Footstep planning on uneven terrain with mixed-integer convex optimization

By Robin Deits, Russ Tedrake. IEEE-RAS International Conference on Humanoid Robots, 2014

370 citations recorded by the source corpus.

We present a new method for planning footstep placements for a robot walking on uneven terrain with obstacles, using a mixed-integer quadratically-constrained quadratic program (MIQCQP). Our approach is unique in that it handles obstacle avoidance, kinematic reachability, and rotation of footstep placements, which typically have required non-convex constraints, in a single mixed-integer optimization that can be efficiently solved to its global optimum. Reachability is enforced through a convex inner approximation of the reachable space for the robot's feet. Rotation of the footsteps is handled by a piecewise linear approximation of sine and cosine, designed to ensure that the approximation never overestimates the robot's reachability. Obstacle avoidance is ensured by decomposing the environment into convex regions of obstacle-free configuration space and assigning each footstep to one such safe region. We demonstrate this technique in simple 2D and 3D environments and with real environments sensed by a humanoid robot. We also discuss computational performance of the algorithm, which is currently capable of planning short sequences of a few steps in under one second or longer sequences of 10-30 footsteps in tens of seconds to minutes on common laptop computer hardware. Our implementation is available within the Drake MATLAB toolbox [1].

Subfields: Biomedical Engineering, Computer Vision and Pattern Recognition, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/0e851ffd05fb16f152f91b2c39f2460b1777a467

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Citations in the corpus

Optimization-based locomotion planning, estimation, and control design for the atlas humanoid robot (2015, methodology): “The gs;‘; hs;‘ and gc;‘; hc;‘ terms represent a pre-selected piecewise linearization of the sine and cosine functions, described in more detail in [22].”
Discrete Control Barrier Functions for Safety-Critical Control of Discrete Systems with Application to Bipedal Robot Navigation (2017, methodology): “In [8], a Mixed Integer Convex Optimization Program is used to plan footstep placements for bipedal robot walking on uneven terrains with obstacles.”
Survey of Robot 3D Path Planning Algorithms (2016, background): “This paper reviews almost all the representative works and books and sorts out almost all the successful 3D path planning methods such as rapidly exploring random trees (RRT), Probabilistic Road Maps (PRM), Artificial Potential Field [86], and Mixed-Integer Programming [87].”
Gait and Trajectory Optimization for Legged Systems Through Phase-Based End-Effector Parameterization (2018, methodology): “leftfoot, right-foot), Integer Programming can be used to optimize the contact-schedule and footholds, independent from the dynamics of the system [26]–[28].”