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.
Approaches to synthesize dynamically feasible multi-contact motions have also been extensively studied @cite_8 @cite_14 @cite_31 @cite_40 @cite_36 . However, it is not trivial to include planning of contact poses in these approaches because contacts planning in general involves discrete or non-convex constraints for the contact poses. @cite_21 addresses the non-convexity by decomposing the environment into a set of convex regions and approximating the rotation using piecewise affine functions. The problem is then formulated as a mixed integer convex program and solved to global optimality. Although @cite_21 only uses foot contact, and does not consider dynamics, it points a direction to include contact planning in an optimization problem.
@cite_14 @cite_8 @cite_36 @cite_21 @cite_40 @cite_31
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Most animal and human locomotion behaviors for solving complex tasks involve dynamic motions and rich contact interaction. In fact, complex maneuvers need to consider dynamic movement and contact events at the same time. We present a hierarchical trajectory optimization approach for planning dynamic movements with unscheduled contact sequences. We compute whole-body motions that achieve goals that cannot be reached in a kinematic fashion. First, we find a feasible CoM motion according to the centroidal dynamics of the robot. Then, we refine the solution by applying the robot's full-dynamics model, where the feasible CoM trajectory is used as a warm-start point. To accomplish the unscheduled contact behavior, we use complementarity constraints to describe the contact model, i.e. environment geometry and non-sliding active contacts. Both optimization phases are posed as Mathematical Program with Complementarity Constraints (MPCC). Experimental trials demonstrate the performance of our planning approach in a set of challenging tasks. This paper presents the contact-consistent elastic strips (CES) framework, a motion planning approach capable of producing complex multi-contact whole-body humanoid behaviors in dynamic environments. Planning multi-contact motions for humanoid robots is known to be non-trivial since it involves aspects of autonomous balancing, obstacle avoidance, ensuring global connectivity of the workspace and concurrent consideration of the kinematic and dynamic constraints. Previous works at motion planning for humanoid systems tend to focus on joint space planning and deal with obstacle avoidance and contact-point searching as the separated problems. CES framework, however, simultaneously considers all these requirements and constraints in task space while planning a valid sequence of contact-points and corresponding motions. This resulted in considerable improvements to efficiency and significantly reduced planning time. With the use of CES framework, complex multi-contact locomotion behaviors and real-time adjustments to the robot motions in 3D unstructured environments is possible. Several simulations are demonstrated to evaluate and verify the performance of CES framework. Traditional motion planning approaches for multilegged locomotion divide the problem into several stages, such as contact search and trajectory generation. However, reasoning about contacts and motions simultaneously is crucial for the generation of complex whole-body behaviors. Currently, coupling theses problems has required either the assumption of a fixed gait sequence and flat terrain condition, or nonconvex optimization with intractable computation time. In this letter, we propose a mixed-integer convex formulation to plan simultaneously contact locations, gait transitions, and motion, in a computationally efficient fashion. In contrast to previous works, our approach is not limited to flat terrain nor to a prespecified gait sequence. Instead, we incorporate the friction cone stability margin, approximate the robot's torque limits, and plan the gait using mixed-integer convex constraints. We experimentally validated our approach on the HyQ robot by traversing different challenging terrains, where nonconvexity and flat terrain assumptions might lead to suboptimal or unstable plans. Our method increases the motion robustness while keeping a low computation time. 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.