text: Humanoid robots dynamically navigate an environment by interacting with it via contact wrenches exerted at intermittent contact poses. Therefore, it is important to consider dynamics when planning a contact sequence. Traditional contact planning approaches assume a quasi-static balance criterion to reduce the computational challenges of selecting a contact sequence over a rough terrain. This however limits the applicability of the approach when dynamic motions are required, such as when walking down a steep slope or crossing a wide gap. Recent methods overcome this limitation with the help of efficient mixed integer convex programming solvers capable of synthesizing dynamic contact sequences. Nevertheless, its exponential-time complexity limits its applicability to short time horizon contact sequences within small environments. In this paper, we go beyond current approaches by learning a prediction of the dynamic evolution of the robot centroidal momenta, which can then be used for quickly generating dynamically robust contact sequences for robots with arms and legs using a search-based contact planner. We demonstrate the efficiency and quality of the results of the proposed approach in a set of dynamically challenging scenarios.
  @cite_13: We tackle the transition feasibility problem, that is the issue of determining whether there exists a feasible motion connecting two configurations of a legged robot. To achieve this we introduce CROC, a novel method for computing centroidal dynamics trajectories in multi-contact planning contexts. Our approach is based on a conservative and convex reformulation of the problem, where we represent the center of mass trajectory as a Bezier curve comprising a single free control point as a variable. Under this formulation, the transition problem is solved efficiently with a Linear Program (LP)of low dimension. We use this LP as a feasibility criterion, incorporated in a sampling-based contact planner, to discard efficiently unfeasible contact plans. We are thus able to produce robust contact sequences, likely to define feasible motion synthesis problems. We illustrate this application on various multi-contact scenarios featuring HRP2 and HyQ. We also show that we can use CROC to compute valuable initial guesses, used to warm-start non-linear solvers for motion generation methods. This method could also be used for the 0 and 1-Step capturability problem. The source code of CROC is available under an open source BSD-2 License.
  @cite_32: We present a novel method for synthesizing collision-free, dynamic locomotion behaviors for legged robots, including jumping, going down a very steep slope, or recovering from a push using the arms of the robot. The approach is automatic and generic: non-gaited motions, comprising arbitrary contact postures can be generated along any environment. At the core of our framework is a new steering method that generates trajectories connecting two states of the robot. These trajectories account for the state-dependent, centroidal dynamic constraints inherent to legged robots. The method, of low dimension, formulated as a Linear Program, is really efficient to compute, and can find an application in various problems related to legged locomotion. By incorporating this steering method into an existing sampling-based contact planner, we propose the first kinodynamic contact planner for legged robots.
  @cite_2: In this paper we show that optimal stepping trajectories and trajectory cost for a walking biped robot on rough terrain can be encoded as simple quadratic functions of initial state and footstep sequence. In order to find this encoding, we build a database of optimal walking trajectories for a 3D humanoid model by sampling the input space (initial state and footstep sequence) and solving a physically-based trajectory optimization problem for each sample. Then, the function coefficients are obtained by fitting the data using least squares. The performance of the proposed method is evaluated by comparing the function values with other optimal walking motion data generated with different footstep samples. As an application, we use a quadratic function to calculate the effort cost used in finding an optimal footstep sequence with an A* algorithm. Our study shows that a simple function can encode optimal walking effectively, which provides a fast alternative to online optimization of walking with full body dynamics.
summary: @cite_32 proposes a kinodynamic sampling-based contact planner to plan kinodynamically feasible contact sequences. They use a simplified robot model to dynamically plan smooth center of mass (CoM) trajectories based on convex optimization and then search for kinematically feasible contact poses around it. It shows a unified planning framework to consider dynamics and kinematics constraints, but it suffers from long planning time. @cite_13 proposes an efficient dynamic feasibility check by conservatively reformulating the problem as a linear program. While the check guarantees to reject dynamically infeasible motions, they do not address dynamical robustness in the stability check. @cite_2 learns quadratic dynamics objective of humanoid walking motion, and apply this learned model to select steps in a search-based footstep planner. However, their dynamics model assumes flat contact, and does not consider palm contacts, which limits the applicability of the approach.