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Robotics
legged-control
legged robot locomotion control
Boston Dynamics
System
Techniques · 19
Primitives · 41
legged-control
Domain randomization
machine-learning · medium: Randomize simulator physics and visuals so policies trained in sim transfer to real robots
Policy gradient and PPO
machine-learning · medium: Raise the log-probability of actions in proportion to their advantage; PPO clips the probability ratio so several epochs on one rollout stay safe.
›
Quadratic programming
optimization · medium: Convex QP solvers (active-set, interior-point, ADMM) for constrained optimization
Rigid body dynamics algorithms
physics · medium: Featherstone RNEA/ABA/CRBA for articulated-body inverse and forward dynamics
Sequential impulse solver
physics · medium: Iterative contact solver applying impulses one constraint at a time with accumulated clamping and warm starting; the standard solver for stacking and friction in real-time physics engines.
›
Field oriented control
robotics · medium: FOC of BLDC/PMSM motors: Clarke/Park transforms, current PI loops, space-vector PWM
Impedance control
robotics · medium: Make a robot behave like a spring-damper at the contact point for safe interaction
LU and Cholesky factorization
numerics · low: Factor A = PLU (any square matrix, partial pivoting) or A = LLᵀ (SPD) once in O(n³), then solve each right-hand side in O(n²).
›
Rigid-body transforms (SE(3) poses)
robotics · low: Represent, compose, invert, integrate and interpolate 3D poses as unit quaternion plus translation, with exp/log maps for small motions and uncertainty.
›
Fixed-rate control loop
embedded · low: Run a controller at an exact period using absolute deadlines and a fixed dt, so jitter never accumulates and the math stays valid.
›
Extended Kalman filter
robotics · low: Kalman filter for nonlinear motion and measurement models: linearize f and h with Jacobians at the current estimate each step. The default estimator in robot navigation.
›
Real time linux scheduling
embedded · low: PREEMPT_RT, SCHED_FIFO/DEADLINE, CPU isolation and mlockall for low-jitter loops
Gait phase scheduling
robotics · low: Contact schedules and phase oscillators deciding stance and swing per leg
Data augmentation
machine-learning · low: Generate label-preserving variants of each training example on the fly to enlarge the effective dataset and bake in invariances.
›
PRNGs (PCG, xoshiro)
numerics · low: Small, fast, statistically strong non-cryptographic generators: PCG32 and xoshiro256**, with seeding, parallel streams and unbiased ranges.
›
Rigid-body dynamics
physics · low: Advance one 3D rigid body per step from force and torque: semi-implicit Euler for position, an inertia tensor in the body frame, and quaternion orientation updated by the exponential map.
›
AdamW
ml-training · low: Adam's per-parameter adaptive steps with weight decay applied directly to the weights; the default optimizer for transformers and LLM pretraining.
›
Gradient clipping
ml-training · low: Clipping gradients by global norm (or value) to prevent loss spikes; interaction with mixed precision
Reverse-mode automatic differentiat…
ml-training · low: Record the forward computation on a tape, then sweep it backwards once to get the gradient of a scalar loss for all inputs.
›
Sparse matrices (CSR)
numerics · low: Compressed sparse row stores only nonzeros as row pointers, column indices and values; SpMV streams them once, so it is memory-bandwidth bound.
›
Quaternion rotations
geometry · low: Unit quaternions as 3D rotations: 4 floats, cheap composition, no gimbal lock, plus the conversions, interpolation choices and numerical care needed in practice.
›
Simulation islands sleeping
physics · low: Group touching bodies into islands, solve them independently and put resting islands to sleep
PWM generation
embedded · low: A timer's counter, period and compare registers draw the pulse train; preload, dead time and DMA make duty changes glitch-free, shoot-through-free and cheap.
›
+ 12 more techniques
+ 25 more primitives
System
Techniques · 19
Primitives · 41
legged-control
Domain randomization
machine-learning · medium: Randomize simulator physics and visuals so policies trained in sim transfer to real robots
Policy gradient and PPO
machine-learning · medium: Raise the log-probability of actions in proportion to their advantage; PPO clips the probability ratio so several epochs on one rollout stay safe.
›
Quadratic programming
optimization · medium: Convex QP solvers (active-set, interior-point, ADMM) for constrained optimization
Rigid body dynamics algorithms
physics · medium: Featherstone RNEA/ABA/CRBA for articulated-body inverse and forward dynamics
Sequential impulse solver
physics · medium: Iterative contact solver applying impulses one constraint at a time with accumulated clamping and warm starting; the standard solver for stacking and friction in real-time physics engines.
›
Field oriented control
robotics · medium: FOC of BLDC/PMSM motors: Clarke/Park transforms, current PI loops, space-vector PWM
Impedance control
robotics · medium: Make a robot behave like a spring-damper at the contact point for safe interaction
Inverse kinematics
robotics · medium: CCD/FABRIK/Jacobian solvers posing joint chains to reach targets
Model predictive control
robotics · medium: Each tick, solve a small optimization over a predicted horizon, apply only the first input, repeat. Handles constraints and multiple inputs that a PID loop cannot.
›
Sensor fusion
robotics · medium: Combining IMU, GNSS, camera, lidar and radar estimates with Kalman-type filters and time alignment
Whole body control
robotics · medium: Prioritized task-space control solved as a QP over joint torques and contact forces
Levenberg marquardt
numerics · medium: Damped Gauss-Newton nonlinear least squares for model calibration
Interior-point method (primal-dual,…
optimization · medium: Follows the central path with Newton steps on the perturbed KKT system, one sparse Cholesky per iteration; Mehrotra's predictor-corrector makes it fast.
›
Contact manifold generation
physics · medium: Build persistent contact point sets from collision normals by clipping, with feature IDs for warm starts
Transform tree
robotics · medium: Time-indexed tree of coordinate frames with interpolated lookups between any two frames
Polygon clipping
geometry · medium: Polygon intersection/union/difference (Weiler-Atherton, Martinez) for spatial predicates
Sparse direct solver
numerics · medium: Solve sparse Ax = b exactly by reordering, symbolic analysis, numeric LLᵀ/LU and triangular solves; fill-in, not flops per entry, decides the cost.
›
Fill-reducing ordering
numerics · medium: Permute a sparse symmetric matrix before Cholesky/LU so the factor has few new nonzeros; minimum degree, nested dissection and RCM trade quality, speed and parallelism.
›
Graph partitioning
graphs · medium: Split a graph into k balanced parts with few edges between them; multilevel coarsen-partition-refine (METIS, KaHIP) for quality, streaming heuristics (LDG, Fennel) for one-pass scale.
›
LU and Cholesky factorization
numerics · low: Factor A = PLU (any square matrix, partial pivoting) or A = LLᵀ (SPD) once in O(n³), then solve each right-hand side in O(n²).
›
Rigid-body transforms (SE(3) poses)
robotics · low: Represent, compose, invert, integrate and interpolate 3D poses as unit quaternion plus translation, with exp/log maps for small motions and uncertainty.
›
Fixed-rate control loop
embedded · low: Run a controller at an exact period using absolute deadlines and a fixed dt, so jitter never accumulates and the math stays valid.
›
Extended Kalman filter
robotics · low: Kalman filter for nonlinear motion and measurement models: linearize f and h with Jacobians at the current estimate each step. The default estimator in robot navigation.
›
Real time linux scheduling
embedded · low: PREEMPT_RT, SCHED_FIFO/DEADLINE, CPU isolation and mlockall for low-jitter loops
Gait phase scheduling
robotics · low: Contact schedules and phase oscillators deciding stance and swing per leg
Data augmentation
machine-learning · low: Generate label-preserving variants of each training example on the fly to enlarge the effective dataset and bake in invariances.
›
PRNGs (PCG, xoshiro)
numerics · low: Small, fast, statistically strong non-cryptographic generators: PCG32 and xoshiro256**, with seeding, parallel streams and unbiased ranges.
›
Rigid-body dynamics
physics · low: Advance one 3D rigid body per step from force and torque: semi-implicit Euler for position, an inertia tensor in the body frame, and quaternion orientation updated by the exponential map.
›
AdamW
ml-training · low: Adam's per-parameter adaptive steps with weight decay applied directly to the weights; the default optimizer for transformers and LLM pretraining.
›
Gradient clipping
ml-training · low: Clipping gradients by global norm (or value) to prevent loss spikes; interaction with mixed precision
Reverse-mode automatic differentiat…
ml-training · low: Record the forward computation on a tape, then sweep it backwards once to get the gradient of a scalar loss for all inputs.
›
Sparse matrices (CSR)
numerics · low: Compressed sparse row stores only nonzeros as row pointers, column indices and values; SpMV streams them once, so it is memory-bandwidth bound.
›
Quaternion rotations
geometry · low: Unit quaternions as 3D rotations: 4 floats, cheap composition, no gimbal lock, plus the conversions, interpolation choices and numerical care needed in practice.
›
Simulation islands sleeping
physics · low: Group touching bodies into islands, solve them independently and put resting islands to sleep
PWM generation
embedded · low: A timer's counter, period and compare registers draw the pulse train; preload, dead time and DMA make duty changes glitch-free, shoot-through-free and cheap.
›
PID controller
robotics · low: Drive a measured value to a setpoint with three terms on the error: proportional, integral, derivative. The default feedback loop for motors, heaters, drones and gimbals.
›
Phase-locked loop (digital)
signal-processing · low: Feedback loop that locks a local oscillator to the phase and frequency of an input tone; the core of carrier recovery, clock recovery and GNSS tracking.
›
PCA and SVD
machine-learning · low: Find orthogonal directions of maximum variance by an SVD of the centred data; randomized SVD gets the top k components in a few passes.
›
Runge-Kutta 4
numerics · low: The classic four-stage, fourth-order ODE step; error drops 16× when the step halves, with no derivatives or past steps needed.
›
Kalman filter
robotics · low: Optimal recursive estimator for a linear system with Gaussian noise: fuses a motion model with noisy measurements into a state estimate plus its covariance.
›
SPSC ring buffer
data-structures · low: Bounded wait-free queue for exactly one producer and one consumer thread, built from an array and two indices with acquire/release ordering.
›
Complementary filter
robotics · low: Blend high-passed gyro integration with low-passed accelerometer/magnetometer attitude (Mahony/Madgwick)
Finite differences
numerics · low: Replace derivatives with weighted differences of grid values; simple stencils plus a stability condition (CFL) turn PDEs like heat, advection and waves into array loops.
›
Newton root finding
numerics · low: Linearize at the guess and jump to the tangent root; quadratic convergence near a simple root, made robust by brackets (1D) or line search.
›
GJK and EPA
physics · low: GJK decides whether (and how far apart) two convex shapes are from their support functions alone; EPA expands its simplex into penetration depth and normal.
›
Separating axis theorem
physics · low: Convex shapes are disjoint iff some axis separates their projections; testing face normals and edge crosses gives overlap, depth and contact normal.
›
Lowest common ancestor
graphs · low: LCA/merge-base computation in trees and DAGs
Spline interpolation
numerics · low: Linear, bilinear/trilinear and cubic spline interpolation on grids and tables
d-ary heap
data-structures · low: Array heap with d children per node (d = 4 typical): half the binary heap's depth, siblings in one cache line, faster priority queues.
›
Exact geometric predicates
geometry · low: Robust orient and incircle tests with adaptive-precision floats (Shewchuk) or exact arithmetic
Point in polygon
geometry · low: Ray-casting/winding tests and indexed polygon lookup for reverse geocoding
False sharing
concurrency · low: Independent variables written by different cores on one cache line force the line to bounce between cores; pad or regroup hot data to fix it.
›
Memory ordering
concurrency · low: What Relaxed, Acquire, Release and SeqCst atomics actually guarantee, what they cost on x86 and ARM, and which one each pattern needs.
›
Dma transfers
embedded · low: DMA controllers: descriptors, circular buffers, cache coherence for zero-CPU data movement
Homogeneous transforms
geometry · low: 4x4 affine and projective matrices, homogeneous coordinates, view and projection, normal matrices
Fixed timestep loop
graphics · low: Fixed simulation dt with accumulator, render interpolation, spiral-of-death guard
CPU caches and the memory hierarchy
hardware-os · low: Sizes, line widths and latencies of L1/L2/L3/DRAM on modern x86 and Apple M-series, and the data-layout rules that follow from them.
›
Explicit Euler
numerics · low: Step an ODE forward by its current slope, y += h·f(t, y); first-order, one evaluation per step, the baseline every other integrator is measured against.
›
Semi-implicit Euler
numerics · low: Update velocity from forces first, then position with the new velocity: explicit Euler cost, but symplectic and stable; the default game-physics integrator.
›
Thomas tridiagonal solver
numerics · low: O(n) tridiagonal linear solve used in implicit finite-difference and spline schemes
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