Motion Planning of Legged Robots

We study the problem of computing the free space F of a simple legged robot called the spider robot. The body of this robot is a single point and the legs are attached to the body. The robot is subject to two constraints: each leg has a maximal extension R (accessibility constraint) and the body of the robot must lie above the convex hull of its feet (stability constraint). Moreover, the robot can only put its feet on some regions, called the foothold regions. The free space F is the set of positions of the body of the robot such that there exists a set of accessible footholds for which the robot is stable. We present an efficient algorithm that computes F in O(n2 log n) time using O(n2 alpha(n)) space for n discrete point footholds where alpha(n) is an extremely slowly growing function (alpha(n) <= 3 for any practical value of n). We also present an algorithm for computing F when the foothold regions are pairwise disjoint polygons with n edges in total. This algorithm computes F in O(n2 alpha8(n) log n) time using O(n2 alpha8(n)) space (alpha8(n) is also an extremely slowly growing function). These results are close to optimal since Omega(n2) is a lower bound for the size of F.Comment: 29 pages, 22 figures, prelininar results presented at WAFR94 and IEEE Robotics & Automation 9

Motion planning algorithms for stratified kinematic systems with application to the hexapod robot

The paper addresses the motion planning problem of legged robots. Kinematic models of these robots are stratified, i.e. the equations of motion differ on different strata. An improved version of the motion planning algorithm proposed in the literature is compared with two alternative solutions via the example of the six-legged (hexapod) robot. The first alternative solution uses explicit integration of the vector fields while the second one exploits the flatness of a restricted subsystem

Keep Rollin' - Whole-Body Motion Control and Planning for Wheeled Quadrupedal Robots

We show dynamic locomotion strategies for wheeled quadrupedal robots, which combine the advantages of both walking and driving. The developed optimization framework tightly integrates the additional degrees of freedom introduced by the wheels. Our approach relies on a zero-moment point based motion optimization which continuously updates reference trajectories. The reference motions are tracked by a hierarchical whole-body controller which computes optimal generalized accelerations and contact forces by solving a sequence of prioritized tasks including the nonholonomic rolling constraints. Our approach has been tested on ANYmal, a quadrupedal robot that is fully torque-controlled including the non-steerable wheels attached to its legs. We conducted experiments on flat and inclined terrains as well as over steps, whereby we show that integrating the wheels into the motion control and planning framework results in intuitive motion trajectories, which enable more robust and dynamic locomotion compared to other wheeled-legged robots. Moreover, with a speed of 4 m/s and a reduction of the cost of transport by 83 % we prove the superiority of wheeled-legged robots compared to their legged counterparts.Comment: IEEE Robotics and Automation Letter

Online Dynamic Motion Planning and Control for Wheeled Biped Robots

Wheeled-legged robots combine the efficiency of wheeled robots when driving on suitably flat surfaces and versatility of legged robots when stepping over or around obstacles. This paper introduces a planning and control framework to realise dynamic locomotion for wheeled biped robots. We propose the Cart-Linear Inverted Pendulum Model (Cart-LIPM) as a template model for the rolling motion and the under-actuated LIPM for contact changes while walking. The generated motion is then tracked by an inverse dynamic whole-body controller which coordinates all joints, including the wheels. The framework has a hierarchical structure and is implemented in a model predictive control (MPC) fashion. To validate the proposed approach for hybrid motion generation, two scenarios involving different types of obstacles are designed in simulation. To the best of our knowledge, this is the first time that such online dynamic hybrid locomotion has been demonstrated on wheeled biped robots

Hierarchical Reinforcement Learning for Precise Soccer Shooting Skills using a Quadrupedal Robot

We address the problem of enabling quadrupedal robots to perform precise shooting skills in the real world using reinforcement learning. Developing algorithms to enable a legged robot to shoot a soccer ball to a given target is a challenging problem that combines robot motion control and planning into one task. To solve this problem, we need to consider the dynamics limitation and motion stability during the control of a dynamic legged robot. Moreover, we need to consider motion planning to shoot the hard-to-model deformable ball rolling on the ground with uncertain friction to a desired location. In this paper, we propose a hierarchical framework that leverages deep reinforcement learning to train (a) a robust motion control policy that can track arbitrary motions and (b) a planning policy to decide the desired kicking motion to shoot a soccer ball to a target. We deploy the proposed framework on an A1 quadrupedal robot and enable it to accurately shoot the ball to random targets in the real world.Comment: Accepted to 2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2022

Real-Time Motion Planning of Legged Robots: A Model Predictive Control Approach

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.Comment: 8 page