Effective collaboration is based on online adaptation of one's own actions to the actions of their partner. This article provides a principled formalism to address online adaptation in joint planning problems such as Dyadic collaborative Manipulation (DcM) scenarios. We propose an efficient bilevel formulation that combines graph search methods with trajectory optimization, enabling robotic agents to adapt their policy on-the-fly in accordance to changes of the dyadic task. This method is the first to empower agents with the ability to plan online in hybrid spaces; optimizing over discrete contact locations, contact sequence patterns, continuous trajectories, and force profiles for co-manipulation tasks. This is particularly important in large object co-manipulation that requires changes of grasp-holds and plan adaptation. We demonstrate in simulation and with robot experiments the efficacy of the bilevel optimization by investigating the effect of robot policy changes in response to real-time alterations of the dyadic goals, eminent grasp switches, as well as optimal dyadic interactions to realize the joint task. Index Terms-Dual arm manipulation (DaM), manipulation planning, optimization and optimal control, physical human-robot interaction. I. INTRODUCTION D YADIC collaborative Manipulation (DcM) is a term we use to refer to a set of two individuals jointly manipulating an object, as shown in Fig. 1. The two individuals partner together to form a distributed system, augmenting their Manuscript

This paper aims to achieve automatic tuning of optimal parameters for whole-body control algorithms to achieve the best performance of high-DoF robots. Typically the control parameters at a scale up-to hundreds are often hand-tuned yielding sub-optimal performance. Bayesian Optimization (BO) can be an option to automatically find optimal parameters. However, for high dimensional problems, BO is often infeasible in realistic settings as we studied in this paper. Moreover, the data is too little to perform dimensionality reduction techniques such as Principal Component Analysis or Partial Least Square. We hereby propose an Alternating Bayesian Optimization (ABO) algorithm that iteratively learns the parameters of sub-spaces from the whole high-dimensional parametric space through interactive trials, resulting in sample efficiency and fast convergence. Furthermore, for the balancing and locomotion control of humanoids, we developed techniques of dimensionality reduction combined with the proposed ABO approach that demonstrated optimal parameters for robust whole-body control.

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.

We present an optimization-based motion planning framework for producing dynamically rich and feasible motions for a 3D one-leg hopper in challenging terrains. We formulate dynamic motion planning as a nonlinear optimization problem that computes position and orientation of the centroidal model, position of the limb, contact forces, contact locations, and timings of the gait in one unified framework. The dynamics are represented as a single rigid body, while the equations of motion are derived using discrete mechanics with a variational quaternion-based integrator for the orientation. We validate the capabilities by planning complex motions in three challenging tasks: jumping over an obstacle, leaping over a gap, and performing a somersault. All contact forces generated by the proposed optimization are verified with accurate numerical simulation to prove the feasibility of the generated agile motions with respect to the kinematic, dynamic, and environmental constraints.

This paper studies bipedal locomotion as a nonlinear optimization problem based on continuous and discrete dynamics, by simultaneously optimizing the remaining step duration, the next step duration and the foot location to achieve robustness. The linear inverted pendulum as the motion model captures the center of mass dynamics and its lowdimensionality makes the problem more tractable. We first formulate a holistic approach to search for optimality in the three-dimensional parametric space and use these results as baseline. To further improve computational efficiency, our study investigates a sequential approach with two stages of customized optimization that first optimizes the current step duration, and subsequently the duration and location of the next step. The effectiveness of both approaches is successfully demonstrated in simulation by applying different perturbations. The comparison study shows that these two approaches find mostly the same optimal solutions, but the latter requires considerably less computational time, which suggests that the proposed sequential approach is well suited for real-time implementation with a minor trade-off in optimality.

This paper presents a Differential Dynamic Programming (DDP) approach for systems characterized by implicit dynamics using sensitivity analysis, such as those modelled via inverse dynamics, variational, and implicit integrators. It leads to a more general formulation of DDP, enabling the use of the faster recursive Newton-Euler inverse dynamics. We leverage the implicit formulation for precise and exact contact modelling in DDP, where we focus on two contributions: (1) contact dynamics at the acceleration level; (2) formulation using an invertible contact model in the forward pass and a closed-form solution in the backward pass to improve the numerical resolution of contacts. The performance of the proposed framework is validated by comparing implicit versus explicit DDP for the swingup of a double pendulum, and by planning motions for two tasks using a single leg model making multi-body contacts with the environment: standing up from ground, where a priori contact enumeration is challenging, and maintaining balance under an external perturbation.

An important issue when synthesizing legged locomotion plans is the combinatorial complexity that arises from gait pattern selection. Though it can be defined manually, the gait pattern plays an important role in the feasibility and optimality of a motion with respect to a task. Replacing human intuition with an automatic and efficient approach for gait pattern selection would allow for more autonomous robots, responsive to task and environment changes. To this end, we propose the idea of building a map from task to gait pattern selection for given environment and performance objective. Indeed, we show that for a 2D half-cheetah model and a quadruped robot, a direct mapping between a given task and an optimal gait pattern can be established. We use supervised learning to capture the structure of this map in a form of gait regions. Furthermore, we propose to construct a warmstarting trajectory for each gait region. We empirically show that these warm-starting trajectories improve the convergence speed of our trajectory optimization problem up to 60 times when compared with random initial guesses. Finally, we conduct experimental trials on the ANYmal robot to validate our method.

No abstract