and the 2D position of the pelvis and the length of each case are known. The support foot uses the maximum height for the heel to keep the foot sole in contact with the ground, and the swing foot uses the maximum height for the toe to generate tip-toe pose at the time of contact engagement. In a transit key-pose, the swing foot is out of contact, so only the height of the support foot is considered.

Appendix B: Swing foot at transit key-pose

In an obstacle-free environment, only the preparation and touchdown key-poses are relevant to the path of the swing foot. Therefore, we use the two poses to generate a simple cubic Bezier curve for the swing footpath. As shown in Fig. 4, the tangents at both ends are computed from the vector from the foot to the hip at each key-pose, respectively. In addition, at the touchdown key-pose, the vector from the foot position to the foot at the preparation pose is added to the tangent:

$$\begin{aligned} \begin{aligned} v_0&=\alpha \Big (p^\mathrm{{prep}}_\mathrm{{hip}}-p^\mathrm{{prep}}_\mathrm{{foot}}\Big )\\ v_1&=\beta \Big (p^{td}_\mathrm{{hip}}-p^{td}_\mathrm{{foot}}\Big )+\alpha \Big (p^\mathrm{{prep}}_\mathrm{{foot}}-p^{td}_\mathrm{{foot}}\Big ) \end{aligned}s \end{aligned}$$

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where $\alpha \in (0,1)$ is a small value and $\beta \in (0,1)$ is set to a value inversely proportional to $|| p^\mathrm{{prep}}_\mathrm{{foot}}-p^{td}_\mathrm{{foot}} ||$. A larger distance between the feet, i.e., a smaller beta, produces a curve similar to the foot trajectory in walking [22, 39]. From the Bezier curve, its extreme point is chosen as the point of the swing foot at the transit key-pose. Given the configuration of the pelvis and the swing foot position, we can easily determine the pose of the swing leg. The goal-directed motion monotonically moves from the initial pose to the goal pose unless there are external constraints, so the rotation of the swing foot is determined by using spherical linear interpolation of both end poses, $Slerp(R_f^\mathrm{{prep}}, R_f^{td};t_{sw})$, where $R_f$ denotes the rotation of the foot at key-poses. We use the ratio of arc length as the parameter $t_{sw}=l_\mathrm{{ext}}/L_\mathrm{{arc}}$, where $l_\mathrm{{ext}}$ is the arc length at the extreme point and $L_\mathrm{{arc}}$ is the total arc length of the curve. Given the facing direction of the leg and the extreme point, determining the leg pose is a problem of finding the knee angle using three lengths in the plane. The rotations of the ankle and toe are set to zero in the body frame to have a neutral pose.