A direct method for trajectory optimization of rigid bodies through contact

By Michael Posa, Cecilia Cantu, Russ Tedrake. 2014

738 citations recorded by the source corpus.

Direct methods for trajectory optimization are widely used for planning locally optimal trajectories of robotic systems. Many critical tasks, such as locomotion and manipulation, often involve impacting the ground or objects in the environment. Most state-of-the-art techniques treat the discontinuous dynamics that result from impacts as discrete modes and restrict the search for a complete path to a specified sequence through these modes. Here we present a novel method for trajectory planning of rigid-body systems that contact their environment through inelastic impacts and Coulomb friction. This method eliminates the requirement for a priori mode ordering. Motivated by the formulation of multi-contact dynamics as a Linear Complementarity Problem for forward simulation, the proposed algorithm poses the optimization problem as a Mathematical Program with Complementarity Constraints. We leverage Sequential Quadratic Programming to naturally resolve contact constraint forces while simultaneously optimizing a trajectory that satisfies the complementarity constraints. The method scales well to high-dimensional systems with large numbers of possible modes. We demonstrate the approach on four increasingly complex systems: rotating a pinned object with a finger, simple grasping and manipulation, planar walking with the Spring Flamingo robot, and high-speed bipedal running on the FastRunner platform.

Subfields: Biomedical Engineering, Computer Vision and Pattern Recognition, Control and Systems Engineering

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Citations in the corpus

Learning Complex Dexterous Manipulation with Deep Reinforcement Learning and Demonstrations (2017, background): “a) Model-based trajectory optimization: : Modelbased trajectory optimization methods [31], [24], [38] have demonstrated impressive results in simulated domains, particularly when the dynamics can be adjusted or relaxed to make them more tractable (as, e.”
Deep Imitation Learning for Complex Manipulation Tasks from Virtual Reality Teleoperation (2017, background): “Demonstrations could instead be collected from running trajectory optimization [12], [13], [14], [15] or reinforcement learning [16], [17], [18], [19], [20], [21], [22], but these meth-ods require well-shaped, carefully designed reward functions, access to dynamics model, and substantial robot…”
Differentiable Physics and Stable Modes for Tool-Use and Manipulation Planning (2018, methodology): “…leads to non-regular time stepping); and (3) choosing a ﬁxed coarse time stepping scheme but formulating the next state x t + 1 = argmin x P ( x, x t ) as the solution of a non-linear constrained mathematical program P , typically a so-called linear complementary problem (LCP) [Posa et al. , 2014].”
Planning with Diffusion for Flexible Behavior Synthesis (2022, methodology): “Afterwards, the learned model may be plugged into classical trajectory optimization routines (Tassa et al., 2012; Posa et al., 2014; Kelly, 2017), which are similarly wellunderstood in their original context.”
Making Sense of Vision and Touch: Learning Multimodal Representations for Contact-Rich Tasks (2019, background): “Modeling contact interactions and multicontact planning still result in complex optimization problems [72]–[74] that remain sensitive to inaccurate actuation and state estimation.”
Combining the benefits of function approximation and trajectory optimization (2014, background): “But at least in simulation, recent advances suggest that many problems in robotic control can be solved fully automatically [19, 18, 23, 2].”
Models, feedback control, and open problems of 3D bipedal robotic walking (2014, methodology): “In [146], complementarity Lagrangian models have been used for trajectory optimization, without a priori enumeration of the type and order of the contact events.”
Vision-Only Robot Navigation in a Neural Radiance World (2021, background): “This approach is common in robotic trajectory optimization [20], [21], especially when performing contactimplicit trajectory optimization [22], which seeks to reason about contact geometry when optimizing contact sequences”
Logic-Geometric Programming: An Optimization-Based Approach to Combined Task and Motion Planning (2015, methodology): “Section 4 discusses our proposed solver, and section 5 experiments on building a stable construction that is as high as possible.”
Sampling-based Planning of In-Hand Manipulation with External Pushes (2017, methodology): “ make assumptions of point contact interactions modelled with polyhedral friction cones or patch contacts modelled as soft point contacts to alleviate the computational complexity of contact modeling [7, 21, 16]. Shi et al [19], Vina B et al [23]˜ and Hou et al [8] demonstrate application of such ap”
Making Sense of Vision and Touch: Self-Supervised Learning of Multimodal Representations for Contact-Rich Tasks (2018, background): “lems [42, 43, 52] that remain sensitive to inaccurate actuation”
Feedback Control of the Pusher-Slider System: A Story of Hybrid and Underactuated Contact Dynamics (2016, methodology): “[10] proposed to apply trajectory opti mization tools to determine the motion of the robot and the manipulated object by inc luding contact reaction forces along with motions as decision variables in a large op timization program.”
Ensemble-CIO: Full-body dynamic motion planning that transfers to physical humanoids (2015, methodology): “We and others have recently developed optimization methods that can generate complex and dynamically-consistent movements in simulation [5]–[8], [10].”
Whole-body motion planning with centroidal dynamics and full kinematics (2014, background): “approach can produce beautiful trajectories [16] [20] [4], but due to the complexity of the full-body dynamics, these optimizations can take an excessively long time to run, and may also suffer from local minima.”