Trajectory Optimization With Implicit Hard Contacts

Self Cite

The dynamics of legged systems are characterized by under-actuation, instability, and contact state switching. We present a trajectory optimization method for generating physically consistent motions under these conditions. By integrating a custom solver for hard contact forces in the system dynamics model, the optimal control algorithm has the authority to freely transition between open, closed, and sliding contact states along the trajectory. Our method can discover stepping motions without a predefined contact schedule. Moreover, the optimizer makes use of slipping contacts if a no-slip condition is too restrictive for the task at hand. Additionally, we show that new behaviors like skating over slippery surfaces emerge automatically, which would not be possible with classical methods that assume stationary contact points. Experiments in simulation and on hardware confirm the physical consistency of the generated trajectories. Our solver achieves iteration rates of 40 Hz for a 1 s horizon and is therefore fast enough to run in a receding horizon setting.

Section: A Related Workmentioning

confidence: 99%

“…) by a time-stepping scheme [18]. The generalized positions are first updated by a forward-Euler step over half the time interval.…”

Section: Algorithm 1 State Integration By Time-steppingmentioning

confidence: 99%

Section: Algorithm 1 State Integration By Time-steppingmentioning

confidence: 99%

See 1 more Smart Citation

Trajectory Optimization for Legged Robots With Slipping Motions

Carius

Ranftl

Koltun

et al. 2019

Self Cite

“…According to the solutions (10) and 14, the contact impulses are described as a function of joint configurations and velocities, and the Jacobian can be used to map these quantities to the contact velocity in (14). Afterwards, these terms can be substituted in (8b), which becomes a function of the joint positions, velocities, and accelerations only.…”

Section: Direct Transcriptionmentioning

confidence: 99%

Contact-Implicit Trajectory Optimization Using an Analytically Solvable Contact Model for Locomotion on Variable Ground

Chatzinikolaidis

You

2020

This paper presents a novel contact-implicit trajectory optimization method using an analytically solvable contact model to enable planning of interactions with hard, soft, and slippery environments. Specifically, we propose a novel contact model that can be computed in closed-form, satisfies friction cone constraints and can be embedded into direct trajectory optimization frameworks without complementarity constraints. The closed-form solution decouples the computation of the contact forces from other actuation forces and this property is used to formulate a minimal direct optimization problem expressed with configuration variables only. Our simulation study demonstrates the advantages over the rigid contact model and a trajectory optimization approach based on complementarity constraints. The proposed model enables physics-based optimization for a wide range of interactions with hard, slippery, and soft grounds in a unified manner expressed by two parameters only. By computing trotting and jumping motions for a quadruped robot, the proposed optimization demonstrates the versatility for multi-contact motion planning on surfaces with different physical properties.

“…Using analytical derivatives (instead of Automatic Differentiation or finite differences) allows for efficient computation [2]. Differentiable physics has proven to be very useful for gradient-based algorithms for optimal control and trajectory optimization [3], [4], [5], [6], [7]. However, the case of simulation with frictional contacts remains a challenging problem for the control community [8].…”

mentioning

confidence: 99%

Differentiable Simulation for Physical System Identification

Lidec

Kalevatykh

Laptev

et al. 2021

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