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.

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To generate dynamic motions such as hopping and running on legged robots, model-based approaches are usually used to embed the well studied spring-loaded inverted pendulum (SLIP) model into the whole-body robot. In producing controlled SLIP-like behaviors, existing methods either suffer from online incompatibility or resort to classical interpolations based on lookup tables. Alternatively, this paper presents the application of a data-driven approach which obviates the need for solving the inverse of the running return map online. Specifically, a deep neural network is trained offline with a large amount of simulation data based on the SLIP model to learn its dynamics. The trained network is applied online to generate reference foot placements for the humanoid robot. The references are then mapped to the whole-body model through a QP-based inverse dynamics controller. Simulation experiments on the WALK-MAN robot are conducted to evaluate the effectiveness of the proposed approach in generating bio-inspired and robust running motions.

This paper presents a novel foot placement control algorithm for adaptive bipedal walking. In this method, the torso attitude and height are stabilized by synergic patterns so that the forward velocity and its change have a stable and nearly linear relation with the foot placement. Hence, our proposed online linear regression analysis well represents the local linear models by estimating continuously from measured data. Based on this estimation, an appropriate foot placement can be determined to control the forward velocity. Our simulation study successfully demonstrates the natural gait with accurate tracking of walking velocity, and the robustness of walking over uneven terrain.

Most humanoid robots walk in an unhuman-like way with bent knees due to the use of the simplified Linear Inverted Pendulum Model (LIPM) which constrains the Center of Mass (CoM) in a horizontal plane. Therefore it results in high knee joint torque and extra energy consumption. To address this issue, we propose a simple yet efficient c ontrol s trategy to realize straight leg walking. First, theoretical analyses of simplified m odels p rovide i nsight i nto Z ero M oment P oint (ZMP) deviations during straight knee walking. Based on the finding that the deviation is limited comparing to the support polygon, we decide to keep using the LIPM for high-level planning, but let the robot perform straight leg walking automatically via the optimization-based low-level controller. By setting the desired CoM height slightly over the robot's reachable height, the lowlevel controller will attempt to straighten the robot's leg to reach this vertical reference, in the meanwhile, also satisfy the constraints (i.e. dynamic feasibility, friction cone, torque limits). The simulation results of the humanoid robot WALK-MAN demonstrate the feasibility of proposed control strategy with relatively high energy efficiency. A t ypical b utterfly sh ape of CoM trajectory was also observed in the frontal plane which is common in human walking.

Quadruped robots are widely applied in real-world environments where they have to face the challenges of walking on unknown rough terrains. This paper presents a control pipeline that generates robust and compliant legged locomotion for torque-controlled quadruped robots on uneven terrains. The Cartesian motion planner is designed to be reactive to unexpected early and late contacts using the estimated contact forces. Moreover, we present a novel scheme of optimal stiffness modulation that aims to coordinate desired compliance and tracking performance. It optimizes joint stiffness and contact forces coordinately in a quadratic programming (QP) formulation, where the constraints of non-slipping contacts and torque limits are imposed as well. In addition, the issue of stability under variable stiffness control is solved by imposing a tank-based passivity constraint explicitly. We finally validate the proposed control pipeline on our quadruped robot CENTAURO in experiments on uneven terrains and, through comparative tests, demonstrate the improvements of the variable stiffness locomotion.

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