Abstract-We introduce a real-time, constrained, nonlinear Model Predictive Control for the motion planning of legged robots. The proposed approach uses a constrained optimal control algorithm known as SLQ. We improve the efficiency of this algorithm by introducing a multi-processing scheme for estimating value function in its backward pass. This pass has been often calculated as a single process. This parallel SLQ algorithm can optimize longer time horizons without proportional increase in its computation time. Thus, our MPC algorithm can generate optimized trajectories for the next few phases of the motion within only a few milliseconds. This outperforms the state of the art by at least one order of magnitude. The performance of the approach is validated on a quadruped robot for generating dynamic gaits such as trotting.

Wheeled-legged robots are an attractive solution for versatile locomotion in challenging terrain. They combine the speed and efficiency of wheels with the ability of legs to traverse challenging terrain. In this paper, we present a trajectory optimization formulation for wheeled-legged robots that optimizes over the base and wheels' positions and forces and takes into account the terrain information while computing the plans. This enables us to find optimal driving motions over challenging terrain. The robot is modeled as a single rigid-body, which allows us to plan complex motions and still keep a low computational complexity to solve the optimization quickly. The terrain map, together with the use of a stability constraint, allows the optimizer to generate feasible motions that cannot be discovered without taking the terrain information into account. The optimization is formulated as a Nonlinear Programming (NLP) problem and the reference motions are tracked by a hierarchical whole-body controller that computes the torque actuation commands for the robot. The trajectories have been experimentally verified on quadrupedal robot ANYmal equipped with non-steerable torque-controlled wheels. Our trajectory optimization framework enables wheeled quadrupedal robots to drive over challenging terrain, e.g., steps, slopes, stairs, while negotiating these obstacles with dynamic motions.

We introduce a robust control architecture for the whole-body motion control of torque controlled robots with arms and legs. The method is based on the robust control of contact forces in order to track a planned Center of Mass trajectory. Its appeal lies in the ability to guarantee robust stability and performance despite rigid body model mismatch, actuator dynamics, delays, contact surface stiffness, and unobserved ground profiles. Furthermore, we introduce a task space decomposition approach which removes the coupling effects between contact force controller and the other noncontact controllers. Finally, we verify our control performance on a quadruped robot and compare its performance to a standard inverse dynamics approach on hardware.

This article presents a trajectory planning framework for all-terrain vehicles with legs and wheels such as walking excavators. Our formulation takes into account the whole body of the robot while computing the plans for locomotion. Hence, we can produce motion plans over the rough terrain that would be hard to plan without considering all Degrees of Freedom (DoF) simultaneously. Our planner can also optimize over the contact schedule for all limbs, thereby finding the feasible motions even for the infeasible initial contact schedule. Furthermore, we introduce a novel formulation of the support area constraint. We generate plans for a Menzi Muck M545, a 31 DoF walking excavator with five limbs: four wheeled legs and an arm. We show motion plans for traversing a variety of terrains that require whole-body planning. To the best of our knowledge, this is the first work that addresses motion planning in rough terrain for vehicles with legs and wheels.

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