Figure 1: Our algorithm can handle complex balancing and manipulation tasks while adapting to user interactions. All our demonstrated movements emerge from simple cost functions without animation data or offline precomputation. More examples can be found in the supplemental video and on the project homepage. AbstractWe present a novel, general-purpose Model-Predictive Control (MPC) algorithm that we call Control Particle Belief Propagation (C-PBP). C-PBP combines multimodal, gradient-free sampling and a Markov Random Field factorization to effectively perform simultaneous path finding and smoothing in high-dimensional spaces. We demonstrate the method in online synthesis of interactive and physically valid humanoid movements, including balancing, recovery from both small and extreme disturbances, reaching, balancing on a ball, juggling a ball, and fully steerable locomotion in an environment with obstacles. Such a large repertoire of movements has not been demonstrated before at interactive frame rates, especially considering that all our movement emerges from simple cost functions. Furthermore, we abstain from using any precomputation to train a control policy offline, reference data such as motion capture clips, or state machines that break the movements down into more manageable subtasks. Operating under these conditions enables rapid and convenient iteration when designing the cost functions.

Fig. 1. Two paths (green and blue arrows) to the top hold in a bouldering problem, as discovered by our method. Compared to previous work, we are not limited to only moving one limb at a time or having the climber's hands and feet on predefined climbing holds; limbs can also hang free for balance, or use the wall for friction. The dashed rectangles highlight the one-to-many mapping from stances (assignments of holds to limbs) to climber states. This paper addresses the problem of offline path and movement planning for wall climbing humanoid agents. We focus on simulating bouldering, i.e. climbing short routes with diverse moves, although we also demonstrate our system on a longer wall. Our approach combines a graph-based highlevel path planner with low-level sampling-based optimization of climbing moves. Although the planning problem is complex, our system produces plausible solutions to bouldering problems (short climbing routes) in less than a minute. We further utilize a k-shortest paths approach, which enables the system to discover alternative paths-in climbing, alternative strategies often exist, and what might be optimal for one climber could be impossible for others due to individual differences in strength, flexibility, and reach. We envision our system could be used, e.g. in learning a climbing strategy, or as a test and evaluation tool for climbing route designers. To the best of our knowledge, this is the first paper to solve and simulate rich humanoid wall climbing, where more than one limb can move at the same time, and limbs can also hang free for balance or use wall friction in addition to predefined holds.

Figure 1: A humanoid, a quadruped and a monoped controlled by our learning backed sampling based model predictive controller. The various characters learn a stable gait in under a minute on a 4-core desktop computer.

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